Fundamentals of Corporate Finance, 4th Edition Solution Manual.pdf (13)

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Solution Manual

Resource:

Fundamentals of Corporate Finance

Edition:

4th Edition

Author(s):

Robert Parrino Thomas W. Bates Stuart L. Gillan David S. Kidwell

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Chapter 1 The Financial Manager and the Firm Before You Go On Questions and Answers Section 1.1 1. What are the three most basic types of financial decisions managers must make?

The three most basic decisions each business must make are the capital budgeting decision, the financing decision, and the working capital management decision. These decisions determine which productive assets to buy, how to pay for or finance these purchases, and how to manage the day-to-day financial matters so the company can pay its bills.

2. Explain why you would make an investment if the value of the expected cash flows exceeds the cost of the project.

You would accept an investment project whose cash flows exceed the cost of the project because such projects will increase the value of the firm, making the owners wealthier. Most people start a business to increase their wealth. Remember that the cost of capital (time value of money) will affect the decision about whether to invest.

3. Why are capital budgeting decisions among the most important decisions in the life of a firm?

The capital budgeting decisions are considered the most important in the life of the firm because these decisions determine which productive assets the firm purchases and these assets generate most of the firm’s cash flows. Furthermore, capital budgeting decisions are long-term decisions and if you make a mistake in selecting a productive asset, you are stuck with the decision for a long time.

Section 1.2

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1. Why are many businesses operated as sole proprietorships or partnerships?

Many businesses elect to operate as sole proprietorships or partnerships because of the small operating scale and capital base of their firms. Both of these forms of business organization are fairly easy to start and impose few regulations on the owners.

2. What are some advantages and disadvantages of operating as a public corporation?

The main advantages of operating as a public corporation are the access to the public securities markets, which makes it easier to raise large amounts of capital, and the ease of ownership transfer. All the shareholders have to do is to call their broker to buy or sell shares of stock. And because a public corporation usually has many shares outstanding, large blocks of securities can be purchased or sold without an appreciable impact on the price of the stock.

The major disadvantage of corporations is the tax situation. Not only must the corporation pay taxes on its income, but the owners of the corporation get taxed again when dividends are paid to them. This is referred to as double taxation. In addition to taxes, public corporations are subject to stringent reporting requirements, and the incentives may convince managers to focus on shorter-term profitability than longer-term wealth creation.

3. Explain why professional partnerships such as physicians’ groups organize as limited liability partnerships.

Professional partnerships such as physicians’ groups desire to organize as limited liability partnerships (LLPs) to take advantage of the tax arrangements of partnerships combined with the advantages of the limited liability of a corporation. By operating as an LLP, the partnership is able to avoid a potential financial disaster resulting from the misconduct of one partner.

Section 1.3 1. What are the major responsibilities of the CFO? The major responsibilities of a CFO are recommendation and financial analysis of financial decisions. Although all top managers in a firm participate in these decisions, the final report and analysis is ultimately the responsibility of the CFO.

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2. Identify three financial officers who typically report to the CFO and describe their duties.

The financial officers discussed in the chapter who report to the CFO are the controller, the treasurer, and the internal auditor. The controller is the firm’s chief accounting officer, and thus prepares the financial statements and taxes. This position also requires close cooperation with the external auditors. The treasurer’s responsibility is the collection and disbursement of cash, investing excess cash, raising new capital, handling foreign exchange, and overseeing the company’s pension fund management. (S)he also assists the CFO in handling important Wall Street relationships. Finally, the internal auditor is responsible for conducting risk assessment and for performing audits of high-risk areas.

3. Why does the internal auditor report to both the CFO and the board of directors?

The internal auditor reports to the CFO on a day-to-day basis but is ultimately accountable for reporting any accounting irregularities to the board of directors. The dual reporting system serves as a check to ensure that there are no discrepancies in the company’s financial statements.

Section 1.4 1. Why is profit maximization an unsatisfactory goal for managing a firm?

Profit maximization is not a satisfactory goal when managing a firm because it is rather difficult to define profits since accountants can apply and interpret the same accounting principles differently. Also, profit maximization does not define the size, the uncertainty, and the timing of cash flows; it ignores the time value of money concept.

2. Explain why maximizing the current market price of a firm’s stock is an appropriate goal for the firm’s management.

Maximizing the current market price of a firm’s stock is an appropriate goal for the firm’s management because it is an unambiguous objective and it is easy to measure. One can simply look at the value of the company’s stock on any given day to determine whether it went up or down.

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3. What is the fundamental determinant of an asset’s value?

The fundamental determinant of an asset’s value is the future cash flow the asset is expected to generate. Other factors that may help determine the price of an asset are internal decisions, such as the company’s expansion strategy, as well as external stimulants, such as the state of the economy.

Section 1.5 1. What are agency conflicts?

An agency conflict occurs when the goals of the principals are not aligned with the goals of the agents. Management is often more concerned with pursuing its own self-interest, and so the maximization of shareholder value is pushed to the side.

2. What are corporate raiders?

Corporate raiders can make the economy more efficient by keeping the top managers on their toes. Top managers know that if the company’s performance declines and its stock slips, it makes itself vulnerable to takeovers by corporate raiders who are just waiting to temporarily acquire a company, turn it around, and sell it for profit. Therefore, the role of the corporate raiders in the economy is twofold: first, the fear of takeovers pushes managers to do a better job, and second, if the managers are not performing up to expectations, the company can be rescued and restructured into a contributor again. However, the threat of a corporate raider could result in an incentive conflict for managers, inducing them to focus on short-term profitability over long-term value creation.

3. List the three main objectives of the Sarbanes-Oxley Act. The three main goals of the Sarbanes-Oxley Act are to reduce agency costs in corporations, to restore ethical conduct in the business sector, and to improve the integrity of accounting reporting systems within firms.

Section 1.6 1. What is a conflict of interest in a business setting?

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Conflict of interest in the business setting refers to a conflict between a person’s personal or institutional gain and the obligation to serve the interest of another party. For example, the chapter discussed the problem that arises when the real estate agent helping you buy a house is also the listing agent.

2. How would you define an ethical business culture?

An ethical business culture means that people have a set of principles, or moral values, that helps them identify moral issues and then make ethical judgments without being told what to do.

Self-Study Problems and Solutions 1.1

Give an example of a capital budgeting decision and a financing decision.

Solution:

Capital budgeting involves deciding which productive assets the firm invests in, such as buying a new plant or investing in the renovation of an existing facility.

Financing decisions determine how a firm will raise capital. Examples of financing decisions include the decision to borrow from a bank or issue debt in the public capital markets.

LO: 1 Level: Basic

1.2

What is the appropriate decision criterion for financial managers to use when selecting a capital project?

Solution:

Financial managers should select a capital project only if the value of the project’s expected future cash flows exceeds the cost of the project. In other words, managers should only make investments that will increase firm value, and thus increase the stockholders’ wealth.

LO: 1 Level: Basic

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Solutions Manual

What are some of the things that managers do to manage a firm’s working capital?

Solution:

Working capital management is the day-to-day management of a firm’s shortterm assets and liabilities. Working capital can be managed by maintaining the optimal level of inventory, managing receivables and payables, deciding to whom the firm should extend credit, and making appropriate investments with excess cash.

LO: 1 Level: Basic

1.4

Which one of the following characteristics does not pertain to corporations? a.

Can enter into contracts

b.

Can borrow money

c.

Are the easiest type of business to form

d.

Can be sued

e.

Can own stock in other companies

Solution:

The answer that does not pertain to corporations is: c. Are the easiest type of business to form.

LO: 2 Level: Basic

1.5

What are typically the main components of an executive compensation package?

Solution:

The three main components of a typical executive compensation package are: base salary, bonus based on accounting performance, and compensation tied to the firm’s stock price.

LO: 5 Level: Basic

Discussion Questions and Answers

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Describe the cash flows between a firm and its stakeholders.

Cash flows are generated by a firm’s productive assets that were purchased through either issuing debt or raising equity. These assets generate revenues through the sale of goods and services. A portion of this revenue is then used to pay wages and salaries to employees, pay suppliers, pay taxes, and pay interest on the borrowed money. The leftover money, residual cash, is then either reinvested back in the business or is paid out to stockholders in the form of dividends.

LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

1.2

What are the three fundamental decisions the financial manager is concerned with, and how do they affect the firm’s balance sheet?

The primary financial management decisions every company faces are capital budgeting decisions, financing decisions, and working capital management decisions. Capital budgeting addresses the question of which productive assets to buy; thus, it affects the asset side of the balance sheet. Financing decisions focus on raising the money the firm needs to buy productive assets. This is typically accomplished by selling long-term debt and equity. Finally, working capital decisions involve how firms manage their current assets and liabilities. The focus here is seeing that a firm has enough money to pay its bills and that any spare money is invested to earn a return.

LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Decision Analysis AICPA: Decision Modeling

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Solutions Manual

What is the difference between stockholders and stakeholders?

Stockholders, also referred to as shareholders, are the owners of the company. A stakeholder, on the other hand, is anyone with a claim on the assets of the firm, including, but not limited to, shareholders. Stakeholders include the firm’s employees, suppliers, creditors, and the government.

LO: 1 Level: Basic Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

1.4

Suppose that a group of accountants wants to start an accounting business. What organizational form would they most likely choose, and why?

Most lawyers, accountants, and doctors form what are known as limited liability partnerships. This formation combines the tax advantages of partnerships with the limited liability of corporations.

LO: 2 Level: Basic Bloomcode: Application AACSB: Analysis IMA: Business Economics AICPA: Industry/Sector Perspective

1.5

Why would the owners of a business choose to form a corporation even though they will face double taxation?

Because the benefits, such as limited liability and access to large amounts of capital at relatively low cost in the public markets, outweigh the cost of double taxation (as well as the higher costs associated with forming a corporation).

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LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.6

Explain why profit maximization is not the best goal for a company. What is a better goal?

Although profit maximization appears to be the logical goal for any company, it has many drawbacks. First, profit can be defined in a number of different ways, and variations in net income for similar firms can vary widely. Second, accounting profits do not exactly equal cash flows. Third, profit maximization does not account for timing and ignores risk associated with cash flows. An appropriate goal for financial managers who do not have these objections is to maximize the value of the firm’s current stock price. In order to achieve this goal, management must make financial decisions so that the total value of cash inflows exceeds the total value of cash outflows.

LO: 4 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Performance Measurement AICPA: Strategic/Critical Thinking

1.7

What are some of the major external and internal factors that affect a firm’s stock price?

What is the difference between the two general types of factors?

External factors that affect the firm’s stock price are: (1) economic shocks, such as natural disasters or wars, (2) the state of the economy, such as the level of interest rates, and (3) the business environment, such as taxes or regulations. On one hand, external factors are variables over which the management has no control. On the other hand, internal factors that affect the stock price can be controlled by management to some degree, because they are firm specific, such as financial management decisions, product

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quality and cost, and the line of business, the management has selected to enter. Finally, perhaps the most important internal variable that determines the stock price is the expected cash flow stream: its magnitude, timing, and riskiness.

LO: 4 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Strategic Marketing AICPA: Measurement

1.8

Identify the sources of agency costs. What are some ways these costs can be controlled in a company?

Agency costs are the costs that result from conflicts of interest between the agent and the principal. They can either be direct, such as lavish dinners or trips, or indirect, which are usually missed investment opportunities. A company can control these costs by tying management compensation to company’s performance and by establishing an independent board of directors. Outside factors that contribute to the minimization of agency costs are the threat of corporate raiders that can take over a company not performing up to expectations and the competitive nature of the managerial labor market.

LO: 5 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.9

What is the Sarbanes-Oxley Act, and what does it focus on? Why does it focus in these areas?

The Sarbanes-Oxley Act is an act of Congress that was passed in 2002. This act was passed in the aftermath of several corporate scandals that occurred at the turn of the century. The act focuses on (1) reducing agency costs in corporations, (2) restoring ethical conduct within the business sector, and (3) improving the integrity of accounting

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reporting system within firms. Failures in these areas led to the corporate scandals that preceded passage of Sarbanes-Oxley.

LO: 5 Level: Basic Bloomcode: Knowledge AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective

1.10 Give an example of a conflict of interest in a business setting, other than the one involving the real estate agent discussed in the chapter text.

For example, imagine a situation in which you are a financial officer at a growing software company and your firm has decided to hire outside consultants to formulate a global expansion strategy. Coincidentally, your wife works for one of the major consulting firms that your company is considering hiring. In this scenario, you have a conflict of interest, because instinctively, you might be inclined to give the business to your wife’s firm, because it will benefit your family’s financial situation if she lands the contract, regardless of whether or not it makes the best sense for your firm.

LO: 6 Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

Questions and Problems and their Solutions BASIC

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Solutions Manual

Capital: What are the two basic sources of funds for all businesses?

Solution: The two basic sources of funds for all businesses are debt and equity.

LO:

1.1

Bloomcode: Knowledge AACSB: Analytic IMA: Investment Decisions; Corporate Finance AICPA: Resource Management

1.2

Management role: What is net working capital?

Solution: Net working capital is the difference between a firm’s total current assets and its total current liabilities.

LO:

1.1

Bloomcode: Knowledge AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

1.3

Cash flows: Explain the difference between profitable and unprofitable firms.

Solution: A profitable firm is able to generate enough cash flows from productive assets to cover its operating expenses, taxes, and payments to creditors. Unprofitable firms fail to do this, and therefore they may be forced to declare bankruptcy.

LO:

1.1

Bloomcode: Analysis AACSB: Analytic IMA: Cost Management AICPA: Measurement

1.4

Management role: What three major decisions are of most concern to financial managers?

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Solution: Financial managers are most concerned with the capital budgeting decisions, the financing decisions, and the working capital management decisions.

LO:

1.1

Bloomcode: Comprehension AACSB: Analytic IMA: FSA AICPA: Resource Management

1.5

Cash flows: What is the appropriate decision rule for a firm considering undertaking a capital project? Give a real-life example.

Solution: A firm should undertake a capital project only if the value of its future cash flows exceeds the cost of the project. For example, a financial manager would not invest $10,000,000 in a new production line if the net present value of future cash flows from that line are expected to be only $9,000,000. That would be like throwing $1,000,000 away.

LO:

1.1

Bloomcode: Application AACSB: Analytic IMA: Decision Analysis AICPA: Problem Solving and Decision Making

1.6

Management role: What is a firm’s capital structure, and why is it important?

Solution: Capital structure shows how a company is financed; it is the mix of debt and equity on the liability side of the balance sheet. It is important as it affects the risk and the value of the company. In general, companies with higher debt-to-equity proportions are riskier because debt comes with legal obligations to pay periodic payments to creditors and to repay the principal at the end.

LO:

1.1

Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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1.7

Solutions Manual

Management role: What are some of the working capital decisions that a financial manager faces?

Solution: The financial manager must make working capital decisions regarding the level of inventory to hold, the terms of granting credit (accounts receivable), and the firm’s policy on paying accounts payable.

LO:

1.1

Bloomcode: Comprehension AACSB: Analytic IMA: Decision Analysis AICPA: Strategic/Critical Thinking

1.8

Organizational form: What are the common forms of business organization discussed in this chapter?

Solution: The common forms of business organization discussed are sole proprietorship, partnership, corporation, and limited liability company and partnership.

LO:

1.2

Bloomcode: Knowledge AACSB: Reflective Thinking IMA: Business Economics AICPA: Industry/Sector Perspective

1.9

Organizational form: What are the advantages and disadvantages of a sole proprietorship?

Solution: Advantages: •

It is the easiest business organization to start.

•

It is the least regulated.

• Owners keep all the profits and do not have to share the decision-making authority with anyone.

• All income is taxed as personal income, which is usually in a lower tax bracket than corporate income.

Disadvantages: .

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• The proprietor has an unlimited liability for all business debt and financial obligations of the firm.

• The amount of capital that can be invested in the firm is limited by the proprietor’s wealth.

• LO:

It is difficult to transfer ownership (requires sale of the business).

1.2

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.10 Organizational form: What is a partnership, and what is the biggest disadvantage of this form of business organization? How can this disadvantage be avoided?

Solution: A partnership consists of two or more owners legally joined together to manage a business. The major disadvantage to partnerships is that all partners have unlimited liability for the organization’s debts and legal obligations no matter what stake they have in the business. One way to avoid this is to form a limited partnership in which only general partners have unlimited liability and limited partners are only responsible for business obligations up to the amount of capital they have invested in the partnership.

LO:

1.2

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.11 Organizational form: Who are the owners in a corporation, and how is their ownership represented?

Solution: The owners of a corporation are its stockholders or shareholders, and the evidence of their ownership is represented by shares of common stock. Other types of ownership do exist and include preferred stock.

LO: .

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Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective 1.12 Organizational form: Explain what is meant by stockholders’ limited liability.

Solution: Limited liability for a stockholder means that the stockholder’s legal liability extends only to the capital contributed or the amount invested.

LO:

1.2

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Strategic/Critical Thinking

1.13 Organizational form: What is double taxation?

Solution: Double taxation occurs when earnings are taxed twice. The owners of a C-corporation are subject to double taxation—first at the corporate level when the firm’s earnings are taxed and then again at a personal level when they receive dividends.

LO:

1.2

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.14 Organizational form: What is the form of business organization taken by most large companies and why?

Solution: Most large companies prefer to operate as public corporations because large amounts of capital can be raised in public markets at a relatively low cost.

LO:

1.2

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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1.15 Finance function: What is the primary responsibility of the board of directors in a corporation?

Solution: The board of directors of a corporation is responsible for serving the interests of stockholders in managing the corporation. It is possible that the interest of managers may deviate from those of the stockholders. The board’s objective is to monitor and correct any management decisions that might not be in the best interest of the stockholders. For example, board duties include hiring and firing the CEO, setting CEO pay, and monitoring the investment decisions of managers.

LO:

1.3

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Resource Management

1.16 Finance function: All public companies must hire a certified public accounting firm to perform an independent audit of their financial statements. What exactly does the term audit mean?

Solution: An independent CPA firm that performs an audit of a firm ensures that the financial numbers are reasonably accurate, that accounting principles have been adhered to year after year and not in a manner that distorts the firm’s performance, and that the accounting principles used are in accordance with generally accepted accounting principles (GAAP).

LO:

1.3

Bloomcode: Comprehension AACSB: Analytic IMA: FSA; Reporting AICPA: Risk Analysis; Reporting

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1.17 Firm’s goal: What are some of the drawbacks to setting profit maximization as the main goal of a company?

Solution: • It is difficult to determine what is meant by “profit”.

• It does not address the size and timing of cash flows—it does not account for the time value of money.

• LO:

It ignores the uncertainty or risk of cash flows.

1.4

Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Corporate Finance

1.18 Firm’s goal: What is the appropriate goal of financial managers? How do managers’ decisions affect how successful the firm is in achieving this goal?

Solution: The appropriate goal of financial managers should be to maximize the current value of the firm’s stock price. Managers’ decisions affect the stock price in many ways as the value of the stock is determined by the future cash flows the firm can generate.

Managers can affect the cash flows by, for example, selecting what products or services to produce, what type of assets to purchase, or what advertising campaign to undertake.

LO:

1.4

Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Decision Analysis

1.19 Firm’s goal: What are the major factors that affect a firm’s stock price?

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Solution: The factors affecting the stock price include: the characteristics of the firm, the economy, economic shocks, the business environment, expected cash flows, and current market conditions.

LO:

1.4

Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Corporate Finance

1.20 Agency conflicts: What is an agency relationship, and what is an agency conflict? How can agency conflicts be reduced in a corporation?

Solution: Agency relationships develop when a principal hires an agent to perform some service or represent the firm. An agency conflict arises when the agent’s interests and behaviors are at odds with those of the principal. Agency conflicts can be reduced through the following three mechanisms: management compensation, control of the firm, and the board of directors.

LO:

1.5

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.21 Firm’s goal: What can happen if a firm is poorly managed and its stock price falls substantially below its maximum potential price?

Solution: If the stock price falls below its maximum potential price, it attracts corporate raiders, who look for fundamentally sound but poorly managed companies they can buy, turn around, and sell for a handsome profit.

LO:

1.4

Bloomcode: Comprehension

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AACSB: Analytic IMA: Corporate Finance AICPA: Strategic/Critical Thinking

1.22 Agency conflicts: What are some of the regulations that pertain to boards of directors that were put in place to reduce agency conflicts?

Solution: Some of the regulations include: • The majority of board members must be outsiders.

• A separation of the CEO and chairman of the board positions is recommended.

• Firm is required to have a code of ethics approved by the board.

LO:

1.5

Bloomcode: Comprehension AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective 1.23 Business ethics: How can a lack of business ethics negatively affect the performance of an economy? Give an example.

Solution: A lack of business ethics can lead to corruption, which, in turn, creates inefficiencies in an economy, inhibits the growth of capital markets, and slows the rate of overall economic growth. For example, the Russian economy has had a relatively difficult time attracting foreign investment since the fall of the Soviet Union due, in part, to weak ethics and corruption in the business community and local and national governments. Lower foreign investment has led to slower overall economic growth than the country might otherwise have enjoyed.

LO:

1.6

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Global Perspective

1.24 Agency conflicts: What are some ways to resolve a conflict of interest?

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Solution: One way to resolve a conflict of interest is by complete disclosure. As long as both parties are aware of the fact that, for example, both parties in a contract negotiation are represented by the same firm, disclosure is sufficient. Another way to avoid a conflict of interest is for the company to remove itself from serving the interest of one of the parties. This is, for example, the case with accounting firms not being allowed to serve as consultants to companies for whom they perform audits.

LO:

1.5

Bloomcode: Application AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective

1.25 Information asymmetry: Describe what an information asymmetry is in a business transaction. Explain how the inequity associated with an information asymmetry might be, at least partially, solved through the market for goods or services.

Solution: An information asymmetry exists when one party to a business transaction possesses information that is not available to the other parties in the transaction. If the parties with less information understand their relative disadvantage, they are likely to pay lower prices for the goods and services they purchase, or charge higher prices for the goods and services they sell.

LO:

1.6

Bloomcode: Comprehension AACSB: Analytic IMA: Strategic Marketing AICPA: Marketing/Client Focus

1.26 Business ethics: What ethical conflict does insider trading present?

Solution: Insider trading is an example of information asymmetry. The main idea is that investment decisions should be made on an even playing field. Insider trading is

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illegal because it puts one party at a significant disadvantage in trading. If insider trading were allowed, capital transfers would be much more difficult.

LO: 1.6 Bloomcode: Comprehension AACSB: Ethics IMA: Business Applications AICPA: Professional Demeanor

Sample Test Problems 1.1

Identify three fundamental types of decisions that financial managers make and identify which part of the balance sheet each of these decisions affects.

Solution: 1. Capital Budgeting Decisions – identifying the productive assets the firm should buy.

These decisions affect long-term assets on the balance sheet.

2. Financing Decisions – determining how the firm should finance or pay for assets.

These decisions affect long-term debt and stockholders’ equity on the balance sheet.

3. Working Capital Management Decisions – determining how day-to-day financial matters should be managed. These decisions affect current assets and current liabilities on the balance sheet.

LO:

1

Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Decision Analysis AICPA: Decision Modeling

1.2 Which of the following is/are advantages of the corporate form of organization? a. Reduced start-up costs

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b. Greater access to capital markets c. Unlimited liability d. Single taxation Solution: b. (Shares in a corporation can be sold to raise capital from investors who are not involved in the business. This greatly increases the amount of capital that can be raised to fund the business.)

LO:

2

Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.3

Why is stock value maximization superior to profit maximization as a goal for management?

Solution: While profit maximization appears to be a logical goal at first glance, it has some serious drawbacks. First, since accounting profit is the difference between revenues and expenses, it can be distorted by accounting decisions. Second, accounting profits are quite different from cash flows. Since cash flows are the focus of investors, they should also be the focus of managers. Third, profit maximization does not account for when cash flows actually occur. Finally, profit maximization as a goal ignores the risk involved in generating the cash flows.

Stock value maximization is superior to profit maximization because it overcomes all of the listed shortcomings of profit maximization. This is because the value of a firm’s stock is determined by the cash flows that the firm is expected to produce. It accounts for (1) the size of the expected cash flows, (2) the timing of the expected cash flows, and (3) the riskiness of the expected cash flows.

LO:

4

Level: Intermediate Bloomcode: Comprehension AACSB: Analytic

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IMA: Strategic/Critical thinking AICPA: Corporate Finance

1.4

What are agency costs? Explain.

Solution: Agency costs are costs that result from an agency relationship in which there is a conflict of interest between a principal and an agent. An agency relationship exists in a business when a firm’s managers (agents) are not also its owners (principals).

Agency costs are incurred when managers act in ways that harm owners’ interests.

The cost of mechanisms, such as audits, that help control agency conflicts are also agency costs.

LO:

5

Level: Intermediate Bloomcode: Comprehension AACSB: Analytic AICPA: Industry/Sector Perpsective IMA: Business Economics

1.5

Identify seven mechanisms that can help better align the goals of managers with those of stockholders.

Solution: Mechanisms that can help align the goals of managers with those of stockholders are as follows: (1) the board of directors, (2) management compensation, (3) the managerial labor market, (4) competition among managers, (5) large stockholders, (6) the takeover market, and (7) the legal and regulatory environment.

Boards of directors that are independent from managers can help limit the extent to which managers are able to act solely in their own interest. Firms design compensation plans that are tied to firm performance in order to provide managers with incentives to make decisions consistent with the goal of stockholder value maximization. A third mechanism that helps align the goals of managers is the managerial labor market. It is difficult for poorly performing managers to find a good

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job elsewhere, and it is difficult for a poorly performing firm to hire good managers, which a firm’s current managers typically want to do. Competition among managers within a firm is a fourth mechanism that helps align the goals of managers with those of stockholders. This is because managers who act in the interest of stockholders are more likely to advance within the firm. Because large stockholders have a lot to gain from aligning the goals of managers with their own, they are likely to expend resources to encourage managers to maximize stock value. Sixth, the threat of a takeover, which leads to firing of poor managers, can provide current managers with incentives to perform well. Finally, laws and regulations limit the ability of managers to make decisions that harm stockholders.

LO:

5

Level: Intermediate Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Performance Measurement

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Chapter 2 The Financial System and the Level of Interest Rates

Before You Go On Questions and Answers Section 2.1 1.

What critical economic role does the financial system play in the economy?

The financial system is in place to gather money from people and businesses and then channel these funds to those who need it. An efficient financial system is essential for a healthy economy. The major players in the U.S. financial system are big institutions such as the New York Stock Exchange, Citigroup, or State Farm Insurance.

2.

What are the two basic ways in which funds flow through the financial system from lender–savers to borrower–spenders?

There are two basic mechanisms by which funds flow through the financial system: 1) Funds can flow directly through financial markets, and (2) funds can flow indirectly through financial institutions.

Section 2.2 1.

Why is it difficult for individuals to participate in the direct financial markets?

The financial markets where direct transactions take place are wholesale markets with a typical minimum transaction size of $1 million. Major buyers and sellers of securities in direct financial markets include commercial banks, large corporations, the federal government, hedge funds, and some wealthy individuals.

2.

Why might a firm prefer to have a security issue underwritten by an investment banking firm?

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In the most common type of underwriting arrangement, called firm-commitment underwriting, the investment banker assumes the risk of buying the new securities from the issuing company and reselling them to investors. The investment banker guarantees to buy the entire security issue from the company at a fixed price.

Section 2.3 1.

What is the difference between primary and secondary markets?

Primary markets are markets where new securities are sold for the first time. Secondary markets are where the owners of outstanding securities can sell them to other investors.

They provide the means for investors to sell their securities and get cash.

2.

How and why do large business firms use money markets?

Large businesses use money markets to adjust their liquidity positions. If a firm has idle cash sitting around, it can invest it in negotiable CDs, Treasury bills, or other money market instruments. On the other hand, if a company has a temporary cash shortage, it can borrow in the money markets by selling commercial paper at lower interest rates than it could borrow through a commercial bank.

3.

What are capital markets, and why are they important to corporations?

Capital markets refer to the segment of the marketplace where capital goods are financed with long-term debt or equities. The most important capital market instruments are common stocks and corporate bonds. Capital markets are important to corporations because they allow them to obtain necessary financing.

Section 2.4 1.

How does information about a firm’s prospects get reflected in its share price?

Investors act upon the expectations of a firm’s prospects through trading of the securities.

The buying and selling then causes the price of the security to reflect their assessment of its value.

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What is strong-form market efficiency? Semistrong-form market efficiency? Weak-form market efficiency?

Strong-form market efficiency is a market in which all information, private and public, is reflected in the price of the security. The semistrong-form of market efficiency suggests that only public information is reflected in a security’s price, while the weak-form of market efficiency holds that only information contained in the past price of a security is reflected in its current price (it does not reflect public or private information).

Section 2.5 1.

What is financial intermediation, and why is it important?

Financial intermediation is the process of converting financial securities with one set of characteristics into securities with another set of characteristics. For example, commercial banks use consumer CD deposits to make loans to small businesses.

2.

What are some services that commercial banks provide to businesses?

Commercial banks are the largest financial intermediaries in the economy and offer the widest range of financial services to businesses. Nearly every business has a significant relationship with a commercial bank – usually a checking or transaction account and some type of credit or loan arrangement. In addition, banks do a significant amount of equipment lease financing.

3.

What is an IPO, and what role does an investment banker play in the process?

Investment bankers specialize in helping firms to sell their new debt or equity issues in financial markets. In an initial public offering (IPO), the investment banker prepares the new issue for sale and then underwrites the deal. Other functions of the investment banker in an IPO process include preparing the prospectus, registering the documentation with the SEC, and providing general financial advice to the issuer.

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Section 2.6 1. Explain how the real rate of interest is determined.

The real rate of interest depends on interaction between the rate of return that businesses can expect to earn on investments in capital goods and savers’ time preference for consumption today versus willingness to save. Therefore, the real rate of interest is determined when the desired saving level equals the desired level of investment.

2. How are inflationary expectations accounted for in the nominal rate of interest?

The nominal interest rate is the rate that is actually observed in the financial markets, and it is equal to the real interest rate plus the expected annualized changes in commodity prices, or inflation premium. This is commonly referred to as the Fisher effect.

3. Explain why interest rates follow the business cycle.

Interest rates tend to follow the business cycle to rise during economic expansion and decline during recession. On the one hand, during an expansion, there is upward pressure on interest rates as businesses begin to grow and borrow more money. On the other hand, during a recession, the demand for goods and services is lower, businesses borrow less, and as a result the economy slows down and the interest rates decline.

Typically, the Fed also loosens credit to stimulate the economy, which puts further downward pressure on the interest rates.

Self-Study Problems and Solutions 2.1

.

Economic units that need to borrow money are said to be: a.

Lender–savers

b.

Borrower–spenders

c.

Balanced budget keepers.

d.

None of the above.

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Solution:

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Such units are said to be (b) Borrower-spenders.

LO: 1 Level: Basic

2.2

Explain what the marketability of a security is and how it is determined.

Solution:

Marketability refers to the ease with which a security can be sold and converted into cash. The level of marketability depends on the cost of trading the security and the cost of searching for information. The lower these costs are, the greater the security’s marketability.

LO:

3

Level: Basic

2.3

What are over-the-counter markets (OTCs), and how do they differ from organized exchanges?

Solution:

Securities that are not listed on an organized exchange are sold OTC. An OTC market differs from an organized exchange in that there is no central trading location. OTC security transactions are made via phone or computer as opposed to on the floor of an exchange.

LO:

3

Level: Basic

2.4

What effect does an increase in the demand for business goods and services have on the real interest rate? What other factors can affect the real interest rate?

Solution:

An increase in the demand for business goods and services will cause the borrowing schedule in Exhibit 2.4 to shift to the right, thus increasing the real rate of interest. Other factors that can affect the real interest rate include increases in productivity, changes in technology, or changes in the corporate tax rate.

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Demographic factors, such as growth or age of the population, and cultural differences can also affect the real rate of interest.

LO:

6

Level: Intermediate

2.5

How does the business cycle affect the nominal interest rate and inflation rate?

Solution:

Both the nominal interest and inflation rates tend to follow the business cycle; that is, they rise with economic expansion and fall during a recession.

LO: 6 Level: Basic 2.6.1 You lent $100 to a friend for one year at a nominal rate of interest of 3 percent. Inflation during that year was 2 percent. Did you experience an increase or decrease in the purchasing power of your money? How much did it increase or decrease?

Solution:

Since the interest rate that you received (3 percent) exceeded the rate of inflation, the amount that you received from your friend when the loan was repaid had greater purchasing power than $100. The amount by which the purchasing power increased can be calculated using Equation 2.1:

1 + i = (1 + r) × (1+ Pe) Solving for r yields: r = (1 + i)/(1 + Pe) - 1 r = (1 + 0.03)/(1 + 0.02) - 1 r = 0.0098, or 0.98% Therefore, the purchasing power increased by slightly less than 1 percent.

LO: Level:

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Discussion Questions 2.1

Explain why total financial assets in the economy must equal total financial liabilities.

Every financial asset must be financed with some type of a claim or liability. Since all of an economy’s financial assets are just a collection of the individual financial assets, then they should also sum to the collective claims on those assets in the economy.

LO:

1

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance; Business Economics AICPA: Resource Management 2.2

Why don’t small businesses make greater use of the direct credit markets since these markets enable firms to finance their activities at a very low cost?

Direct credit markets are geared toward big, established companies since they are wholesale in nature and the minimum transaction size is far beyond the needs of a small business. Small businesses are better off borrowing money from financial intermediaries, such as commercial banks.

LO:

5

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management 2.3

Explain the economic role of brokers and dealers. How does each make a profit?

Brokers and dealers play a similar economic role in that they both bring buyers and sellers of a commodity together in a market. However, brokers only facilitate a transaction by helping the two parties make a transaction and brokers are therefore only compensated for taking on that role. They bear no risk of ownership of securities during the transaction. Dealers on the other hand, take risk in that they will purchase (sell) a commodity from a seller (buyer) without another buyer (seller) necessarily being

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available. In other words, a dealer will take the risk of purchasing (selling) a commodity and will therefore be compensated for taking that risk.

LO:

3

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Resource Management 2.4

Why were commercial banks prohibited from engaging in investment banking activities until 1999?

Banks had been barred from investment banking following the Great Depression because it was believed that these activities were too risky for banks. At the time, it was believed that excessive risk taking by banks had resulted in a large number of bank failures, which precipitated the Great Depression. Recent research has exonerated the banking system of this charge.

LO:

2

Level: Basic Bloomcode: Knowledge AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective 2.5

What are two basic services that investment banks provide in the economy?

Investment banks specialize in helping companies sell new debt or equity as well as provide other services such as broker and dealer services.

LO:

2

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective 2.6

.

How do large corporations adjust their liquidity in the money markets?

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Large corporations can take advantage of money markets to adjust for their liquidity by selling or buying short-term financial instruments such as commercial paper, CDs, or Treasury bills. Large corporations with cash surplus can invest in short-term securities, while corporations with cash shortfalls can sell securities or borrow funds on a short-term basis. Money market instruments have a maturity anywhere between one day and one year and therefore are very liquid and less risky than long-term debt.

LO:

3

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management 2.7

The CFO of a certain company always wears his green suit on a day that the firm is about to release positive information about his company. You believe that you can profit from this information by buying the firm’s shares at the beginning of every day that the CFO shows up wearing this green suit. Describe which form of market efficiency is consistent with your belief.

You believe that the CFO’s decision to wear a green suit indicates that positive information will be announced and that the company’s stock price will increase following that announcement. If you are correct, knowing what the CFO is wearing before any announcement is valuable private information which should enable you to earn abnormally high returns. Therefore, your belief is consistent with the semistrong-form of market efficiency – according to which it is possible to earn abnormally high returns by trading on private information.

LO:

4

Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Strategic/Critical Thinking

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Solutions Manual

Shouldn’t the nominal rate of interest (Equation 2.1) be determined by the actual rate of inflation (∆Pa), which can be easily measured, rather than by the expected rate of inflation (∆Pe)?

The nominal rate of interest is a forward-looking measure, and therefore it makes sense that it is using the expected rate of inflation as opposed to the actual rate of inflation. The expected rate of inflation is the market’s best estimate of what the inflation rate will be in the future.

LO:

6

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.9

How does Exhibit 2.5 help explain why interest rates were so high during the early 1980s as compared to the relatively low interest rates in the early 1960s?

The nominal rate of interest is determined by the real rate of interest plus the expected rate of inflation, and during the 1980s, the U.S. economy experienced a very high rate of inflation and, thus, high interest rates. Looking at Exhibit 2.5, we can see that the inflation increased from less than 2 percent in the 1960s to almost 13 percent in the 1980s. This was a result of the monetary policy instituted by the U.S. government during this period of time.

LO:

6

Level: Basic Bloomcode: Analysis AACSB: Analytic IMA: Business Economics AICPA: Resource Management

2.10 When determining the real interest rate, what happens to businesses that find themselves with unfunded capital projects whose rate of return exceeds the cost of capital?

The real rate of interest reflects a complex set of forces that control the desired level of lending and borrowing in the economy. In this example, businesses are not investing in

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projects where the rate of return exceeds the cost of capital. This means that there is reduced demand for investment funds at the current real interest rate. This will remain so until either the real interest rate changes or until something changes for the firm such as introducing a new technology that will increase the rate of return on projects for the firm.

LO:

6

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

Questions and Problems BASIC 2.1

Financial System: What is the role of the financial system, and what are the two major components of the financial system?

Solution: The role of the financial system is to gather money from businesses and individuals who have surplus funds and channel funds to those who need them. The financial system consists of financial markets and financial institutions.

LO: 2.1 Bloomcode: Knowledge AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.2

Financial System: What does a competitive financial system imply about interest rates?

Solution: If the financial system is competitive, one will receive the highest possible rate for money invested with a bank and the lowest possible interest rate when borrowing money. Also, only firms with good credit ratings and projects with high rates of return will be financed.

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LO: 2.1 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 2.3

Financial System: What is the difference between saver–lenders and borrower–spenders, and who are the major representatives of each group?

Solution: Saver–lenders are those who have more money than they need right now. The principal saver–lenders in the economy are households. Borrower–spenders are those who need the money saver–lenders are offering. The main borrower–spenders in the economy are businesses followed by the federal government, although households are important mortgage borrowers.

LO: 2.1 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Business Economics AICPA: Industry/Sector Perspective

2.4

Financial Markets: List the two ways in which a transfer of funds takes place in an economy. What is the main difference between these two?

Solution: Funds can flow directly through financial markets or indirectly through intermediation markets where funds flow through financial institutions first.

LO: 2.2 Bloomcode: Knowledge AACSB: Analytic IMA: Business Economics AICPA: Resource Management

2.5

Financial Markets: Suppose you own a security that you know can be easily sold in the secondary market, but the security will sell at a lower price than you paid for it. What does this imply for the security’s marketability and liquidity?

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Solution: As the price of the security is lower than that you paid for it, it has a lower degree of liquidity to you, the owner. That is because the security cannot now be sold without a loss in value to the owner. Marketability refers to the ease with which a security can be sold or converted to cash. The information in the problem mentions that the security could be easily sold in secondary market, which implies it has high degree of marketability to you.

LO: 2.3 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.6

Financial Markets: Why are direct financial markets also called wholesale markets?

Solution: The financial markets are also called wholesale markets because the minimum transaction or security denomination is $1 million or more.

LO: 2.2 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.7

Financial Markets: Trader Inc.is a $300 million company, as measured by asset value, and Horst Corp. is a $35 million company. Both are privately held corporations. Explain which firm more likely to go public and register with the SEC, and why.

Solution: Trader Inc. is more likely to go public because of its larger size. Though the cost of SEC registration and compliance is very high, larger firms can offset these costs by the lower funding cost in public markets. Smaller companies find the cost prohibitive for the dollar amount of securities they sell.

LO: 2.3 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Solutions Manual

Primary Markets: What is a primary market? What does IPO stand for?

Solution: A primary market is where new securities are sold for the first time. IPO stands for Initial Public Offering.

LO: 2.3 Bloomcode: Knowledge AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.9

Primary Markets: Identify whether the following transactions are primary market or secondary market transactions. a. Jim Hendry bought 300 shares of IBM through his brokerage account. b. Peggy Jones bought $5,000 of General Motors bonds from another investor. c. Hathaway Insurance Company bought 500,000 shares of Trigen Corp. when the company issued stock.

Solution: a. Secondary market transactions. b.

Secondary market transactions. c.

Primary market transactions.

LO: 2.3 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.10 Investment Banking: What does it mean to “underwrite” a new security issue? What compensation does an investment banker get from underwriting a security issue?

Solution: To underwrite a new security issue means that the investment banker buys the entire issue from the firm at a guaranteed price and then resells the security to individual investors or

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other institutions at a higher price. The difference between the banker’s purchase price and the total resale price is called the underwriting spread, and it is the banker’s compensation. In addition to underwriting new securities, investment banks also provide other services, such as preparing the prospectus, preparing legal documents to be filed with the SEC, and providing general financial advice to the issuer.

LO: 2.2 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.11 Investment Banking: Cranjet Inc. is issuing 10,000 bonds, and its investment banker has guaranteed a price of $985 per bond. If the investment banker sells the entire issue to investors for $10,150,000. a. What is the underwriting spread for this issue? b. What is the percentage underwriting cost? c. How much did Cranjet raise?

Solution: a. $300,000 ($10,150,000 – $985 x 10,000) b. 3.05 percent [($1,105-985) /$985] c. $9,850,000 ($985 x 10,000) LO: 2.2 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.12 Financial Institutions: What are some of the ways in which a financial institution or intermediary can raise money?

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Solution: A financial intermediary can raise money through the sale of financial products that individuals or businesses will purchase, such as checking and savings accounts, life insurance policies, pension or retirement funds.

LO: 2.1 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.13 Financial Institutions: How do financial institutions act as intermediaries to provide services to small businesses?

Solution: Financial intermediaries allow smaller companies to access the financial markets.

They do this by converting securities with one set of characteristics into securities with another set of characteristics that meets the needs of smaller companies. By repackaging securities, they are able to meet the needs of different clients.

LO: 2.5 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.14 Financial Institutions: Which financial institution is usually the most important to businesses?

Solution: The primary financial intermediaries are commercial banks, life insurance companies, casualty insurance companies, pension funds, investment funds, and business finance companies.

Commercial banks are the largest and most prominent financial intermediaries in the economy and offer the widest range of financial services to businesses.

LO: 2.5 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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2.15 Financial Markets: What is the main difference between money markets and capital markets?

Solution: Money markets are markets in which short-term debt instruments with maturities of less than one year are bought and sold. Capital markets are markets in which equity securities and debt instruments with maturities of more than one year are bought and sold.

LO: 2.3 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.16 Money Markets: What is the primary role of money markets? Explain how the money markets work.

Solution: Money markets provide an option for large corporations to adjust their liquidity positions. Since only seldom are cash receipts and cash expenditures perfectly synchronized, money markets allow companies to temporarily invest idle cash in Treasury bills or negotiable CDs. If a company is short on cash, it can borrow the money from money markets by selling commercial paper at lower interest rates than through commercial banks.

LO: 2.3 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.17 Money Markets: What are the main types of securities in the money markets?

Solution: Treasury bills, bank negotiable CDs, and commercial paper.

LO: 2.3 Bloomcode: Knowledge AACSB: Analytic IMA: Corporate Finance

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AICPA: Industry/Sector Perspective

2.18 Capital Markets: How do capital market instruments differ from money market instruments?

Solution: Capital market instruments are less liquid or marketable, they have longer maturities, usually between 1 and 30 years, and they carry more financial risk.

LO: 2.3 Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.19 Market Efficiency: Describe the informational differences that distinguish the three forms of market efficiency.

Solution: The strong-form of market efficiency states that all information is reflected in the security prices. In other words, there is no private or inside information, that if released would potentially change the price. The semistrong-form holds that all public information available to investors is reflected in the security’s price. Therefore, insiders with access to private information could potentially profit from trading on this knowledge before it becomes public.

Finally, the weak-form of market efficiency holds that there is both public and private information that is not reflected in the security’s price and having access to it can lead to abnormal profits.

LO: 2.4 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.20 Market Efficiency: Zippy Computers announced strong fourth quarter results. Sales and earnings were both above analysts’ expectations. You notice in the newspaper that

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Zippy’s stock price went up sharply on the day of the announcement. If no other information about Zippy became public on the day of the announcement and the overall market was down, is this evidence of market efficiency?

Solution: Yes, if no other information became public and the market was down, the increase in Zippy’s price most likely reflects the effects of investors trading on the good news. Investors, believing that Zippy is now more valuable than they had thought, are willing to pay a higher price for the shares.

LO: 2.4 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.21 Market Efficiency: In problem 2.20, if the market is efficient, would it have been possible for Zippy’s stock price to go down on the day that the firm announced the strong fourth quarter results?

Solution: Yes. The last sentence in the statement of problem 2.20 suggests why this might happen. If, on the same day of the announcement, some very bad news about the future prospects for Zippy became public or if the market went down substantially, Zippy’s stock price might also have gone down despite the positive sales and earnings announcement. Zippy’s stock price may also go down if strong results were anticipated and this information was already reflected in the stock price, but the actual results were not as strong as anticipated.

LO: 2.4 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.22 Market Efficiency: If the market is strong-form efficient, then trading on tips you hear from Jim Cramer (the host of Mad Money on CNBC) will generate no excess returns (i.e., returns in excess of fair compensation for the risk you are bearing). True or false?

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Solution: True. If the market is strong-form efficient then all new information gets reflected in stock prices very quickly. In such a market, there is nothing you will hear from Jim Cramer on his TV show that will enable you to consistently earn excess returns. The information in his tips will already be reflected in stock prices by the time you can trade on them.

LO: 2.4 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.23 Financial Markets: What are the major differences between public and private markets?

Solution: Public markets are organized financial markets (also referred to as Exchanges) where the public buys and sells securities through their stock brokers. The SEC regulates public securities markets in the United States. In contrast, private markets involve direct transactions between two parties. These transactions lack SEC regulation.

LO: 2.3 Bloomcode: Analysis AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.24 Financial Instruments: What are the two risk-hedging instruments discussed in the chapter?

Solution: The two risk-hedging instruments discussed are futures and options contracts.

LO: 2.3 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Risk Analysis

2.25 Interest Rates: What is the real rate of interest, and how is it determined?

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Solution: The real rate of interest measures the return earned on savings, and it represents the cost of borrowing to finance capital goods. It is the interest rate determined in the absence of inflation. The real rate of interest is determined by the interaction between firms that invest in capital projects and the rate of return businesses can expect to earn on investments in capital goods, and individuals’ time preference for consumption. Graphically, it is that point when the desired saving level equals the desired level of investment in the economy.

LO: 2.6 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.26 Interest Rates: How does the nominal rate of interest vary over time?

Solution: The nominal rate is the rate that we observe in the marketplace. It is determined by both the real rate as well as expected inflation. Therefore, the nominal rate will fluctuate with changes in the real rate as well as changes in expected inflation.

LO: 2.6 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.27 Interest Rates: What is the Fisher equation, and how is it used?

Solution: The Fisher equation reflects the expected, not the reported or actual, annualized change in commodity prices (∆Pe). It is used to protect the buying power from changes in inflation, and it is incorporated into a loan contract by including the real interest rate that would exist in the absence of inflation.

LO: 2.6 Bloomcode: Knowledge AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

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2.28 Interest Rates: Imagine you borrow $500 from your roommate, agreeing to pay her back $500 plus 7 percent nominal interest in one year. Assume inflation over the life of the contract is expected to be 4.25 percent. What is the total dollar amount you will have to pay her back in a year? What percentage of the interest payment is the result of the real rate of interest?

Solution: You will pay her back $535 ($500 × 1.07) in one year. Given an inflation of 4.25 percent, the real rate of interest is approximately 2.368 percent using the Fisher equation: 1 + i = (1 + r) × (1 + ΔPe) 1 + 0.07 = (1 + r) × (1 + 0.0425) r = (1.07/1.0425) – 1 = 0.02638, or 2.638% This means that $13.19 ($500 × 0.02638) will be a result of the real interest rate which is 37.69 percent of the total interest payment.

The simplified, or approximate, Fisher equation yields a real interest rate of 2.75 percent: i = r + ΔPe r = 0.07 - 0.0425 = 0.0275, or 2.75% This means that $13.75 ($500 × 0.0275) will be a result of the real interest rate which is 39.29 percent of the total interest payment.

LO: 2.6 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Corporate Finance AICPA: Resource Management

2.29 Interest Rates: Your parents have given you $1,000 a year before your graduation so that you can take a trip when you graduate. You wisely decide to invest the money in a bank CD that pays 6.75 percent interest. You know that the trip costs $1,025 right now

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and that the inflation for the year is predicted to be 4 percent. Will you have enough money in a year to purchase the trip?

Solution: Yes. The CD will be worth $1,067.50 at the end of the year ($1,000 x 6.75% + $1,000), and the price of the trip will be $1,066 ($1,025 x 4% + $1,025). The CD will be able to cover the trip.

LO: 2.6 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Corporate Finance AICPA: Resource Management

2.30 Interest Rates: When are the nominal and real interest rates equal?

Solution: The only time the nominal and real interest rates are equal is when the expected rate of inflation over the contract period is zero.

LO: 2.6 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

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Sample Test Problems 2.1

What are the two basic mechanisms through which funds flow through the financial

system, and how do they differ?

Solution: The two basic mechanisms are the direct financing mechanism and the indirect financing mechanism. In the direct financing mechanism, issuers of securities (borrowerspenders) sell the securities directly to investors (lender-savers). In the indirect financing mechanism, financial institutions aggregate money from lender-savers and make this capital available through loans to borrower-spenders.

LO: 1 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.2

You just purchased a share of IBM stock on the New York Stock Exchange. What kind of

transaction was this? a.

Primary market transaction.

b.

Secondary market transaction.

c.

Futures market transaction.

d.

Private placement.

Solution: b. (The secondary market is the one in which owners of outstanding securities sell their securities to other investors.)

LO: 3 Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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How are brokers different from dealers?

Solution: Brokers bring buyers and sellers together. They execute a transaction for their client and are compensated with a commission fee. Brokers never own the securities being sold and therefore do not bear any risk of ownership.

In contrast, dealers purchase securities and sell them from an inventory that they own. Dealers profit if they are able to sell securities for a price greater than they paid for them. Because they own the securities, dealers face the risk that the prices of the securities in their inventory will fall below what they paid for those securities.

LO: 3 Level: Intermediate Bloomcode: Analysis AACSB: Reflective Thinking IMA: Business Economics AICPA: Industry/Sector Perspective

2.4

List the three forms of the efficient market hypothesis, and describe what information is

assumed to be reflected in security prices under each of these hypotheses.

Solution: 1) Strong-Form Efficiency – all information is reflected in the security prices.

2) Semistrong-Form Efficiency – all public information is reflected in the security prices.

3) Weak-Form Efficiency – all information contained in past prices is reflected in security prices.

LO: 4 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.5 If the nominal rate of interest is 4.25 percent and the expected rate of inflation is 1.75 percent, what is the real rate of interest?

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Solution: Using the Fisher equation: i = r + ∆Pe + r ∆Pe where i = 0.0425 and ∆Pe = 0.0175 Solving for r, we get r = 0.02457, or 2.457% LO: 6 Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.6

What is the relation between business cycles and the general level of interest rates?

Solution: As Exhibit 2.5 shows, interest rates tend to follow the business cycle. The level of interest rates tends to rise during periods of economic expansion and decline during periods of economic contraction.

LO: 6 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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Chapter 3 Financial Statements, Cash Flows, and Taxes

Before You Go On Questions and Answers Section 3.1 1.

What types of information does a firm’s annual report contain?

A firm’s annual report is typically divided into three sections: financial tables with an accompanying verbal explanation of the firm’s performance over the past year; a corporate public relations section discussing the firm’s operations, and the audited financial statements (balance sheet, income statement, statement of cash flows, and statement of retained earnings).

2.

What is the realization principle, and why may it lead to a difference in the timing of when revenues are recognized on the books and cash is collected?

According to the realization principle, revenue should only be recognized when the earning process is completed and the exchange of goods or services can be determined by an arm’s length transaction. Although this principle works in theory, it still does not specify whether this is the point when the goods are ordered, when they are shipped, or when the payment is actually received from the customer. Also, not many purchases are paid for in cash any more.

Therefore, even if the transaction is recognized at the point at which the customer receives the goods, the actual cash flow might not occur until days later (depending what the terms are).

Section 3.2 1.

What is net working capital? Why might a low value for this number be considered undesirable?

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Net working capital is the difference between total current assets and total current liabilities. A low value for this number is undesirable, for it indicates that the company may not have enough cash on hand to cover its immediate expenses.

2.

Explain the accounting concept behind depreciation.

Depreciation in accounting is a noncash expense that helps to allocate the cost of an item over its expected life. It reflects the estimated decrease in the value of an asset due to wear and tear and obsolescence.

3.

What is treasury stock?

Treasury stock is the stock that the company purchased back from its investors. These shares do not pay dividends, have no voting rights, and should not be included in sharesoutstanding calculations.

Section 3.3 1.

What is the difference between book value and market value?

Book value is the price you paid for a particular asset. This price does not change as long as you own the asset. On the other hand, market value is the price at which you can sell an asset today, as it takes into account how much it can earn in the future.

2.

What are some objections to the preparation of marked-to-market balance sheets?

Marked-to-market balance sheets list the firm’s assets and liabilities at their current market prices. Even though a balance sheet constructed with actual market values might paint a more accurate picture of the company’s financial situation, current values are difficult to estimate, and a lot of the complicated models are potentially open to abuse.

Therefore, as of the present, the norm is to use book values.

Section 3.4 1.

.

How is net income computed?

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Net income is calculated as revenues minus expenses. It is the most comprehensive accounting measure of a company’s performance because it reflects the firm’s accomplishments (revenues) relative to its efforts (expenses) during a time period.

2.

What is EBITDA, and what does it measure?

EBITDA stands for earnings before interest, taxes, depreciation, and amortization. EBIT is defined as earnings before taxes and interest. The main difference between these two figures is that EBITDA shows the income earned purely from operations and reflects how efficiently a firm can manufacture and sell its products without taking into account the cost of the productive asset base.

3.

What accounting events trigger changes to the retained earnings account?

Two events will trigger changes to the retained earnings account: (1) a firm’s report of a net income or loss and (2) the board of directors’ declaration of a cash dividend.

Section 3.5 1.

How do increases in fixed assets from one period to the next affect cash holdings for the firm?

An increase in fixed assets from one period to the next is a use of cash. If a company purchases fixed assets during the year, it decreases cash because it must use cash to pay for the purchase.

2.

Name two working capital accounts that represent sources of cash for the firm.

An increase in current liabilities is a source of cash. Two common current liabilities are accounts and notes payable. An increase in either of these accounts from one period to the next will represent a source of cash for the firm.

3.

.

Explain the difference between cash flows from financing and investing activities.

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Cash flows from financing activities occur when cash is obtained from (cash inflow) or paid to (cash outflow) creditors or owners (stockholders). Cash flows from investing activities relate to the buying (cash outflow) and selling of long-term assets (cash inflow).

Section 3.6 1.

Explain how the four financial statements are related.

The four financial statements are linked together as follows: the ending cash balance from the statement of cash flows is used as the cash balance on the balance sheet, and the net income reported in the income statement is transferred to retained earnings on the balance sheet. So as you can see, the balance sheet is the one financial statement that ties all four statements together.

Section 3.7 1.

How does the calculation of net income differ from the calculation of cash flow to investors from operating activity?

Net income is calculated as the difference between revenues and expenses from the income statement. Cash flow from operating activity is the firm’s earnings before interest and taxes (EBIT) minus taxes paid in cash plus the firm’s noncash expenses, including depreciation and amortization.

2.

All else being equal, if a firm increases its accounts payable, what effect will this have on cash flow to investors?

An increase in a current liability such as accounts payable from one period to the next will reduce the cash flow from net working capital and will, therefore, increase cash flow to investors.

3.

What does it mean when a firm’s cash flow to investors is negative?

When a firm’s investment of cash flow from net working capital and long-term assets exceeds the firm’s cash flow from operating activity, the cash flow to investors will be

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negative. A negative cash flow to investors means that the firm must raise money from new issues of debt or equity.

Section 3.8 1.

Why is it important to consider the consequences of taxes when financing a new project?

When financing a new project, it is important to consider the consequences of taxes because ultimately these have a significant impact on the company’s income.

2.

Which type of tax rate, marginal or average, should be used in analyzing the expansion of a product line, and why?

When analyzing the expansion of a product line, the marginal tax rate should be the type to consider because it is the amount paid on an additional dollar of income earned. Since expansion of a product line is expected to generate new cash flows, the company will be taxed based on the additional earnings. Average tax rate is not as relevant when making financing decisions because it is simply the total taxes paid divided by taxable income.

3.

What are the tax implications of a decision to finance a project using debt rather than new equity?

The difference between debt financing and financing through new equity is in the tax treatment of interest and dividends. While interest payments on debt are tax-deductible business expenses, dividends paid to common or preferred stockholders are not deductible.

Self-Study Problems and Solutions 3.1

.

The going concern assumption of GAAP implies that the firm: a.

Is going under and needs to be liquidated at historical cost.

b.

Will continue to operate and its assets should be recorded at historical cost.

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Will continue to operate and that all assets should be recorded at their cost rather than at their liquidation value.

d.

Solution:

Is going under and needs to be liquidated at liquidation value.

One of the key assumptions under GAAP is the going concern assumption, which states that the firm: (c) will continue to operate and that all assets should be recorded at their cost rather than at their liquidation value.

LO: 1 Level: Basic

3.2

The Ellicott City Ice Cream Company management has just completed an assessment of the company’s assets and liabilities and has obtained the following information. The firm has total current assets worth $625,000 at book value and $519,000 at market value. In addition, its long-term assets include plant and equipment valued at market for $695,000, while their book value is $940,000. The company’s total current liabilities are valued at market for $543,000, while their book value is $495,000. Both the book value and the market value of long-term debt is $350,000. If the company’s total assets are equal to a market value of $1,214,000 (book value of $1,565,000), what are the book value and market value of its stockholders’ equity?

Solution:

The book value and market value of stockholders’ equity are shown below (in thousands of dollars):

Assets

Liabilities and Equity Book

Market

Book

Total current assets

$ 625

$ 519

Total current liabilities

Fixed assets

940

695

Market

$ 495

$ 543

Long-term debt

350

350

Stockholders’ equity

720

321

$1,565

$1,214

Total liabilities and Total assets

$1,565

$1,214

stockholders’ equity

LO: 3 Level: Basic

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Solutions Manual

Depreciation and amortization expenses are: a.

Part of current assets on the balance sheet.

b.

After-tax expenses that reduce a firm’s cash flows.

c.

Long-term liabilities that reduce a firm’s net worth.

d.

Noncash expenses that cause a firm’s after-tax cash flows to exceed its net income.

Solution:

Depreciation and amortization expenses are: (d) noncash expenses that cause a firm’s after-tax cash flows to exceed its net income.

LO: 4 Level: Basic

3.4

You are given the following information about Clarkesville Plumbing Company.

Revenues in 2017 totaled $896, depreciation expenses $75, costs of goods sold $365, and interest expenses $54. At the end of the year, current assets were $121 and current liabilities were $107. The company has an average tax rate of 34 percent. Calculate its net income by setting up an income statement.

Solution:

Clarkesville’s income statement and net income are as follows: Clarkesville Plumbing Company Income Statement for the Fiscal Year Ending December 31, 2017 Amount Revenues

$896.00

COGS

365.00

EBITDA

$531.00

Depreciation

.

75.00

EBIT

$456.00

Interest

54.00

EBT

$402.00

Taxes (34%)

136.68

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Net income

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$265.32

LO: 4 Level: Basic

3.5

The Huntington Rain Gear Company had $633,125 in taxable income in the year ending September 30, 2017. Calculate the company’s tax using the tax schedule in Exhibit 3.6.

Solution:

Huntington’s tax bill is calculated as follows: Tax rate

Income

Tax

15%

$50,000

$ 7,500

25

(75,000–50,000)

6,250

34

(100,000–75,000)

8,500

39

(335,000–100,000)

91,650

34

(633,125–335,000)

101,363

Total taxes payable

$215,263

LO: 8 Level: Basic

Discussion Questions 3.1

What is a major reason for the accounting scandals in the early 2000s? How do firms sometimes attempt to meet Wall Street analysts’ earnings projections?

Most people believe that managers’ short-term focus is driven by Wall Street’s demand that companies meet or beat the earnings forecasted by stock analysts. Rather than report the actual earnings of the firm, managers try to meet the market’s expectations by starting with the bottom-line number and backing into a sales figure. Thus, the sales may be consistent with the reported earnings figure, but do not represent the true revenue generated by the firm.

LO: 1

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Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.2

Why are taxes and the tax code important for managerial decision making?

Understanding the tax code is critical to finance managers, since most decisions are made on an after-tax basis. Furthermore, taxes affect any valuation analysis and also determine the bottom-line figure that is of concern to shareholders and managers.

LO: 8 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Budget Preparation AICPA: Decision Modeling

3.3

Identify the five fundamental principles of GAAP, and explain briefly their importance. The assumption of arm’slength transaction assumes that all business transactions between two parties are made rationally from an economic perspective and both parties will make the deal that provides them the best value. The cost principle calls for the recognition of all accounting transactions at historic cost, or the amount paid or received when the transaction was concluded at arm’s length. The realization principle implies that revenue should be recognized only at the time of the sale. The matching principle dictates that revenue is first recognized and then is matched with the costs incurred in producing the revenue. Finally, the going concern assumption implies that the firm will continue to operate and that all assets should be recorded at their cost rather than at their liquidation value.

LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Communication

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IMA: Reporting AICPA: Reporting

3.4

Explain why firms prefer to use accelerated depreciation methods over the straight-line method for tax purposes.

When a firm uses accelerated depreciation, the depreciation expense is higher than with the straight-line method. This reduces the taxable income and the amount of tax paid by the firm. As a result of this higher noncash expense, the firm’s cash flow is higher.

LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Budget Preparation AICPA: Reporting

3.5

What is treasury stock? Why do firms have treasury stock?

Any shares repurchased by the company in the open market are recorded as treasury stock in the shareholders’ equity account in the balance sheet. The most common reason for firms doing this is to reduce the number of shares outstanding in the market when the management believes that its firm’s stock is undervalued. This reduction in the number of shares outstanding is expected to boost the share price.

LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Coorporate Finance AICPA: Resource Management

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Solutions Manual

Define book-value accounting and market-value accounting.

Book-value accounting implies that all assets and liabilities are recorded and reported at the historical cost when they were acquired. Market-value accounting requires that all assets and liabilities are reported at their current market value.

LO: 3 Level: Basic Bloomcode: Knowledge AACSB: Analytic IMA: Reporting AICPA: Reporting

3.7

Compare and contrast depreciation expense and amortization expense.

Depreciation expense is the amount by which a firm’s fixed assets are written down in a period during which the assets are utilized for generating cash flows. Amortization is the amount by which intangible assets like goodwill, patents, license, copyrights, and trademarks are written down in any period that they are utilized by the firm to generate benefits. Both depreciation and amortization are noncash expenses that will serve to boost the firm’s after-tax cash flows, and generate actual value of the asset at the end of a period.

LO: 4 Level: Basic Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Measurement

3.8

Why are retained earnings not considered an asset of the firm?

Retained earnings are part of shareholders’ equity that has already been utilized by the company. It is a liability of the company and corresponds to a claim by the firm’s

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shareholders. The retained earnings reported on the balance sheet have already been allocated by the company among various assets and hence are not available for current or future uses. New retained earnings have to be generated to provide for new uses.

LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.9

What is the statement of cash flows, and what is its role?

This financial statement records both the cash inflows and cash outflows for a period of time. Thus, it reports the changes in the cash position of a firm between successive accounting periods.

LO: 5 Level: Basic Bloomcode: Knowledge AACSB: Communication IMA: Reporting AICPA: Reporting

3.10 How does a firm’s cash flow to investors from operating activity differ from net income, and why?

Net income is an accounting figure that includes both cash and noncash expenses. In addition, revenues are recognized before they are collected and expenses are recognized before they are paid. Cash flow from operating activity recognizes that certain revenues and expenses, while recognized for accounting purposes, do not actually involve a cash flow and ignores the effects of these non-cash items on the income statement. .

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LO: 5 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

Questions and Problems BASIC 3.1

Balance sheet: Given the following information about Elkridge Sporting Goods, Inc., construct a balance sheet for June 30, 2017. On that date the firm had cash and marketable securities of $25,135, accounts receivables of $43,758, inventory of $167,112, net fixed assets of $325,422, and other assets of $13,125. It had accounts payables of $67,855, notes payables of $36,454, long-term debt of $223,125, and common stock of $150,000. How much retained earnings did the firm have?

Solution: Assets

Book Value

Liabilities and Stockholders’

Book Value

Equity

Cash and marketable

$ 25,135

Accounts payables

$ 67,855

Notes payables

36,454

securities Accounts receivable

43,758

Inventories

167,112

Total current assets

$236,005

Total current liabilities

$104,309

Net fixed assets

325,422

Long-term debt

223,125

Other assets

13,125

Common stock

150,000

Retained earnings

97,118

Total liabilities and Total assets

$574,552

stockholders’ equity

$574,552

LO: 3.2 Bloomcode: Analysis

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AACSB: Communication IMA: Reporting AICPA: Reporting

3.2

Inventory accounting: What is the difference between FIFO and LIFO accounting.

Solution: FIFO (first in, first out) refers to the practice of firms, when making sales, assuming that the inventory that came in first (at a lower price) is being sold first. During the period of rising prices, LIFO (last in, last out) implies that a firm is selling the higher cost, newer inventory first, leaving the lower cost, older inventory on the balance sheet.

LO: 3.2 Bloomcode: Comprehension AACSB: Communication IMA: Budget Preparation AICPA: Reporting

3.3

Inventory accounting: Explain how the choice of FIFO versus LIFO can affect a firm’s balance sheet and income statement.

Solution: FIFO makes sense during times of rising prices because it allows the firm to eliminate the lower priced inventory first, resulting in higher profit margin. This allows the firm to leave higher valued inventory on the balance sheet. During inflationary times, a firm using LIFO would see a lower profit margin and lower values of inventory on the balance sheet. It is important that anyone who is analyzing firms using different accounting methods on inventory recognize the impact on the bottom line (profit margin and net income) and on current assets.

LO: 3.2 Bloomcode: Comprehension AACSB: Communication IMA: Budget Preparation AICPA: Reporting .

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Market-value accounting: How does the use of market-value accounting help managers?

Solution: Market-value accounting of both assets and liabilities allows managers to have a truer picture of their company’s financial condition and to do a better job of estimating cash flows that the assets would generate. However, marking-to-market is not as easy as it sounds because of the difficulties involved in coming up with the correct market value of current assets and liabilities.

LO: 3.3 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.5

Working capital: Laurel Electronics reported the following information at its annual meetings: The company had cash and marketable securities worth $1,235,455, accounts payables worth $4,159,357, inventory of $7,121,599, accounts receivables of $3,488,121, short-term notes payable worth $1,151,663, and other current assets of $121,455. What is the company’s net working capital?

Solution: Total current assets

= $1,235,455 + $3,488,121 + $7,121, 599 + $121,455 = $11,966,630

Total current liabilities = $4,159,357 + $1,151,663 = $5,311,020 Net working capital

= $11,966,630 - $5,311,020 = $6,655,610

LO: 3.2

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Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Reporting

3.6

Working capital: The financial information for Laurel Electronics referred to in Problem 3.5 is all at book value. Suppose marking to market reveals that the market value of the firm’s inventory is 20 percent below its book value, its receivables are 25 percent below their book value, and the market value of its current liabilities is identical to the book value. What is the firm’s net working capital using market values? What is the percentage difference net working capital using market versus book values?

Solution: Market value of inventory = $7,121,599 × 0.80 = $5,697,279 Market value of receivables = $3,488,121 × 0.75 = $2,616,091 Total current assets

=

$1,235,455 + $2,616,091 + $5,697,279 + $121,455

= $9,670,280 Total current liabilities = $4,159,357 + $1,151,663 = $5,311,020 Net working capital = $9,670,280 - $5,311,020 = $4,359,260 Percent Change =

$4,359,260 −$6,655,610 $6,655,610

= −𝟑𝟒.𝟓% LO: 3.2 Bloomcode: Analysis AACSB: Communication IMA: Reporting AICPA: Reporting

3.7

Income statement: The Oakland Mills Company has disclosed the following financial information in its annual reports for the period ending March 31, 2017: sales of $1.45

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million, cost of goods sold of $812,500, depreciation expenses of $175,000, and interest expenses of $89,575. Assume that the firm has an average tax rate of 35 percent. What is the company’s net income? Set up an income statement to answer the question.

Solution: Oakland Mills Company Income Statement For the period ended on March 31, 2017 Amount Revenues

$1,450,000.00

COGS

812,500.00

EBITDA

$ 637,500.00

Depreciation

175,000.00

EBIT

$ 462,500.00

Interest

89,575.00

EBT

$ 372,925.00

Taxes (35%)

130,523.75

Net income

$ 242,401.25

LO: 3.4 Bloomcode: Analysis AACSB: Communication IMA: Reporting AICPA: Reporting

3.8

Cash flow: Describe the organization of the statement of cash flows.

Solution: The statement of cash flows identifies the cash inflows and cash outflows of the firms for a specified period. This allows one to estimate the net cash flows from operations.

This financial statement is organized to report the cash flows resulting from the three basic activities in any firm—operating, investing, and financing. The cash flows from operations are the results of netting all revenues and expenses that result from the operating activities of the firm. Buying and selling a firm’s assets lead to cash flows

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from investing activities. Cash flows from financing activities arise from the firm borrowing from its investors and/or making payments to its lenders and shareholders.

LO: 3.5 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.9

Cash flows: During 2017, Towson Recording Company increased its investment in marketable securities by $36,845, funded fixed-assets acquisitions of $109,455, and had marketable securities of $14,215 mature. What is the net cash used in investing activities?

Solution: Long-Term Investing Activities Net property, equipment, and other assets Net acquisitions and dispositions Investments in marketable securities Net cash used in investing activities

$(109,455.00) 0.00 (22,630.00) $(132,085.00)

LO: 3.5 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.10 Cash flows: Caustic Chemicals management identified the following cash flows as significant in its year-end meeting with analysts. During the year Caustic had repaid existing debt of $312,080 and raised additional debt capital of $650,000. It also repurchased stock in the open market for a total of $45,250. What is the net cash provided by financing activities?

Solution:

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Financing Activities Loan repayment Increase

$(312,080)

in long-term debt Purchase

650,000

of treasury stock

(45,250)

Net cash provided by financing activities

$ 292,670

LO: 3.5 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

3.11 Cash flows: Identify and describe the noncash expenses that a firm may incur.

Solution: A firm may have several items on its income statement that did not result in any cash outflow to the firm. The two largest are depreciation expenses and amortization expenses. Other non-cash expenses include deferred taxes, deferred wages, and depletion charges, which is similar to depreciation and used for natural resource assets. Prepaid expenses also fit into this category as they represent expenses to the firm that were paid in previous period, but yet to incur.

LO: 3.5 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.12 Cash flows : Given the data for Oakland Mills Company in problem 3.7 above, compute the cash flows to investors from operating activity.

Solution: CFOA = EBIT – current taxes + Non-cash expenses = $462,500.00 - $130,523.75 + $175,000.00 = $506,976.25 LO: 3.7 Bloomcode: Application

.

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AACSB: Communication IMA: Reporting AICPA: Reporting

3.13 Cash flows: Hillman Corporation reported current assets of $3,495,055 for the year ending December 31, 2017 and current assets of $3,103,839 on December 31, 2016. Current liabilities for the firm were $2,867,225 and $2,760,124 at the end of 2017 and 2016 respectively.

Compute the cash flow invested in net working capital at Hillman

Corporation during 2017.

Solution: CFNWC = ($3,495,055 - $2,867,225) – ($3,103,839 - $2,760,124) = $284,115 LO: 3.7 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

3.14 Cash flows: Del Bridge Construction had long- term assets before depreciation of $990,560 on December 31, 2016 and $1,211,105 on December 31, 2017. How much cash flow was invested in long-term assets for Del Bridge during 2017?

Solution: CFLTA = $1,211,105 - $990,560 = $220,545.

LO: 3.7 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

3.15 Tax: Define average tax rate and marginal tax rate. .

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Solution: The average tax rate is defined as the total taxes paid divided by taxable income.

The marginal tax rate, meanwhile, represents the tax rate that is paid on the last dollar of income earned, or the rate that will be paid on the next dollar earned.

LO: 3.8 Bloomcode: Knowledge AACSB: Communication IMA: Reporting AICPA: Reporting

3.16 Tax: What is the relevant tax rate to use when making financial decisions? Explain why.

Solution: Managers need to use the marginal tax rate for making financial decisions. This is because any additional cash flows that result from a firm’s new projects will be taxed at the marginal tax rate. Thus, this is the appropriate rate to use.

LO: 3.8 Bloomcode: Comprehension AACSB: Communication IMA: Investment Decisions AICPA: Decision Modeling

3.17 Tax: Manz Property Management Company announced that in the year ended June 30, 2017, its earnings before taxes amounted to $1,478,936. Calculate its taxes using Exhibit 3.6.

Solution: Earnings before tax = $1,478,936 Tax rate

.

Income

Tax

15%

$0 to $50,000

$ 7,500.00

25

50,001 − 75,000

6,250.00

34

75,001 − 100,000

8,500.00

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39

100,001

−

335,000

91,650.00

34

335,001 − 10,000,000

388,938.24

35

10,000,001 − 15,000,000

38

15,000,001 − 18,333,333

35

More than $18,333,333 Total taxes payable

$502,838.24

LO: 3.8 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Measurement

INTERMEDIATE 3.18 Balance sheet: Tim Dye, the CFO of Blackwell Automotive, Inc., is putting together this year’s financial statements. He has gathered the following balance sheet information. The firm had a cash balance of $23,015, accounts payable of $163,257, common stock of $313,299, retained earnings of $512,159, inventory of $212,444, goodwill and other assets equal to $78,656, net plant and equipment of $711,256, and short-term notes payable of $21,115. It also has accounts receivables of $141,258 and other current assets of $11,223. How much long-term debt does Blackwell Automotive have?

Solution: Blackwell Automotive, Inc. Balance Sheet as of December 31 Liabilities and Stockholders’ Assets Cash

.

Equity $

23,015

Accounts payable and accruals

Accounts receivable

141,258

Notes payable

Inventories

212,444

$ 163,257 21,115

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Other current assets

11,223

Total current assets

$ 387,940

Net plant and equipment

711,256

Long-term debt

168,022

Goodwill and other assets

78,656

Total liabilities

$ 352,394 313,299

Total current liabilities

Common stock

$ 184,372

512,159

Retained earnings Stockholders’ Equity

$

825,458

Total liabilities and Total assets

$1,177,852

stockholders’ equity

$1,177,852

LO: 3.2 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.19 Working capital: Mukhopadhya Network Associates has a current ratio of 1.60, where the current ratio is defined as follows: current ratio = current assets/current liabilities. The firm’s current assets are equal to $1,233,265, its accounts payables are $419,357, and its notes payables are $351,663. Its inventory is currently at $721,599. The company plans to raise funds in the short-term debt market and invest the entire amount in additional inventory. How much can notes payable increase without the current ratio falling below 1.50?

Solution: Let x be the amount raised through notes payables.

New current liabilities = $419,357+ $351,663 + x New current assets = $1,233,265 + x

.

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$1, 233, 265 + x Current assets = 1.5= $771, 020 + x Current liabilities 1.5($771,020+ ) x = $1, 233, 265 + x 1.5x − x = $1, 233, 265 − $1,156, 530 0.5x = $76, 735 x = $76,735 0.5 $153, 470 =

Thus the firm can add up to $153,470 in inventory by raising money through notes payable without changing the ratio of current assets to current liabilities to more than 1.50. (This ratio of current assets to current liabilities is known as the current ratio and will be discussed in the next chapter.)

LO: 3.2 Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Measurement

3.20 Market value: Reservoir Bottling Co. reported the following information at the end of the year. Total current assets are worth $237,513 at book value and $219,344 at market value. In addition, plant and equipment have a market value of $343,222, and a book value of $362,145. The company’s total current liabilities are valued at market for $134,889 and have a book value of $129,175. Both the book value and the market value of long-term debt is $144,000. If the company’s total assets have a market value of $562,566 and a book value of $599,658, what is the difference between the book value and market value of its stockholders’ equity?

Solution: Assets

Book

Market

Value

Value

Book Value Liabilities and

Market Value

stockholders’ equity

.

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Total current assets

$237,513

$219,344

Total current liabilities

$129,175

$134,889

Net fixed assets

362,145

343,222

Long-term debt

144,000

144,000

Other assets

0

0

Common stock

326,483

283,677

Total assets

$599,658

$562,566

Total liabilities and

$599,658

$562,566

stockholders’ equity

Change in value of stockholders’ equity = $283,677 – $326,483 = $(42,806) LO: 3.3 Bloomcode: Analysis AACSB: Analytic IMA: Corporate finance AICPA: Measurement

3.21 Income statement: Nimitz Rental Company provided the following information to its auditors. For the year ended March 31, 2017, the company had revenues of $878,412, general and administrative expenses of $352,666, depreciation expenses of $131,455, leasing expenses of $108,195, and interest expenses equal to $78,122. If the company’s average tax rate is 34 percent, what is its net income after taxes?

Solution: Nimitz Rental Company Income Statement as of March 31, 2017 Amount Revenues

$878,412

General and administrative expenses

352,666

Leasing expenses

108,195

EBITDA

$417,551

Depreciation expenses

131,455

EBIT

$286,096

Interest expenses EBT Taxes (34%)

.

78,122 $207,974 70,711

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Net income

Solutions Manual

$137,263

LO: 3.4 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.22 Income statement: Sosa Corporation recently reported an EBITDA of $31.3 million and net income of $9.7 million. The company had $6.8 million in interest expense, and its average corporate tax rate was 35 percent. What was its depreciation and amortization expense?

Solution: Amount EBITDA

$31,300,000.00

Less: Depreciation and amortization

9,576,923.08

EBIT

$21,723,076.92

Interest

6,800,000.00

EBT

$14,923,076.92

Taxes (35%)

5,223,076.92

Net income

$ 9,700,000.00

LO: 3.4 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.23 Income statement: Fraser Corporation has announced that its net income for the year ended June 30, 2017, was $1,353,412. The company had EBITDA of $ 4,967,855, and its

.

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depreciation and amortization expense was equal to $1,112,685. The company’s average tax rate is 34 percent. What was its interest expense?

Solution: Amount EBITDA

$4,967,855.00

Depreciation and Amortization

1,112,685.00

EBIT

$3,855,170.00

Interest

1,804,545.76

EBT

$2,050,624.24

Taxes (34%)

697,212.24

Net income

$1,353,412.00

LO: 3.4 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.24 Income Statement: For its most recent fiscal year, Carmichael Hobby Shop recorded EBITDA of $512,725.20, EBIT of $362,450.20, zero interest expense, and cash flow to investors from operating activity of $348,461.25. Assuming there are no non-cash revenues recorded on the income statement, what is the firm’s net income after taxes?

Solution: We know that:

Cash flow from operating activity = CFOA = EBIT − Current taxes+ Noncash expenses Since interest expense = $0, we know that: EBIT = EBT Therefore, Net income = EBIT - Current taxes and so: Current taxes = EBIT – Net income Substituting into the equation for CFOA above (Equation 3.4) yields:

.

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CFOA = EBIT – (EBIT – Net Income) + Noncash expenses CFOA = Net income + Noncash expenses Since:

Depreciation and amortization = Noncash expenses = EBITDA − EBIT = $512, 275.20 − $362, 450.20$150, = 275 We can calculate net income as:

Net income = CFOA−Depreciation & amortization = $348,461.25-$150,275 = $198, 186.25 LO: 3.4, 3.7 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.25 Retained earnings: Columbia Construction Company earned $451,888 during the year ended June 30, 2017. After paying out $225,794 in dividends, the balance went into retained earnings. If the firm’s total retained earnings were $846,972 at the end of fiscal year 2017, what were the retained earnings on its balance sheet on July 1, 2016?

Solution: Columbia Construction Company Retained Earnings for 2017 Balance of retained earnings, July 1, 2016

$ 620,878.00

Add: Net income for the year

451,888.00

Less: Dividends to common stockholders

(225,794.00)

Balance of retained earnings, June 30, 2017

$ 846,972.00

LO: 3.4 Bloomcode: Application AACSB: Analytic .

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IMA: Reporting AICPA: Measurement

3.26 Cash flow: Refer to the information given in Problem 3.21. What is the cash flow from operating activity for Nimitz Rental?

Solution: Cash flow from operations

=

Net income + Depreciation

=

$137,263 + $131,455

=

$268,718

LO: 3.5 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.27 Tax: Mount Hebron Electrical Company’s financial statements indicated that the company had earnings before interest and taxes of $718,323. The interest rate on its $850,000 debt was 8.95 percent. Calculate the taxes the company is likely to owe. What are the marginal and the average tax rates for this company?

Solution: EBIT

$718,323.00

Interest

76,075.00

EBT

Tax rate

.

$642,248.00

Income

Tax

15%

$0 to $50,000

$ 7,500.00

25

50,001 − 75,000

6,250.00

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34

75,001

−

100,000

8,500.00

39

100,001

−

335,000

91,650.00

34

335,001 − 10,000,000

104,464.32

35

10,000,001 − 15,000,000

38

15,000,001 − 18,333,333

35

More than $18,333,333 Total taxes payable

$218,364.32

Marginal tax rate

=

34%

Average tax rate

=

Total taxes payable / Taxable income (EBT) $218,364.22 / $642,248

=

34%

LO: 3.8 Bloomcode: Analysis AACSB: Analytic IMA: Budget Preparation AICPA: Measurement

ADVANCED 3.28 The Centennial Chemical Corporation announced that, for the period ending March 31, 2017, it had earned income after taxes of $2,768,028.25 on revenues of $13,144,680. The company’s costs (excluding depreciation and amortization) amounted to 61 percent of sales and it had interest expenses of $392,168. What is the firm’s depreciation and amortization expense if its average tax rate is 34 percent?

Solution: Centennial Chemical Corporation Income statement For the period ending March 31, 2017

.

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Amount Revenues

$13,144,680.00

Costs

$8,018,254.80

EBITDA

$5,126,425.20

Depreciation and amortization

$540,275.00

EBIT

$4,586,150.20

Interest

$392,168.00

EBT

$4,193,982.20

Taxes (34%)

$1,425,953.95

Net income

$2,768,028.25

LO: 3.4 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.29 Eau Claire Paper Mill, Inc., had, at the beginning of the current fiscal year, April 1, 2016, retained earnings of $323,325. During the year ended March 31, 2017, the company produced net income after taxes of $713,445 and paid out 45 percent of its net income as dividends. Construct a statement of retained earnings and compute the year-end balance of retained earnings.

Solution: Eau Claire Paper Mill, Inc. Retained Earnings for 2017 Balance of retained earnings, April 1, 2016 Add: Net income, 2017

.

$ 323,325.00 713,445.00

Less: Dividends to common stockholders

(321,050.25)

Balance of retained earnings, March 31, 2017

$ 715,719.75

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LO: 3.4 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement 3.30 Menomonie Casino Company earned $23,458,933 before interest and taxes for the fiscal year ending March 31, 2017. If the casino had interest expenses of $1,645,123, calculate its tax obligation using Exhibit 3.6. What are the marginal and the average tax rates for this company?

Solution: EBIT

$23,458,933.00

Interest

1,645,123.00

EBT

Tax rate

$21,813,810.00 Tax

Income

15%

$0 to $50,000

25

50,001 − 75,000

6,250.00

34

75,001 − 100,000

8,500.00

39

100,001 − 335,000

91,650.00

34

335,001 − 10,000,000

3,286,100.00

35

10,000,001 − 15,000,000

1,750,000.00

38

15,000,001 − 18,333,333

1,266,666.54

35

More than $18,333,333

1,218,166.95

Total taxes payable

$7,634,833.49

$

Marginal tax rate

=

Average tax rate

=

35% Total taxes payable / Taxable income

=

$7,634,833.49 / $21,813,810

=

35%

7,500.00

LO: 3.8

.

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Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.31 Vanderheiden Hog Products Corp. provided the following financial information for the quarter ending June 30, 2017: Net income: $189,425 Depreciation and amortization: $63,114 Increase in receivables: $ 62,154 Increase in inventory: $57,338 Increase in accounts payables: $37,655 Decrease in other current assets: $27,450 What is this firm’s cash flow from operating activities during this quarter?

Solution: Vanderheiden Hog Products Corp.

Statement of Cash Flows (Partial) For the quarter ended on June 30, 2017 Operating Activities Net income

$189,425

Additions (sources of cash) Depreciation and amortization

63,114

Increase in accounts payable

37,655

Decrease in other current assets

27,450

Increase in accrued income taxes

0

Subtractions (uses of cash) Increase in receivable

(62,154)

Increase in inventories

(57,338) $198,152

Net cash provided by operating activities LO: 3.5 Bloomcode: Analysis

.

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AACSB: Analytic IMA: Reporting AICPA: Measurement

3.32 Cash flows: Analysts following the Tomkovick Golf Company were given the following balance sheet information for the years ended June 30, 2017 and June 30 2016: 2017

2016

$

$

Assets Cash and marketable securities

16,566

Accounts receivable

260,205

318,768

Inventory

423,819

352,740

Other current assets

41,251

29,912

Total current assets

$ 758,686

$ 717,986

Plant and equipment

1,931,719

1,609,898

Less: Accumulated depreciation

(419,044)

(206,678)

Net plant and equipment

$1,512,675

$1,403,220

Goodwill and other assets

382,145

412,565

Total assets

$2,653,506

$2,533,771

Liabilities and Equity

2017

2016

Accounts payable and accruals

$ 378,236

$ 332,004

Notes payable

14,487

7,862

Accrued income taxes

21,125

16,815

$ 413,848

$ 356,681

Long-term debt

679,981

793,515

Total liabilities

$1,093,829

$1,150,196

Preferred stock

__

__

Common stock (10,000 shares)

10,000

10,000

Additional paid-in capital

975,465

975,465

Retained earnings

587,546

398,110

Less: Treasury stock

(13,334)

__

Total common equity

$1,559,677

$1,383,575

Total liabilities and equity

$2,653,506

$2,533,771

Total current liabilities

.

33,411

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In addition, it was reported that the company had a net income of $ 3,155,848 and that depreciation expenses were equal to $212,366 during 2017. Assume amortization expense was $0 in 2017. a. Construct a 2014 cash flow statement for this firm. b. Calculate the net cash provided by operating activities for the statement of cash flows. c. What is the net cash used in investing activities? d. Compute the net cash provided by financing activities.

Solution: a.

Tomkovick Golf Company Statement of Cash FlowsYear Ended June 30, 2017 Operating Activities Net income

$ 3,155,848.00

Additions (sources of cash) Depreciation

212,366.00

Increase in accounts payable

46,232.00

Decrease in accounts receivable

58,563.00

Increase in accrued income taxes

4,310.00

Subtractions (uses of cash) Increase in other current assets

(11,339.00)

Increase in inventories

(71,079.00)

Net cash provided by operating activities

$ 3,394,901.00

Long-Term Investing Activities Increase in property equipment

$ (321,821.00)

Decrease in goodwill and other assets

30,420.00 $ (291,401.00)

Net cash used in investing activities Financing Activities Increase in notes payable

6,625.00

Decrease in long-term debt

(113,534.00)

Payment of cash dividends

(2,966,412.00)

Purchase of treasury stock

(13,334.00)

Net cash provided by financing activities

$(3,086.655.00)

Effect of exchange rates on cash

$

Net increase in cash and marketable securities

.

$

0.00 16,845.00

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Cash and marketable securities at beginning of

16,566.00

year Cash and marketable securities at end of year

$

33,411.00

b. $ 3,394,901.00 c. $ (291,401.00) d. $(3,086.655.00) LO: 3.5 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.33 Cash flows: Based on the financial statements for Tomkovick Golf Company in Problem 3.32, compute the cash flow invested in net working capital and the cash flow invested in long-term assets that you would use in a calculation of the cash flows to investors for 2017.

Solution: CFNWC = ($758,686 – $413,848) – ($717,986 – $356,681) = -$16,467 CFLTA = ($1,931,719 – $1,609,898) + ($382,145 - $412,565) = $291,401 LO: 3.7 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

Sample Test Problems 3.1

What is the matching principle, and how can it cause accounting expenses to differ from actual cash outflows?

Solution:

.

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The matching principle is an accounting principle under which accountants match revenues with the costs incurred to generate those revenues when they prepare an income statement. Because the actual cash flows associated with expenses might not be incurred in the same period that those expenses are recognized in the income statement, the accounting expenses can differ from actual cash outflows.

LO: 1 Level: Intermediate Bloomcode: Knowledge AACSB: Analytic IMA: Budget Preparation AICPA: Measurement

3.2

Wolf Pack Enterprises has total current assets of $346,002 and fixed assets of $476,306.

The company also has long-term debt of $276,400, $100,000 in its common stock account, and retained earnings of $187,567. What is the value of its total current liabilities?

Solution: Assets

Liabilities and Equity

Total current assets

$346,002

Total current liabilities

$???????

Fixed assets

$476,306

Long-term debt

$276,400

Common stock

$100,000

Retained earnings

$187,567

Liabilities and Total assets

$???????

stockholders’ equity

$???????

First, calculate total assets: $346,002 + $476,306 = $822,308 From Equation 3.1: $822,308 - $276,400 – 100,000 – 187,567 = $258,341 (total current liabilities) LO: 2 Level: Intermediate

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Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.3

What is the difference between a book-value balance sheet and a market-value balance sheet? Which provides better information to investors and management?

Solution: A book-value balance sheet is an accounting balance sheet in which asset values are listed at their historical cost. A market-value balance sheet reflects current asset values (what the assets are worth today). Market values provide better economic information for investors and managers than book values. Therefore, a market-value balance sheet provides better decision-making information.

LO: 3 Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Reporting

3.4

ACME Corporation had revenues of $867,030 in 2017. It also had expenses (excluding depreciation) of $356,240, depreciation of $103,456, and interest expense of $52,423.

What was the company’s net income after taxes if its average tax rate was 40 percent?

Solution: Amount

.

Revenues

$867,030.00

Expenses

356,240.00

EBITDA

$510,790.00

Depreciation

103,456.00

EBIT

$407,334.00

Interest

52,423.00

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EBT

$354,911.00

Taxes (40%)

141,964.40

Net income

$212,946.60

LO: 4 Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.5

True Blue Company increased its investments in marketable securities by $323,370 and paid $1,220,231 for new fixed assets during 2017. The company also repaid $779,200 of existing long-term debt while raising $913,455 of new debt capital. In addition, True Blue had a net cash inflow of $345,002 from the sale of fixed assets, and repurchased stock in the open markets for a total of $56,001. What is the net cash used in long term investing activities by True Blue? What is the net cash provided by the company’s financing activities?

Solution: Investing Activities Net property, equipment and other assets Net acquisitions and dispositions

$(1,220,231) 345,002

Investments in marketable securities Net cash used in investing activities

$(875,229)

Financing Activities Long-term debt repayment

$(779,200)

Increase in long-term debt

913,455

Purchase of treasury stock

(56,001)

Net cash provided by financing activities

$ 78,254

LO: 5 Level: Intermediate

.

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Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.6

Sun Devil Corporation reported EBITDA of $7,300,125 and net income of $3,328,950 for the fiscal year ended December 31, 2017. During the same period, the company had $1,155,378 in interest expense, $1,023,285 in depreciation and amortization expense, and an average corporate tax rate of 35 percent. What was the cash flow to investors from operating activity during 2017?

Solution: CFOA = EBIT – Current taxes + Noncash expenses CFOA = EBITDA – Current taxes CFOA = $7,300,125 – [0.35 × ($7,300,125 - $1,023,285 - $1,155,378)] = $5,507,613 LO: 7 Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

.

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Chapter 4 Analyzing Financial Statements Before You Go On Questions and Answers Section 4.1 1.

Why is it important to look at a firm’s historical financial statements?

When one does a ratio analysis on a firm, it is important to do the analysis over a three- to five-year period. Looking at the historical financial statements allows one to see the trends on the various ratios—whether they are improving, worsening, or staying the same.

2.

What is the primary concern of a firm’s creditors?

The creditors of a firm will want to know if the firm is generating enough cash flows to meet all of its required obligations, like employee wages and trade credit, and still has enough to meet the principal and interest payments due periodically. Their ultimate concern is being paid on time and being repaid in full.

Section 4.2 1.

Why does it make sense to standardize financial statements?

Standardized, or common-size, financial statements allow you to make meaningful comparisons of financial statements between two firms that are dramatically different in size. They also make interpretation of data much easier. Standardized or common-size financial statements are those that are prepared with numbers that have been compiled using a common measure of the firm’s size.

2.

What are common-size, or standardized, financial statements, and how are they prepared?

Typically, balance sheets are standardized by dividing each asset and liability by total assets (or total deposits in the case of banks) and expressing it as a percentage of total assets. For income statements the scaling factor is sales or revenue, thus expressing each item as a percentage of sales.

Section 4.3 1.

.

What are the efficiency ratios, and what do they measure? Why, for some firms, is the total asset turnover more important than the fixed asset turnover?

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Efficiency ratios (also called turnover ratios) measure how efficiently a firm uses its assets to generate sales. The following ratios were discussed: • Inventory turnover/days’ sales in inventory—calculated as cost of goods sold divided by inventory; it shows how many times the inventory of a firm is sold and replaced over a specific period.

• Accounts receivable turnover/days’ sales outstanding—computed as net sales divided by accounts receivable; it is a measure used to quantify a firm’s effectiveness in extending credit and success in collection of debts.

• Total asset turnover—calculated as net sales divided by total assets; it gives us the amount of sales generated for every dollar’s worth of assets.

• Fixed asset turnover—calculated by dividing sales by net fixed assets; it shows the amount of sales generated with each dollar of fixed assets.

The fixed asset turnover is not very useful for service-oriented firms with little plant or equipment. Instead, the total asset turnover is more relevant.

2.

List the leverage ratios discussed in this section, and explain how they are related.

Leverage ratios measure the extent to which a firm uses debt rather than equity financing and show the firm’s ability to meet its long-term financial obligations. The three leverage ratios discussed in this book are total debt ratio (plus its variations of debt-equity ratio and the equity multiplier), times interest earned, and cash coverage ratio. This is how all three ratios are linked together: the total debt ratio indicates what proportion of assets are financed from other sources than shareholders, and times interest earned measures how effectively the firm can meet the interest obligations on this financing based on operating earnings (EBIT). Cash coverage takes the analysis a step further, determining whether the firm has enough cash on hand to cover the interest payments.

3.

List the profitability ratios discussed in this section, and explain how they differ from each other.

The most commonly used profitability ratios are profit margin (gross profit margin, operating profit margin, and net profit margin), return on assets (ROA), and return on equity (ROE). The profit margin ratios examine the company’s profitability as a percentage of sales, whereas ROE and ROA help us analyze profitability as percentage of an investment, either in assets or in the firm’s equity. In other words, ROA tells us what earnings were generated from invested capital, and ROE indicates how well management is employing the investors’ capital invested in the company.

Section 4.4 1.

.

What is the purpose of the DuPont system of analysis?

The purpose of the DuPont system of analysis is to determine a company’s financial health. It breaks down ROE into three parts: profit margin, total asset turnover, and

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financial leverage (equity multiplier). If ROE is unsatisfactory, the DuPont identity helps locate which part of the business is underperforming.

2.

What is the equation for ROA in the DuPont system, and how do the factors in that equation influence the ratio?

ROA is calculated as net income divided by total assets. Modifying the equation by dividing both the numerator and denominator by net sales and rearranging the terms, we can rewrite the equation as: ROA= Net income/Net sales x Net sales/Total assets or ROA = Net profit margin x Total asset turnover Therefore, based on the above equation, we can conclude that ROA is a combination of the firm’s ability to efficiently manage its operating expenses (operating efficiency) and efficient asset management (asset use efficiency). In order for the management to increase ROA, it can increase either the profit margin or asset turnover, or both. The strategies that companies choose to pursue to increase their ROA depend on their business type and long-term goals.

3.

What are the three major shortcomings of ROE? The three major shortcomings of ROE are that it does not consider the size of the initial investment or the size of future cash payments, it ignores risk, and it does not directly consider the cash flow involved in the business decision-making process. However, despite the ratio’s drawbacks, it is a handy tool for measuring a company’s profitability and identifying industry leaders, as long as you know where the numbers are coming from.

Section 4.5 1.

In what three ways can a financial manager choose a benchmark?

A financial manager can choose a benchmark based on either of the following methods: trend analysis, industry average analysis, or peer group analysis. Trend analysis uses history as its standard by evaluating the firm’s performance against itself over time.

Industry average analysis compares the firm’s performance to the performance of sameindustry companies, and peer group analysis benchmarks the company’s performance to that of its competitors. Most of the time, a combination of all three methods is used when analyzing the company.

2.

Explain what the SIC codes are, and discuss the pros and cons of using them in financial analysis.

Standard Industrial Classification (SIC) codes are four-digit numbers that are used to categorize business activities. The first two digits determine the broad type of business,

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such as mining of metals, and then each additional digit narrows down the industry in greater detail. The advantage of using SIC codes in financial analysis is that the financial ratio data can be segmented into six size categories by asset size or by sales, which allows for more meaningful comparisons of like firms. The main drawback to using SIC codes is that companies with similar business lines, but not necessarily similar target markets, often have the same SIC codes (for example, Neiman Marcus and Wal-Mart). Therefore, using SIC codes as a basis for financial analysis requires more thought than just relying on the classification numbers.

Section 4.6 1.

Explain how the DuPont identity allows us to evaluate a firm’s performance.

The DuPont identity, which leads to the measurement of a firm’s return on equity (ROE), allows one to break down the measure into three areas of performance. First, a firm’s operational efficiency is measured by the net profit margin; second, the firm’s efficiency in managing its assets is reflected in its asset turnover ratio; and finally, the impact of financial leverage is shown by the equity multiplier. One is then able to pinpoint areas of strengths and weaknesses by breaking down these measures, which are tied to either the balance sheet or the income statement.

2.

What are the limitations on traditional financial statement analysis?

The main problems with financial statement analysis are that since it is based on book values (historical data), it may not reflect a firm’s true economic condition, and there is a lack of economic underpinning for much of the decision rules. It is difficult to say a current ratio of 2.2 is good or that one ratio is more important than another.

3.

List some of the problems that financial analysts confront when analyzing financial statements.

Some of the problems that financial analysts run into when analyzing financial statements are: • Multiple business lines • Inflation adjustments • Globalization • Seasonality • Different accounting principles Therefore, a good analyst does not simply look at the numbers provided in the financial statements, but instead adjusts these numbers for all of the above factors to provide a meaningful and value-added analysis.

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Self Study Problems 4.1

The Abercrombie Supply Company reported the following information for 2017. Prepare a common-size income statement for the year ended June 30, 2017.

Abercrombie Supply Company Income Statement for the Fiscal Year Ended June 30, 2017 ($ thousands)

Earnings before interest, taxes, depreciation, and amortization (EBITDA)

$2,110,965 1,459,455 312,044 27,215 $ 312,251

Depreciation Earnings before interest and taxes (EBIT) Interest expense Earnings before taxes (EBT) Taxes (35%) Net income

112,178 $ 200,073 117,587 $ 82,486 28,870 $ 53,616

Net sales Cost of goods sold Selling and administrative expenses Nonrecurring expenses

Solution: The common-size income statement for Abercrombie Supply Company should look like the following one: Abercrombie Supply Company Income Statement for the Fiscal Year Ended June 30, 2017 ($ thousands)

Net sales Cost of goods sold Selling and administrative expenses Nonrecurring expenses Earnings before interest, taxes, depreciation and amortization (EBITDA) Depreciation Earnings before interest and taxes (EBIT) Interest expense Earnings before taxes (EBT) Taxes (35%) Net income

.

% of Net Sales $2,110,965 100.0 1,459,455 69.1 312,044 14.8 27,215 1.3 $ 312,251 112,178 $ 200,073 117,587 $ 82,486 28,870 $ 53,616

14.8 5.3 9.5 5.6 3.9 1.4 2.5

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LO: 2 Level: Basic

4.2

Prepare a common-size balance sheet from the following information for Abercrombie Supply Company.

Assets: Cash and marketable securities Accounts receivable Inventory Other current assets Total current assets Net plant and equipment

Total assets

Solution:

Abercrombie Supply Company Balance Sheet as of June 30, 2017 ($ thousands) Liabilities and Equity: $ 396,494 Accounts payable 708,275 Notes payable 1,152,398 Accrued income taxes 42,115 $2,299,282 Total current liabilities 1,978,455 Long-term debt

$4,277,737

$ 817,845 101,229 41,322 $ 960,396 1,149,520 $2,109,916 1,312,137 855,684 $2,167,821 $4,277,737

Total liabilities Common stock Retained earnings Total common equity Total liabilities and equity

Abercrombie Supply Company Balance Sheet as of June 30, 2017 ($ thousands)

Assets Cash and marketable sec.

Accounts receivable Inventory Other current assets Total current assets Net plant and equipment

$ 396,494 708,275 1,152,398 42,115 $2,299,282 1,978,455

% of Assets 9.3 16.5 26.9 1.0 53.7 46.3

Total assets

$4,277,737

100.0

Liabilities and Equity: Accounts payable and accruals Notes payable Accrued income taxes Total current liabilities Long-term debt Total liabilities Common stock Retained earnings Total common equity Total liabilities and equity

$ 817,845 101,229 41,322

% of Assets 19.1 2.4 1.0

$ 960,396

22.5

1,149,520 $2,109,916 1,312,137 855,684 $2,167,821 $4,277,737

26.9 49.3 30.7 20.0 50.7 100.0

LO: 2 Level: Basic

4.3

.

Using the 2017 data above for Abercrombie Supply Company calculate the following liquidity ratios: a.

Current ratio b.

Quick ratio

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Solution: a.

$2,299,282 Current ratio = $960,396 =2.39

b.

Quick ratio =

$2,299,282-$1,152,398 = 1.19 $960,396

LO: 3 Level: Basic

4.4

Refer above to the balance sheet and income statement for Abercrombie Supply Company for the year ended June 30, 2017. Calculate the following ratios: a.

Inventory turnover b.

Days’ sales outstanding c.

Total asset turnover d.

Fixed asset turnover e.

Total debt ratio f.

Debt-to-equity ratio g.

Times interest earned h.

Cash coverage

Solution: Ratio Inventory turnover Days’ sales outstanding Total asset turnover Fixed asset turnover Total debt ratio Debt-to-equity ratio Times interest earned Cash coverage LO: 3 Level: Basic

4.5

.

Calculation $1,459,455 / $1,152,398 / $708,275 ($2,110,965/365) $2,110,965 / $4,277,737 $2,110,965 / $1,978,455 $2,109,916 / $4,277,737 $2,109,916 / $2,167,821 $117,587 / $200,073 $312,251 / $117,587

Value 1.27 122.5 days 0.49 1.07 0.493 0.974 1.7 2.66

Last year ABC companies had accounts receivable turnover of 15, total asset turnover of 4.5, and total assets of $1,000,000. What was the value of ABC’s accounts receivable?

What was the value of its net sales?

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Solution: In this problem we can use the accounts receivable turnover equation (Equation 4.5) and total asset turnover equation (Equation 4.7) to solve for the values of accounts receivable and net sales.

Net sales Accounts receivable turnover = Accounts receivable Total asset turnover=

Net sales Total assets

Dividing accounts receivable turnover by total asset turnover yields: Netsales Netsales Total assets / = Accountsreceivable Accountsreceivable Totalassets 15 = 4.5 = 3.333 With total assets of $1,000,000, accounts must receivable equal: Total assets Accounts receivable= 3.3333 $1,000,000 = 3.3333

= $300, 000 From the total asset turnover equation, net sales equal: Net sales Total asset turnover= Total assets 4.5 Net sales

=

Net sales

$1,000,000 =(4.5)($1,000,000)=$4,500,000

LO: 3 Level: Basic 4.6

The equity multiplier for Spiffy Corporation is 1.75, its EBIT return on assets (EROA) is 0.07, and the value of its equity is $850,000. What is the value of Spiffy’s total assets?

What is the value of its EBIT? Solution: In this problem we can use the Equity multiplier equation (Equation 4.11) and the EROA equation (Equation 4.17) to solve for the values of total assets and EBIT.

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Total assets Equity multiplier= Total equity EBIT EROA= Total assets First use the equity multiplier equation to solve for total assets: Total assets Equity multiplier= Total equity Total assets 1.75 = $850,000 Totalassets

=1.75  $850,000

=$1,487,500 Next, use the EROA equation to solve for EBIT: EBIT EROA= Total assets EBIT $1,487,500 EBIT = 0.07×$1,487,500 = $104,125 LO: 3 Level: Basic 0.07

=

Discussion Questions 4.1

What does it mean when a company’s return on assets (ROA) is equal to its return on equity (ROE)?

When ROA equals ROE, it means that the firm does not use any leverage (debt financing). For firms that do use leverage, ROE will be higher than ROA.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.2

Why is too much liquidity not a good thing?

Too much liquidity could mean that a firm is not putting its money to work as the shareholders would want it to. It could mean that the firm’s managers are being too conservative and investing in low-yield assets, or it could mean that the firm does not

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have enough investment opportunities and is therefore hanging onto its cash. Recently, several firms including Microsoft had several billions of dollars in cash on their books, and, ultimately, Microsoft paid a special dividend to its shareholders. Too much liquidity can also make it a takeover target for firms looking to utilize the debt capacity of the liquid firm.

LO: 3 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement 4.3

Inventory is excluded when the quick ratio or acid-test ratio is calculated because inventory is the most difficult current asset to convert to cash without loss of value.

What types of inventory are likely to be most easily converted to cash without loss of value?

For the quick ratio, one uses only the most liquid of all assets—that is, all current assets less inventory, which is not very liquid relative to cash or receivables. While the current ratio assumes that inventory could be sold at book value, the quick ratio assumes that inventory has no value. Hence, this gives a more conservative estimate of a firm’s liquidity than the current ratio, and gives a better estimate of the firm’s ability to meet its short-term obligations. Inventories of a raw material commodity, such as gold or crude oil, is more likely to be sold with little loss in value.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement 4.4

What does a very high inventory turnover ratio signify?

This could mean a number of things, including that the firm is using up its inventory too fast and is unable to meet the demand for its products, or it has priced its products too low relative to its competitors, or worse, the firm is selling defective products that would eventually be returned.

LO: 3 Level: Basic

4.5

.

How would one explain a low receivables turnover ratio?

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A low receivables turnover implies a high DSO. This could mean that the firm’s customers are not paying on time, either because of an inefficient collection system or because of a slowdown in their customers’ business or even in the entire economy.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement 4.6

What additional information does the fixed asset turnover ratio provide over the total asset turnover ratio? For which industries does it carry greater significance?

The total asset turnover ratio measures the level of sales per dollar invested in total assets.

The higher the number, the more efficiently the management is using the firm’s assets.

Too high a number relative to its peers could imply that the firm is reaching its full capacity and may require an additional investment in plant and equipment to generate additional sales. The fixed asset turnover ratio can be utilized to break down the performance of individual manufacturing facilities or a division. This ratio provides significant information for manufacturing firms that are capital-intensive, while it will be of much less significance for the service industry, where there is less reliance on plant and equipment.

LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.7

How does financial leverage help stockholders?

Financial leverage implies the use of debt capital in addition to the owners’ capital to finance the firm. With the addition of debt, the owners’ capital can go a long way in acquiring assets for the firm. Given that creditors only get the fixed-interest payments and do not get any share of the gains from the company, the stockholders gain from the usage of debt. This is called the leverage multiplier effect. As the company’s revenues grow, stockholders get all the gain and the debt holders merely receive their interest payments.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

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4.8

Solutions Manual

Why is ROE generally much higher than ROA for banks relative to other industries?

Banks have a very small equity base relative to firms in most other industries. Thus, they are highly leveraged with borrowed funds. Since their equity base is small, this magnifies the return on equity, but the return on assets is relatively small for the large asset base.

LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.9

Why is the ROE a more appropriate proxy (for stockholder value maximization) for some firms than for other firms?

The basis on which any business or investment decisions are evaluated must include the size, timing, and uncertainty in the future cash flows. ROE considers neither the risk of the cash flows nor the size of the initial investment or future cash flows from that investment. While the ROE and shareholder wealth are correlated, this is still a problem in large, well-diversified companies with resources from multiple sources. Smaller firms have fewer resources and sources and can better correlate their ROE to shareholder wealth.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.10 Why is it not enough for an analyst to look at just the short-term and long-term debt on a firm’s balance sheet when assessing the firm’s fixed obligations?

The amount of liabilities shown on a firm’s balance sheet is not the total obligation of a firm in any given period. To get a true picture, one needs to look at the financial footnotes that follow the financial statements. This is where you will be able to find the amount of debt repayment that the firm is responsible for in the coming years. In addition, off-balance sheet items could reflect certain future liabilities of the firm that do not have to be reported on the balance sheet. One also should look for lease obligations of the firm that are reported off the balance sheet but nevertheless remain a fixed obligation

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that the firm has to meet with its cash flows. Thus, it is important for an analyst to look beyond the short-term and long-term debt on the balance sheet to get a true measure of the firm’s financial commitments in any given period.

LO: 3, 5 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

Questions and Problems BASIC 4.1

Liquidity ratios: Explain why the quick ratio or acid-test ratio is a better measure of a firm’s liquidity than the current ratio.

Solution: The quick ratio is a better or more conservative measure of liquidity than the current ratio.

The difference in the measurement of the two is that for the quick ratio we exclude the inventory in accounting of the short-term assets. Thus the quick ratio is measured as: Current assets−Inventory Quick ratio= Current liabilities This measure includes only the most liquid of the current assets and hence gives a better measure of liquidity.

LO: 4.3 Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

Liquidity ratios : Flying Penguins Corp. has total current assets of $11,845,175, current liabilities of $5,311,020, and a quick ratio of 0.89. How much inventory does it have?

Solution: Current assets = $11,845,175 4.2

Current liabilities = $5,311,020 Quick ratio = 0.89

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Quick ratio=

Current assets−Inventory Current liabilities

0.89=

$11,845,175 − Inventory $5,311,020

0.89 ×$5,311,020=$11,845,175−Inventory Inventory=$11,845,175−(0.89×$5,311,020) = $𝟕,𝟏𝟏𝟖,𝟑𝟔𝟕

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.3

Efficiency ratio: If Newton Manufacturers has an accounts receivable turnover of 4.8 times and net sales of $7,812,379, what would its receivables be?

Solution: Accounts receivable turnover = 4.8 times Net sales = $7,812,379 Net sales Accounts receivable turnover= Accounts receivable 7,812,379 4.8= Accounts receivable Accounts receivable=

7,812,379 =$𝟏,𝟔𝟐𝟕,𝟓𝟕𝟗 4.8

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Efficiency ratio: Bummel and Strand Corp. has a gross profit margin of 33.7 percent, sales of $47,112,365, and inventory of $14,595,435. What is its inventory turnover ratio?

Solution: Gross profit margin = 33.7% 4.4

Sales = $ 47,112,365 Inventory = $14,595,435

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0.337=

Gross Profit Margin= $47,112,365−𝐶𝑂𝐺𝑆 $47,112,365

Solutions Manual Net sales−Cost of goods sold Net sales

Cost of goods sold = $47,112,365 – (0.337 ×

$47,112,365) = $31,235,498 Inventory Turnover Ratio =

Cost of goods sold Inventory

Inventory Turnover Ratio =

31,235,498 =𝟐.𝟏𝟒 𝐭𝐢𝐦𝐞𝐬 14,595,435

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.5

Efficiency ratio: Sorenson Inc. has sales of $3,112,489, a gross profit margin of 23.1 percent, and inventory of $833,145. What are the company’s inventory turnover ratio and days’ sales in inventory?

Solution: Sales = $3,112,489 Gross profit margin = 23.1% Inventory = $833,145

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Gross profit margin = 0.231=

Solutions Manual

Net Sales-Cost of goods sold Sales 3,112,489−Cost of Goods Sold 3,112,489

Cost of goods sold = 3,112, 489 − (0.231 3,112, 489) = $2, 393, 504

Inventory turnover ratio =

Cost of goods sold $2, 393, 504 = $833, 145 Inventory

= 2.873 times

Day's sales in inventory = =

365 365 = Inventory turnover ratio 2.873 127.1 days

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.6

Leverage ratios: Breckenridge Ski Company has total assets of $422,235,811 and a debt ratio of 29.5 percent. Calculate the company’s debt-to-equity ratio and equity multiplier.

Solution: Total assets = $422,235,811 Debt ratio = 29.5% Total debt = $422,235,811 ×0.295 =$124,559,564 Total equity =Total assets−Total debt =$422,235,811−$124,559,564=$297,676,247 $124,559,564 =𝟎.𝟒𝟐 $297,676,247 Total assets $422,235,811 Equity multiplier = Total equity = $297,676,247=𝟏.𝟒𝟐 Debt to equity ratio =

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LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.7

Leverage ratios: Norton Company has a debt-to-equity ratio of 1.65, ROA of 11.3

percent, and total equity of $1,322,796. What are the company’s equity multiplier, debt ratio, and ROE? Solution: Debt-equity ratio = 1.65 ROA = 11.3% Total equity = $1,322,796 Equity multiplier = 1 +Debt to equity ratio=1+1.65 = 2.65 Total assets Total equity Total assets = Equity multiplier Total equity = 2.65 $1,322,796 = $3,505,409

Equity multiplier =

Net income ROA= Total assets Net income=ROA  Total assets = 0.1133,505,409 = $396,111 ROE=

Net income $396,111 = =29.9% Equity $1,322,796

  1 Equity Debt ratio = 1 - Total assets =1−  Equity multiplier   1 =1 − = 0.623 2.65 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

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4.8

DuPont Equation: The Rangoon Timber Company has the following ratios: Net sales/Total assets = 2.23; ROA = 9.69%; ROE = 16.4% What are Rangoon’s profit margin and debt ratios?

Solution: Total assets turnover = 2.23 ROA = 9.69% ROE = 16.4% ROA = Net profit margin × Total assets turnover ROA 0.0969 = =0.04345 Profit margin = Total assets turnover 2.23 = 4.35%

ROE = ROA x Equity multiplier ROE 0.1 6 4 Equity multiplier = ROA = = 1.69 0.0969 1 Equity = 1 −Equity multiplier Debt ratio = 1 − Total assets 1 =1− =0.41 1.69 LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.9

DuPont Equation: Lemmon Enterprises has a total asset turnover of 2.1 and a net profit

margin of 7.5%. If its equity multiplier is 1.90, what is the ROE for Lemmon Enterprises?

Solution: Total asset turnover = 2.1 Net profit margin = 7.5% Equity multiplier = 1.90 ROE = ROA × Equity multiplier ROA = Net profit margin × Total asset turnover = 7.5% × 2.1 = 15.75% ROE = 15.75% × 1.9 = 29.93% LO: 4.4

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Benchmark analysis: List the ways a company’s financial manager can benchmark the company’s own performance.

Solution: Financial managers can benchmark their firm’s performance by collecting data in three ways: through trend analysis, industry average analysis, and peer group analysis.

LO: 4.5 Bloomcode: Knowledge AASCB: Analytic IMA: FSA AICPA: Measurement 4.10

4.11 Benchmark analysis: Trademark Corp.’s financial manager collected the following information for its peer group to compare its performance against that of its peers.

Ratios Trademark Peer Group DSO 33.5 days 27.9 days Total asset turnover 2.3 3.7 Inventory turnover 1.8 2.8 Quick ratio 0.6 1.3 a. Explain how Trademark is performing relative to its peers. b How do the industry ratios help Trademark’s management? .

Solution: a.

One can see that Trademark is not doing as well as its competitors. The asset turnover ratio indicates that the firm either needs to increase its sales relative to its level of assets or reduce its assets relative to its level of sales. In addition, the lower quick ratio indicates a lower level of liquidity, perhaps because of too much inventory. A reduction in the inventory would help Trademark improve its performance to a level that is comparable to its peer group. In addition, collection of receivables is longer, which could result in cash flow problems and nonpayments. b.

Average industry ratios serve as benchmarks for the firm’s management to measure its own performance. While no two firms are identical in any industry, the average ratios across the industry are good target ratios for a firm.

LO: 4.5

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Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.12 Market-value ratios: Rockwell Jewelers management announced that the company had net earnings of $6,481,778 for this year. The company has 2,543,800 shares outstanding, and the year-end stock price is $54.21. What are Rockwell’s earnings per share and P/E ratio?

Solution: Net earnings = $6,481,778 Shares outstanding = 2,543,800 Year-end stock price = $54.21 Net earnings $6,481,778 Earnings per share = EPS = Shares outstanding = 2,543,800 = $2.55 $54.21 Price per share Price-earnings ratio = Earnings per share = $2.55

= 21.26 times LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.13 Market-value ratios: Chisel Corporation has 3 million shares outstanding at a price per share of $3.25. If the debt-to-equity ratio is 1.7 and total book value of debt equals $12,400,000, what is the market-to-book ratio for Chisel Corporation?

Solution: Shares outstanding = 3,000,000 Market price per share = $3.25 Debt-to-Equity ratio = 1.7 Total book value of debts = $12,400,000 Market value of equity = 3,000,000 × $3.25 = $9,750,000

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Book value of equity =

Solutions Manual

$12,400,000 1.7

= $7,294,117.65 Market-to-book ratio =

$9,750,000 $7,294,117.65 =1.34

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

INTERMEDIATE 4.14 Liquidity ratios : Laurel Electronics has a quick ratio of 1.15, current liabilities of $5,311,020, and inventories of $7,121,599. What is the firm’s current ratio?

Solution: Quick ratio = 1.15 Current liabilities = $5,311,020 Inventory = $7,121,599 Current asset - Inventory Current assets - $7,121,599 = Quick ratio = Current liabilities $5,311,020

= 1.15 =

Current

Current asset - $7,121,599

$5,311,020 = (1.15  $5, 311, 020) + $7,121, 599 assets

Current assets = $13,229,272 Current ratio=

Current assets $13,229,272 Current liabilities= $5,311,020 =𝟐.𝟒𝟗

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

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4.15 Efficiency Ratio: Lambda Corporation has current liabilities of $450,000, a quick ratio of 1.8, inventory turnover of 5.0, and a current ratio of 3.5. What is the cost of goods sold for Lambda Corporation?

Solution: Current Liabilities = $450,000 Quick Ratio = 1.8 Inventory Turnover ratio = 5.0 Current ratio = 3.5 Current assets = 3.5 × $450,000 = $1,575,000 Current assets - Inventory Quick ratio = Current liabilities

1.8 =

$1, 575, 000 − Inventory $450, 000

Inventory = $765,000 Inventory Turnover =

Cost of goods sold Inventory

Cost of goods sold = 5.0$765,000 = $3, 825, 000 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.16 Efficiency ratio: Norwood Corp. currently has accounts receivable of $1,223,675 on net sales of $6,216,900. What are its accounts receivable turnover and days’ sales outstanding (DSO)?

Solution: Accounts receivable = $1,223,675 Net sales = $6,216,900 Net sales Accounts receivables turnover= Accounts receivables=

.

$6,216,900 $1,223,675 ⬚ = 𝟓.𝟎𝟖 𝐭𝐢𝐦𝐞𝐬

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DSO=

Solutions Manual

365 365 = 71.8 days Accounts receivable turnover = 5.08

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.17 Efficiency ratio: If Norwood Corp.’s management wants to reduce the DSO from that calculated in Problem 4.16 to an industry average of 56.3 days and its net sales are expected to decline by about 12 percent, what would be the new level of receivables?

Solution: Target DSO = 56.3 days New level of sales = $6,216,900 x 0.88 = $5,470,872 365 DSO= 56.3 Days= Net sales/Accounts receivable Accounts receivable =

DSO  Net sales

365 56.3  $5, 470, 872 = 365 = $843, 863

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.18 Coverage ratios: Nimitz Rental Company had depreciation expenses of $108,905, interest expenses of $78,112, and an EBIT of $1,254,338 for the year ended June 30, 2017. What are the times interest earned and cash coverage ratios for this company?

Solution: Depreciation = $108,905 Interest expenses = $78,112 EBIT = $1,254,338

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EBIT $1,254,338 Times interest earned = Interest expense= $78,112 = 16.1 times EBIT + Depreciation EBITDA = Cash coverage ratio = Interest expense Interest expense

$1,363,243 $78,112

=

= 17.5 times

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.19 Leverage ratios: Conseco, Inc., has a debt ratio of 0.56. What are the company’s debt-toequity ratio and equity multiplier?

Solution: Debt ratio = 0.56 Total Equity multiplier= assets Total equity

=

1 1−Debt/Total assets

=

1 = Total equity/Total Assets 1

1−0.56

=2.27 Equity multiplier = 1 + (Debt to equity ratio) Debt-to-equity ratio = Equity multiplier-1 =2.27-1 = 1.27 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

.

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4.20 Profitability ratios: Cisco Systems has total assets of $35.594 billion, total debt of $9.678 billion, and net sales of $22.045 billion. Its net profit margin for the year is 20 percent, while the operating profit margin is 30 percent. What are Cisco’s net income, EBIT ROA, ROA, and ROE? Solution: Total assets = $35.594 billion Total debt = $9.678 billion Net sales = $22.045 billion Net profit margin = 20% Operating profit margin = 30% Net income Net profit margin = Sales

Net income = 0.2  $22.045 billion = $4.409 billion Operating profit margin= EBIT Sales EBIT = 0.3 × $22.045billion =$6.614 billion $6.613 EBIT = $35.594 =18.6% Total assets $4.409 Net income = =12.4% ROA = Total assets $35.594 Total equity = Total assets – Total debt = $35.594 - $9.678 = $25.916 billion Total assets $3 5.5 9 4 Equity multiplier = Total equity = $25.916 =1.37 EBIT ROA =

ROE = ROA  EM = 0.124  1.37 = 17%

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

.

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Solutions Manual

4.21 Profitability ratios: Procter & Gamble reported the following information for its fiscal year end: On net sales of $51.407 billion, the company earned net income after taxes of $6.481 billion. It had cost of goods sold of $25.076 billion and EBIT of $9.827 billion. What are the company’s gross profit margin, operating profit margin, and net profit margin?

Solution: Net sales = $51.407 billion Net income = $6.481 billion Cost of goods sold = $25.076 billion EBIT = $9.827 billion Net sales - Cost of goods sold Gross profit margin = Net sales $51.407−$25.076 =51.2% = $5 1.4 0 7 EBIT $9.827 Operating profit margin= = $51.407 =19.1% Net sales Net profit margin= Net income = $6.481 =12.6% Net sales $51.407 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.22 Profitability ratios: Wal-Mart, Inc., has net income of $9,054,000 on net sales of $256,329,812. The company has total assets of $104,912,112 and stockholders’ equity of $43,623,445. Use the extended DuPont identity to find the return on assets and return on equity for the firm.

Solution: Net income = $9,054,000 Net sales = $256,329,812 Total assets = $104,912,112 Stockholders equity = $43,623,445 Net income $9,054,000 Profit margin= Net sales = $256,329,812=3.53% Total assets turnover =

.

Net sales Total assets

=

$256,329,812 $104,912,112

=2.44 times

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Solutions Manual

Return on assets = Profit marginTotal assets turnover = 0.03532.44 = 8.61% ROE = ROA  EM = 0.0861 

Total assets Total equity

= 0.0861 

$104, 912,112 $43,623,445

= 20.71% LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.23 Profitability ratios: Xtreme Sports Innovations has disclosed the following information: EBIT = $25,664,300 Net income = $13,054,000 Net sales = $83,125,336 Total debt = $20,885,753 Total assets = $71,244,863 Compute the following ratios for this firm using the DuPont Identity: debt-to-equity ratio, EBIT ROA, ROA, and ROE. Solution: EBIT = $25,664,300 Net income = $13,054,000 Net sales = $83,125,336 Total debt = $20,885,753 Total assets = $71, 244,863 Debt Debt = (Total assets−Total debt) Equity $20,885,753 =𝟎.𝟒𝟏 = ($71,244,863 − $20,885,753 Equity multiplier=1+Debt to equity ratio =1+0.41 =𝟏.𝟒𝟏 Debt to equity ratio =

EBIT $25,664,300 = Total assets $71,244,863 = 36.02%

EBIT ROA =

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Solutions Manual

Net income $13,054,000 = Total $71,244,863 = 18.32% assets ROE = ROA  EM

ROA =

= 0.18321.41 = 25.83% LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.24 Market-value ratios: Cisco Systems had net income of $4.401 billion and at year end 6.735 billion shares outstanding. Calculate the earnings per share for the company.

Solution: Net income = $4.401 billion Shares outstanding = 6.735 billion Net income $4.401 Earnings per share= Shares outstanding= 6.735 =$𝟎.𝟔𝟓 𝐩𝐞𝐫 𝐬𝐡𝐚𝐫𝐞 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.25 Market-value ratios: Use the information for Cisco Systems in Problem 4.24. In addition, the company’s EBITDA was $6.834 billion and its share price was $22.36.

Compute the firm’s price-earnings ratio and the price-EBITDA ratio.

Solution: EBITDA = $6.834 billion Share price = $22.36 Price -earnings ratio= $22.36 =34.4 times $0.6 5 $6.834 EBITDA per share= 6.735 =$1.015 per share

.

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Fundamentals of Corporate Finance, 4th Edition

Price − EBITDA ratio =

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Solutions Manual

$22.3 =22.03 times 6 $1.0 15

4.26 DuPont equation: Carter, Inc., a manufacturer of electrical supplies, has an ROE of 23.1 percent, a profit margin of 4.9 percent, and a total asset turnover ratio of 2.6 times. Its peer group also has an ROE of 23.1 percent, but has outperformed Carter with a net profit margin of 5.3 percent and a total asset turnover ratio of 3.0 times. Explain how Carter managed to achieve the same level of profitability as reflected by the ROE. Solution: Carter Inc: ROE = 23.1%, PM = 4.9%, TATO = 2.6 times  ROA = PM TATO = 0.049 2.6 = 0.1274 ROE =0.231= ROA EM

EM=

0.2 3 1 =1.81 times 0.1274

Peer Group: ROE = 23.1%, PM = 5.3%, TATO = 3 times =  PM=TATOEM ROE 0.231

0.2 3 1 = 1.45 times 0.053 3 Carter matched its peer group’s ROE by using a higher degree of financial leverage as indicated by its higher equity multiplier.

LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement EM =

4.27 DuPont equation: Grossman Enterprises has an equity multiplier of 2.6 times, total assets of $2,312,000, an ROE of 14.8 percent, and a total asset turnover ratio of 2.8 times.

Calculate the firm’s sales and ROA.

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Solutions Manual

Solution: EM = 2.6 times, TA = $2,312,000, ROE = 14.8%, TATO = 2.8 times

Sal es Total assets Sal es 2.8= $2,312,000 Sal es= 2.8  $2,312,000= $6,473,600

Total asset turnover =

ROE=ROA ×EM ROE ROA= EM 0.148 = 2.6 =0.0569 =𝟓.𝟔𝟗% LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

ADVANCED 4.28 Complete the balance sheet of Flying Roos Corporation.

Flying Roos Corporation Balance Sheet as of December 31, 2017 Assets: Cash and marketable securities Accounts receivable Inventory

Liabilities and Equity: Accounts payable and accruals Notes payable Total current liabilities

$ 300,000

Total current assets Net plant and equipment Total assets

$8,000,000

Long-term debt

$2,000,000

Common stock Retained earnings Total liabilities and equity

$1,250,000

You have the following information: Debt ratio = 40% Current ratio = 1.5 Net sales = $2.25 million DSO = 39 days Inventory turnover ratio = 3.375 Cost of goods sold = $1.6875 million

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Solution: Total debt = 0.4 Total assets 0.4  $8,000,000 = $3,200,000 = Accounts payable = Total debt - (Long term debt + Notes payable)

= $3,200,000 - (2,000,000 + 300,000) = $900,000 Cost of goods sold Inventory turnover ratio = Inventory Cost of goods sold $1,687,500 = ITO 3.375 = $500,000 Accounts receivable DSO= Sales/365 Inventory =

Accounts receivable = DSO 

Sales 39 2, 250, 000 365 = 365

= $240, 411  Current assets = Current ratio Current liabilities = 1.5  $1,200,000 = $1,800,000 Net plant and equipment (Fixed assets) = Total assets – Total Current assets = $8,000,000 - $1,800,000 = $6,200,000 Cash = Current assets – (Accounts receivable + Inventory) = $1,800,000 – ($240,411 + $500,000) = $1,059,589 Common stock = Total liabilities and Equity – (Total liabilities + Retained earnings) = $8,000,000 – ($3,200,000 + $1,250,000) = $3,550,000

Flying Roos Corporation Balance Sheet as of December 31, 2017 Assets Cash and marketable securities Accounts receivable Inventories Total current assets

$1,059,589 240,411 500,000 $1,800,000

Net plant and equipment

6,200,000

Total assets

$8,000,000

Liabilities and Equity Accounts payable Notes payable Total current liabilities Long-term debt Common stock Retained earnings Total liabilities and equity

$ 900,000 300,000 $1,200,000 2,000,000 3,550,000 1,250,000 $8,000,000

LO: 4.3

.

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.29 For the year ended June 30, 2017, Northern Clothing Company has total assets of $87,631,181, ROA of 11.67 percent, ROE of 21.19 percent, and a net profit margin of 11.59 percent. What are the company’s net income and net sales? Calculate the firm’s debt-to-equity ratio.

Solution: Total assets = $87,631,181 ROA = 11.67%, ROE = 21.19%, PM = 11.59% NI = ROA  TA

= 0.1167  87, 631,181 = $10, 226, 559 Net sales =

Net income

=

$10,226,559

Profit margin 0.1159 Total equity = NI/ROE = $10, 226, 559 / 0.2119 = $48, 261, 251 Total debt = Total assets - Total equity

=$88,236,057

= $87,631,181 - $48,261,251 = $39,369,931

Debt $39,369,931 Debt to equity ratio = Equity = $48,261,251 = 81.6% LO: 4.3, 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.30 Blackwell Automotive’s balance sheet at the end of its most recent fiscal year shows the following information: Blackwell Automotive Balance Sheet as of March 31, 2017

.

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Assets: Cash and marketable sec.

Accounts receivable Inventory Total current assets

$

23,015 141,258 212,444 $ 376,717

Solutions Manual

Liabilities and Equity: Accounts payable and accruals Notes payable Total current liabilities

$ 163,257 21,115 $ 184,372

Long-term debt 168,022 Net plant and equipment 711,256 Total liabilities $ 352,394 Common stock Goodwill and other assets 89,879 313,299 Retained earnings 512,159 Total assets $1,177,852 Total liabilities and equity $1,177,852 In addition, it was reported that the firm had a net income of $156,042 on net sales of $4,063,589.

What are the firm’s current ratio and quick ratio? a.

Calculate the firm’s days’ sales outstanding, total asset turnover ratio, and fixed b. asset turnover ratio.

Solution: a.

Current assets $376, 717 Current ratio = Current liabilities = $184,372 = 2.04 times Current assets− Inventory $376, 717 − $212, 444 = Quick ratio = $184,372 Current liabilities

b.

= 0.89 times 365 365 DSO= Accounts receivable turnover = Net sales/Accounts receivable

=

365Accounts receivable 365  $141, 258 = Net sales $4, 063, 589

= 12.69 days

$4,063,589 Net sales Total asset turnover = Total assets = $1,177,852 = 3.45 times Net sales $4, 063, 589 Fixed asset turnover = Net fixed assets = $711,256 = 5.71 times LO: 4.3

.

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.31 The following are the financial statements for Nederland Consumer Products Company for the fiscal year ended September 30, 2017.

Nederland Consumer Products Company Income Statement for the Fiscal Year Ended September 30, 2017

Net sales Cost of products sold Gross profit Marketing, research, administrative exp.

Depreciation Operating income (loss) Interest expense Earnings (loss) before income taxes Income taxes Net earnings (loss)

$51,407 25,076 $26,331 15,746 758 $ 9,827 477 $ 9,350 2,869 $ 6,481

Nederland Consumer Products Company Balance Sheet as of September 30, 2017 Assets: Cash and marketable securities Investment securities Accounts receivable Inventory Deferred income taxes Prepaid expenses & other receivables Total current assets Property, plant, and equip., at cost Less: Accumulated depreciation Net property, plant, and equipment Net goodwill and other intangible assets Other noncurrent assets Total assets

$ 5,469 423 4,062 4,400 958 1,803 $17,115 25,304 11,196 $14,108 23,900 1,925 $57,048

Liabilities and Equity: Accounts payable Accrued and other liabilities Taxes payable Debt due within one year Total current liabilities Long-term debt Deferred income taxes Other noncurrent liabilities Total liabilities Convertible Class A preferred stock Common stock

$ 3,617 7,689 2,554 8,287 $22,147 12,554 2,261 2,808 $39,770 1,526 2,141

Retained earnings

13,611

Total stockholders’ equity Total liabilities and equity

$17,278 $57,048

Calculate all the ratios for which industry figures are available below for Nederland and compare the firm’s ratios with the industry ratios.

Ratio Industry Average

.

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Current ratio Quick ratio Gross margin Net profit margin Debt ratio Long-term debt to equity Interest coverage ROA ROE

Solutions Manual

2.05 0.78 23.9% 12.3% 0.23 0.98 5.62 5.3% 18.8%

Solution: Ratio Current ratio Quick ratio Gross margin Net Profit margin Debt ratio Long-term debt to equity Interest coverage ROA ROE

Industry Average 2.05 0.78 23.9% 12.3% 0.23 0.98 5.62 5.3% 18.8%

Nederland 0.77 0.57 51.2% 12.6% 0.70 0.73 20.6 11.4% 37.5%

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.32 Refer to the preceding information for Nederland Consumer Products Company.

Compute the firm’s ratios for the following categories and briefly evaluate the company’s performance using these numbers. a.

Efficiency ratios Asset turnover ratios b.

Leverage ratios c.

Coverage ratios d.

Solution: Efficiency Ratios Inventory turnover ratio Days sales in inventory Accounts receivables turnover DSO Asset Turnover Ratios

.

5.70 64.05 days 12.66 times 28.84 days

COGS/Inventory 365/ITO Sales/AR 365/AR turnover

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Total asset turnover Fixed assets turnover Leverage Ratios Total debt ratio Debt to equity ratio Equity multiplier Coverage Ratios Times interest earned Cash coverage

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Solutions Manual

0.90 times 3.64 times

Sales/TA Sales/FA

0.70 2.30 3.30

TD/TA D/E TA/E

20.60 22.19

EBIT/Interest (EBIT + Depreciation)/Interest

4.33 Refer to the earlier information for Nederland Consumer Products Company. Using the DuPont identity, calculate the return on equity for Nederland, after calculating the ratios that make up the DuPont identity.

Solution: Net Profit margin Total assets turnover ratio Equity multiplier Return on assets Return on equity

12.61% 0.90 times 3.30 11.4% 37.5%

NI/Sales Sales/TA TA/E NI/TA PM×TATO×EM

LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.34 Nugent, Inc., has a gross profit margin of 31.7 percent on net sales of $9,865,214 and total assets of $7,125,852. The company has a current ratio of 2.7 times, accounts receivable of $1,715,363, cash and marketable securities of $315,488, and current liabilities of $870,938.

What is Nugent’s total current assets? a.

How much inventory does the firm have? What is the inventory turnover ratio? b.

What is Nugent’s days’ sales outstanding? c.

.

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d.

If management sets a target DSO of 30 days, what should Nugent’s accounts receivable be?

Solution: Cash & marketable securities = $315,488; Current liabilities = $870,938; Sales = $9,865,214; Current ratio = 2.7 a.

Current assets Current ratio = Current liabilities

2.7 =

b.

c.

Current assets = 2.7  $870,938= $2, 351, 533 Current assets = Cash + Accounts receivables + Inventory $2,351,533 = $315,488 + $1,715,363 + Inventory Inventory = $2,351,533– ($315,488 + $1,715,363) = $320,682 Cost of goods sold = Sales x (1 – Gross PM) = $9,865,214 × (1 – 0.317) = $6,737,941 Cost of goods sold Inventory turnover ratio = Inventory $6,7 3 7,9 4 1 = =21.01 times $320,682 365 365 ×Accounts receivables Net sales DSO= Net sales/Accounts receivables =

Target DSO = 30 days

365 × $1,715,363 =𝟔𝟑.𝟓 𝐝𝐚𝐲𝐬 $9,865,214

365Accounts receivable 365 DSO= Net sales/Accounts receivable = Net sales

30= Accounts receivable =

.

Accounts receivables = $1,715,363 Total assets = $7,125,852 Gross profit margin = 31.7%

Current assets $870,938

= d.

Solutions Manual

365×Accounts receivable $9,865,214 30  $9,865,214 = $810, 840 365 SM 4-37

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Solutions Manual

The firm has to limit its accounts receivable to $810,840 at its current sales level to achieve its target DSO of 30 days.

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.35 Recreational Supplies Co. has net sales of $11,655,000, an ROE of 17.64 percent, and a total asset turnover of 2.89 times. If the firm has a debt-to-equity ratio of 1.43, what is the company’s net income?

Solution: EM=1+D/E ratio =1+1.43= 2.43   ROE = PMTATOEM PM= ROE 0.1764 TATOEM = 2.892.43

= 2.51% =  0.0251 NI = Sales  PM $11,655,000

= $292, 540.50 LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.36 Nutmeg Houseware, Inc., has an operating profit margin of 10.3 percent on revenues of $24,547,125 and total assets of $8,652,352. a.

Calculate the company’s total asset turnover ratio and its operating profit (EBIT). b.

The company’s management has set a target for the total asset turnover ratio of 3.25 for next year. If there is no change in the total assets of the company, what will the new sales level have to be next year? Calculate the dollar change in sales necessary and the percentage change in sales necessary.

If the operating profit margin declines to 10 percent, what will be the EBIT at the c. new level of net sales?

Solution: Operating PM = 10.3%

.

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a.

Solutions Manual

Sales = $24,547,125 Total assets = $8,652,352 Sal es $24,547,125 = TATO = Total assets $8,652,352 = 2.84 times Operating profit = EBIT = Op. PM  Sales = 0.103  $24,547,125 = $2, 528, 354

b.

New TATO = 3.25 times = New sales/TA New sales = TATO  TA = 3.25  $8,652,352 = $28,120,144

c.

$ Change in Sales = $28,120,144 - $24,547,125 = $3,573,019 % Change in sales = $3,573,019/ $24,547,125 = 14.6% Operating PM = 10% Sales = $28,120,144

New EBIT = Profit margin  Sales = 0.10 $28,120,144 = $2,812,014 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.37 Modern Appliances Corporation has reported its financial results for the year ended December 31, 2017.

Modern Appliances Corporation Income Statement for the Fiscal Year Ended December 31, 2017

Net Sales Cost of goods sold Gross profit Selling, general, and admin. expenses Depreciation

.

$5,398,412,000 3,432,925,255 $1,965,486,745 1,036,311,231 299,928,155

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Operating income Interest expense EBT Income taxes Net earnings

Assets: Cash and cash equivalents Accounts receivable Inventory Other current assets Total current assets Net fixed assets Goodwill Other assets Total assets

$ 629,247,359 35,826,000 $ 593,421,359 163,104,554 $ 430,316,805

Modern Appliances Corporation Balance Sheet as of December 31, 2017 Liabilities and Equity: $ 514,412,159 Short-term borrowings 1,046,612,233 Trade accounts payable 981,870,990 Other current liabilities 313,621,610 $2,856,516,992 Total current liabilities 754,660,275 Long-term debt 118,407,710 Common stock 665,058,761 Retained earnings $4,394,643,738 Total liabilities and equity

$ 117,109,865 466,937,985 994,289,383 $1,578,337,233 1,200,691,565 397,407,352 1,218,207,588 $4,394,643,738

Using the information from the financial statements, complete a comprehensive ratio analysis for Modern Appliances Corporation.

Calculate these liquidity ratios: current and quick ratios. a.

Calculate these efficiency ratios: inventory turnover, accounts receivable b. turnover, DSO. Calculate these asset turnover ratios: total asset turnover, fixed asset turnover. c.

Calculate these leverage ratios: total debt ratio, debt-to-equity ratio, equity d. multiplier.

Calculate these coverage ratios: times interest earned, cash coverage. e.

Calculate these profitability ratios: gross profit margin, net profit margin, ROA, f.

ROE. Use the DuPont identity after calculating the component ratios to compute ROE. g.

Solution: a.

b.

c.

.

Liquidity Ratios Current ratio Quick ratio Efficiency Ratios Inventory turnover ratio Accounts receivable turnover DSO Asset Turnover Ratios Total asset turnover Fixed assets turnover

1.81 Current assets/Current liabilities 1.19 (Current assets-Inventory)/Current liabilities 3.50 times 5.16 times 70.76 days

COGS/Inventory Net sales/AR 365/AR turnover

1.23 times 7.15 times

Net sales/Total assets Net sales/Fixed assets

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Fundamentals of Corporate Finance, 4th Edition

d.

e.

f.

g.

Leverage Ratios Total debt ratio Debt to equity ratio Equity multiplier Coverage Ratios Times interest earned Cash coverage Profitability Ratios Gross profit margin Net profit margin ROA ROE

Solutions Manual

0.63 1.72 2.72

Total debt/Total assets Debt/Equity Total assets/Equity

17.56 25.94

EBIT/Interest (EBIT + Depreciation)/Interest

0.36 0.08 0.10 0.27

Gross profit/Net sales Net income/Net sales Net income/Total assets Net income/Equity

DuPont identity.

Net income ROE= Net Sales

Net Sales Total assets  Total assets  Common equity

= 0.08  1.23  2.72 = 0.27

LO: 4.3, 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

CFA PROBLEMS 4.38 Common-size analysis is used in financial analysis to: evaluate changes in a company’s operating cycle over time. a. predict changes in a company’s capital structure using regression analysis. b. compare companies of different sizes or compare a company with itself over time. c. restate each element in a company’s financial statement as a proportion of the d. similar account for another company in the same industry.

Solution: c is correct. The most significant benefit of using common-size statements is scaling, whether for a given company or over time. Common-size analysis allows us to make comparisons of investments, financing, and profitability between companies of different sizes and over time for a single company.

LO: 4.2

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4.39 The TBI Company has a number of days of inventory of 50. Therefore, the TBI Company’s inventory turnover is closest to: a.

4.8 times. b.

7.3 times. c.

8.4 times. d.

9.6 times.

Solution: b is correct. We perform the calculations using the following relationship: Inventory Cost of goods sold × Inventory Cost of goods sold / 365 = 365 Inventory turnover  Number of days of inventory = 365

Inserting the given information, we have Inventory turnover × 50 = 365, and solving for Inventory turnover provides a turnover of 7.3 times.

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.40 DuPont analysis involves breaking return-on-assets ratios into their a. profit components. b. marginal and average components. c. operating and financing components. d. profit margin and turnover components.

Solution: d is correct. This is the DuPont “triangle,” in which profit margins and turnovers are used to explain returns.

LO: 4.4 Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

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4.41 If a company’s net profit margin is –5 percent, its total asset turnover is 1.5 times, and its equity multiplier is 1.2 times, its return on equity is closest to –9.0 percent. a.

–7.5 percent. b.

–3.2 percent. c.

1.8 percent. d.

Solution: a is correct.

Net income Net income Net sales Average total Average Return on equity= Average total equity = Net sales × Average total assets× assets total equity

Return on equity = –5% × 1.5 × 1.2 = –9.0% LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Sample Test Problems Greenfern Corporation recently filed the following financial statements with the SEC. Greenfern Corporation Income Statement for the Fiscal Year Ended July 31, 2017 Net sales $73,236 Cost of products sold 52,092 Gross profit $21,144 Selling, general, and administrative expenses 9,333 Depreciation 1,060 Operating income (loss) $ 10,751 Interest expense 649 Earnings (loss) before income taxes 10,102 Income taxes 3,536 Net earnings (loss) $ 6,566

Assets .

Greenfern Corporation Balance Sheet as of July 31, 2017 Liabilities and Stockholders’ Equity SM 4-43

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Cash and marketable securities Accounts receivable Inventory Deferred income taxes Prepaid expenses & other receivables Total current assets Property, plant, and equipment Less: Accumulated depreciation Net property plant and equip.

$ 9,118 7,844 8,900 878

Accounts payable Accrued and other liabilities Taxes payable Debt due within one year

$ 6,379 5,663 4,821 10,778

2,803 $29,543 62,467 22,196 $40,271

Goodwill and other assets

16,270

$27,641 24,280 6,903 5,608 $64,432 3,667 17,985 $21,652

Total assets

$86,084

Total current liabilities Long-term debt Deferred income taxes Other non-current liabilities Total liabilities Common stock Retained earnings Total stockholders’ equity (deficit) Total liabilities and stockholders’ equity

$86,084

4.1

Refer to the preceding balance sheet and income statement for Greenfern Corporation for the fiscal year ended July 31, 2017. What are the company’s current ratio and quick ratio? What do these ratios tell us about Greenfern?

Solution: Currentassets $29,543 Currentratio= = $27,641=1.07 Currentliabilities

Quickratio=

Currentassets −Inventory $29,543−$8,900 = =0.75 $27,641 Currentliabilities

The current ratio of just over 1 tells us that Greenfern’s cash and marketable securities, and other current assets, such as accounts receivable and inventory, if liquidated, will just provide enough proceeds to cover short-term liabilities. The quick ratio of Greenfern indicates that if we exclude inventory, which might be considerably less liquid than other current assets, the remaining current assets can cover just 75 percent of the short-term liabilities.

LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

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4.2

Refer to the preceding balance sheet and income statement for Greenfern Corporation for the fiscal year ended July 31, 2017. Calculate the following ratios: a. Inventory turnover b. Days’ sales outstanding. c. Total asset turnover. d. Fixed asset turnover. e. Total debt ratio. f. Debt-to-equity ratio. g. Times interest earned ratio. h. Cash coverage ratio.

Solution: Ratio Calculation Value a. Inventory turnover $52,092/$8,900 5.85 b. Days’ sales outstanding $7,844/($73,236/365) 39.1 days c. Total asset turnover $73,236/$86,084 0.85 d. Fixed asset turnover $73,236/$40,271 1.82 e. Total debt ratio $64,432/$86,084 0.75 f. Debt-to-equity ratio $64,432/$21,652 2.98 g. Times interest earned ratio $10,751/$649 16.57 h. Cash coverage ratio ($10,751 + $1,060)/$649 18.20 LO: 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.3

Refer to the preceding balance sheet and income statement for Greenfern Corporation for

the fiscal year ended July 31, 2017. Use the DuPont identity to calculate the return on equity (ROE). In the process, calculate the following ratios: net profit margin, total asset turnover, equity multiplier, EBIT return on assets (EROA), and return on assets.

Solution: Net profit margin = Net income/Net sales = $ 6,566 / $73,236 = 0.0897 or 8.97% Total asset turnover = Net sales/Total assets = $73,236 / $86,084 = 0.85 Equity multiplier = Total assets/Total equity = $86,084 / $21,652 = 3.98 EROA = EBIT/Total assets = $10,751/$86,084 = 0.1249 or 12.49% Return on assets = Net income/Total assets = $ 6,566 / $86,084 = 0.0763 or 7.63% DuPont identity:

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ROE = ROA × Equity multiplier = Net profit margin × Total asset turnover × Equity multiplier = 0.0897 × 0.85 × 3.98 = 0.3033 = 30.35% LO: 3, 4 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Last year Pontiff Enterprises reported net sales of $13,144,680, a gross profit $4,127,429, EBIT of $2,586,150, and net income of $867,555. Compute Pontiff’s cost of goods sold, gross profit margin, operating profit margin, and net profit margin.

Solution: Costof goodssold = Netsales−Grossprofit 4.4

= $13,144,680-$4,127,429 = $9,017,251 Gross profit margin = Grossprofit/Net sales = $4,127,429/$13,144,680 = 0.3140,or31.40% Operating profit margin = EBIT/Net sales = $2,586,150/$13,144,680 = 0.1967,or19.67% Netprofitmargin= Netincome/Netsales = $867,555/$13,144,680 = 0.0660,or6.60% LO: 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.5

National City Bank has 646,749,650 shares of common stock outstanding that are currently selling for $37.55 per share on the New York Stock Exchange. If National City’s net income was $2,780,955,000 in the year that just ended, what was its earnings

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per share and what is its current price-earnings ratio? If the typical price-earnings ratio for a bank is currently 15, what does the price-earnings ratio for National City tell you about its prospects?

Solution: Net income Earnings per share(EPS) = Shares outstanding

= Price-earnings ratio= =

$2,780,955,000 =$4.30 646,749,650

Share price EPS $37.55

= 8.73

$4.30 The fact that the price-earnings ratio for National City of 8.73 is well below the typical value for a bank tells us that the market places a smaller value on each current dollar of earnings at National City than on each current dollar of earnings at the typical bank. This suggests that the market is less optimistic about National City’s prospects than it is about the prospects of the typical bank.

LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

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Chapter 5 The Time Value of Money Before You Go On Questions and Answers Section 5.1

1.

Why is a dollar today worth more than a dollar one year from now?

A dollar is worth more today than one year from now, due to its potential earning capacity. If you have the money in your hand today, you have the opportunity to invest it and earn interest or you can purchase goods and services for your immediate consumption. Given that people have a positive preference for consumption, time value of money holds true.

2.

What is a time line, and why is it important in financial analysis?

A time line is a horizontal line that starts at time zero (today) and shows cash flows as they occur over time. It is an important tool used to analyze cash flows over certain time periods, as the timing of each cash flow has a big impact on the final figure, and therefore on the resulting investment decision.

Section 5.2 1.

What is compounding, and how does it affect the future value of an investment?

Compounding is the process that refers to converting the initial (principal) amount into a future value. In order to obtain the future value of the principal amount, you calculate what the value of that amount will be at the end of the time period, assuming the initial investment will earn interest and that interest is invested and earns additional interest in future periods.

2.

What is the difference between simple interest and compound interest?

The effect of compounding, where interest is earned on interest, makes an investment grow to a larger value than it would if it only paid simple interest. Simple interest is interest earned only on the original principal.

3.

.

How does changing the compounding period affect the amount of interest earned on an investment?

The more frequent the compounding schedule, the higher the interest earned. For example, $100 invested for one year at 10 percent compounded annually will earn you SM 5-1

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

$10 of interest at the end of the year, but if your bank compounded interest quarterly, your earnings from interest would increase to $10.38.

Section 5.3 1.

What is the present value, and when is it used?

Present value is the amount a future sum is worth today, given a certain rate of return.

The present value concept should be used when calculating how much money you need today in order to reach your financial goal sometime in the future.

2.

What is the discount rate? How does the discount rate differ from the interest rate in the future value equation?

The discount rate is the rate of return used in a discounted cash flow analysis to determine the present value of future cash flows. Both discount and interest rates essentially represent the same concept. The only difference is the context in which they are used.

3.

What is the relation between the present value factor and the future value factor?

The present value factor is the reciprocal of the future value factor. To obtain the present value factor, you divide 1 by the future value factor (1 + i)n.

4.

Explain why you would expect the discount factor to become smaller when based on the longer the time to payment.

The discount factor will become smaller the longer the time to payment due to time value of money. The longer you have to wait to obtain the money, the less value it will have to you. Mathematically, the discount factor is calculated as 1/(1 + i)n. The longer the time to payment, the larger n gets, which will make the discount factor smaller.

Section 5.4 1.

What is the difference between the interest rate (i) and the growth rate (g) in the future value equation?

The interest rate and the growth rate in the future value equation essentially represent the same concept. The growth rate is used when we deal with numerical values such as sales or change over time. When referring to money being invested, we use the term interest rate.

Self-Study Problems and Solutions .

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5.1

Amit Patel is planning to invest $10,000 in a bank certificate of deposit (CD) for five years. The CD will pay interest of 9 percent. What is the future value of Amit’s investment?

Solution: Present value of the investment = PV = $10,000 Interest rate = i = 9% Number of years = n = 5.

0 1 2 3 4 5 Years ├───┼───┼───┼────┼───┤ -$10,000 FV5=?

FV n = PV(1 + i)n FV 5 = $10, 000(1 +0.09 ) 5 = $15, 386.24 Financial Calculator Solution: 5 N

9 i

-10,000 PV

0 PMT

FV 15,386.24

Megan Gaumer expects to need $50,000 for a down payment on a house in six years.

How much does she need to invest today in an account paying 7.25 percent in order to have $50,000 in six years?

Solution: Amount Megan will need in six years = FV6 = $50,000 5.2

Number of years = n = 6 Interest rate = i = 7.25% Amount needed to be invested now = PV = ?

0 1 2 3 4 5 6 Year ├───┼───┼───┼────┼───┼───┤ PV = ?

FV6 = $50,000

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FV𝑛

PV = (1+𝑖)𝑛 $50 ,000 = (1+0.0725)6

= $32,853.84 Financial Calculator Solution: 6 N

7.25 i

PV -32,853.84

0 PMT

50,000 FV

Kelly Martin has $10,000 that she can deposit into a savings account for five years. Bank A pays compounds interest annually, Bank B twice a year, and Bank C quarterly. Each bank has a stated interest rate of 4 percent. What amount would Kelly have at the end of the fifth year if she left all the interest paid on the deposit in each bank?

Solution: Present value of Kelly’s deposit = PV = $10,000 Number of years = n = 5 Interest rate = i = 4% Compound period m: A=1 B=2 C=4 Amount at the end of 5 years = FV5 = ?

5.3

0 4% 1 2 3 4 5 Year ├───┼───┼───┼────┼───┤ -$10,000 FV5 = ?

.

A:

FV n FV 5

= PV × (1 +i /m) m x n = × (1 + 0.04/1)1x5 = 10,000 $12,166.53

B:

FV 5

= 10,000 × (1 + 0.04/2)2x5 = $12,189.94

SM 5-4

Fundamentals of Corporate Finance, 4th edition

= 10,000 × (1 + 0.04/4)4x5 = $12,201.90

FV5

C:

Solutions Manual

Financial Calculator Solution: Bank A: 4 -10,000 0 5 i PV PMT N Bank B: 10 N

2 i

-10,000 PV

0 PMT

Bank C: 20 N

1 i

-10,000 PV

0 PMT

FV 12,166.53

FV 12,189.94

FV 12,201.90

You have an opportunity to invest $2,500 today and receive $3,000 in three years. What would be the return on your investment if you accepted this opportunity?

Solution: Your investment today = PV = $2,500 Amount to be received = FV3= $3,000 Time of investment = n = 3 Return on the investment = i = ?

5.4

0i=?1 2 3 Year ├───┼────┼───┤ -$2,500 $3,000 FV𝑛 = PV ×(1 +𝑖)

𝑛

$3,000 = $2,500 ×(1 +𝑖) $3,000 $2,500

= (1 +𝑖)

3

3

i = 6.27% Financial Calculator Solution:

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3 N

i 6.27

-2,500 PV

0 PMT

Solutions Manual

3,000 FV

Emily Smith deposits $1,200 in her bank today. (a) If the bank pays 4 percent simple interest, how much money will she have at the end of five years? (b) What if the bank pays compound interest? (c) How much of the earnings will be interest on interest?

Solution: Emily’s deposit today= PV = $1,200 Interest rate = i = 4% Number of years = n = 5 Amount to be received = FV5 = ?

5.5

0 4% 1 2 3 4 5 Year ├───┼───┼───┼────┼───┤ -$1.200 FV5 = ? a. Future value with simple interest Simple interest per year = $1,200 × 0.04 = $48 Simple interest for 5 years = $48 × 5 = $240 FV5 = $1,200 + $240 = $1,440 b. Future value with compound interest FV 5 = $1,200 × (1 + 0.04)5 = $1,459.98 Simple interest = ($1,440 – $1,200) = $240 Interest on interest = $1,459.98 – $1,200 – $240 = $19.98

Discussion Questions 5.1

Explain the phrase “a dollar today is worth more than a dollar tomorrow.”

The implication is that if one was to receive a dollar today instead of in the future, the dollar could be invested and will be worth more than a dollar tomorrow because of the interest earned during that one day. This makes it more valuable than receiving a dollar tomorrow.

LO: 1 Level: Basic

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Bloomcode: Knowledge AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.2

Explain the importance of a time line.

Time lines are important tools used to analyze investments that involve cash flow streams over a period of time. They are horizontal lines that start at time zero (today) and show cash flows as they occur over time. Because of time value of money, it is crucial to keep track of not only the size, but also the timing of the cash flows.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.3

What are the two factors to be considered in time value of money?

The factors that are critical in time value of money are the size of the cash flows and the timing of the cash flows.

LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.4

Explain the difference between future value and present value.

Future value measures what one or more cash flows will be worth at the end of a specified period, while present value measures what one or more future cash flows are worth today (at time = 0).

LO: 2, 3 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.5

Explain the difference between compounding and discounting.

The process of converting an amount given at the present time into a future value is called compounding. It is the process of earning interest over time. Discounting is the process of converting future cash flows to their current or present value. In other words,

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present value is the current value of future cash flows that are discounted at an appropriate interest rate.

LO: 2, 3 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.6

Explain how compound interest differs from simple interest.

Suppose I invest $100 for three years at a rate of 10 percent. Simple interest would imply that I will earn $10 for each of the three years for a total of $30 interest. At the end of three years I would have $130. Compound interest recognizes that the interest earned in years 1 and 2 will also earn interest over the remaining period. Thus, the $10 earned in the first year would earn interest at 10 percent for the next two years, and the $10 earned in the second year would earn interest for the third year. Thus the total amount that I would have at the end of three years would be: $100(1.10)3= $133.10. By compounding, I have earned additional interest of $3.10. The total compound interest is the $33.10 earned on the $100 invested, while the simple interest earned is equal to $30.00.

LO: 2 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.7

If you were given a choice between investing in a savings account that paid quarterly interest and one that paid monthly interest, which one should you choose if they both offered the same stated interest rate and why?

The impact of compounding dictates that one should pick the account that pays interest more frequently (as long as the interest rates are the same). This allows for the interest earned in the earlier periods to earn interest and the investment to grow more.

LO: 4 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.8

.

Compound growth is exponential over time. Explain.

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Growth rates, as well as interest rates, are not linear, but rather exponential over time. In other words, the growth rate of the invested funds is accelerated by the compounding of interest. Over time, the principal amount gets larger as interest is added due to the compounding effect.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.9

What is the Rule of 72?

This is a rule of thumb to determine how fast an investment can double. It is a rule that allows you to closely approximate the time that it would take to double your money. It works well with interest rates between 5 and 20 percent, but varies more with higher rates. The Rule of 72 says that the time to double your money (TDM) approximately equals 72/i, where i is the rate of return expressed as a percentage. For example, if a bank paid 10% interest it would take 7.2 (72/10 = 7.2) years to double your money.

LO: 4 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.10 You are planning to take a spring break trip to Cancun your senior year. The trip is exactly two years away, but you want to be prepared and have enough money when the time comes. Explain how you would determine the amount of money you will have to save in order to pay for the trip.

First, determine how much money you will need for the trip. Second, check how much you already have and how it translates into future value cash—how much it will be worth in two years. Next, determine how much you will have to deposit today, given the bank’s offered interest rate, to ensure that you will have saved up the difference when the time for your senior spring break comes.

LO: 4 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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Questions and Problems BASIC 5.1

Future value: Chuck Tomkovick is planning to invest $25,000 today in a mutual fund that will provide a return of 8 percent each year. What will be the value of the investment in 10 years?

Solution: 0 10 years ├────────────────────┤ PV = -$25,000 FV10 = ?

Amount invested today = PV = $25,000 Return expected from investment = i = 8% Duration of investment = n = 10 years Value of investment after 10 years = FV10 FV10= PV (1 + i ) n = $25,000 (1.08)10 = $53,973.12 Financial Calculator Solution: 10 N

8 i

-25,000 PV

0 PMT

FV 53,973.12

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.2

Future value: Ted Rogers is investing $7,500 in a bank CD that pays a 6 percent annual

interest. How much will the CD be worth at the end of five years?

Solution: 0 5 years ├────────────────────┤ PV = $7,500 FV5 = ?

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Amount invested today = PV = $7,500 Return expected from investment = i = 6% Duration of investment = n = 5 years Value of investment after 5 years = FV5 FV 5 = PV (1 + i ) n = $7,500 (1.06)5 = $10,036.69 Financial Calculator Solution: 5 N

6 i

-7,500 PV

0 PMT

FV 10,036.69

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.3

Future value: Your aunt is planning to invest in a bank CD that will pay 7.5 percent interest compounded semiannually. If she has $5,000 to invest, how much will she have at the end of four years?

Solution: 0 4 years ├────────────────────┤ PV = $5,000 FV4 = ?

Amount invested today = PV = $5,000 Return expected from investment = i = 7.5% Duration of investment = n = 4 years Frequency of compounding = m = 2 Value of investment after 4 years = FV4 mxn

2 x4

i   0.0 7 5 FV 4 =PV 1 +  = $5,000  1 +  4   m  =$5,000 (1.0375)8 =$6,712.35 Financial Calculator Solution:

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8 N

3.75 i

-5,000 PV

0 PMT

Solutions Manual

FV 6,712.35

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.4

Future value: Kate Eden received a graduation present of $2,000 that she is planning on investing in a mutual fund that earns 8.5 percent each year. How much money will she have in three years?

Solution: 0 3 years ├────────────────────┤ PV = $2,000 FV3 = ?

Amount Kate invested today = PV = $2,000 Return expected from investment = i = 8.5% Duration of investment = n = 3 years Value of investment after 3 years = FV3 FV3 = PV  (1+ i)n = $2,000 (1.085)3 = $2,554.58 Financial Calculator Solution: 3 N

8.5 i

-2,000 PV

0 PMT

FV 2,554.58

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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Future value: Your bank pays 5 percent interest semiannually on your savings account.

You don’t expect to add to the current balance of $2,700 over the next four years. How much money can you expect to have at the end of this period?

Solution: 0 4 years ├────────────────────┤ PV = -$2,700 FV4 = ?

Amount invested today = PV = $2,700 Return expected from investment = i = 5% Duration of investment = n = 4 years Frequency of compounding = m = 2 Value of investment after 4 years = FV4 5.5

mxn

2 4

i  0.05   FV 4 = PV 1 +  = $2, 700  1 + 2   m  = $2,700(1.025)8 = $3, 289.69 Financial Calculator Solution: 8 N

2.50 i

-2,700 PV

0 PMT

FV 3,289.69

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.6

Future value: Your birthday is coming up and instead of other presents, your parents

promised to give you $1,000 in cash. Since you have a part time job and thus don’t need the cash immediately, you decide to invest the money in a bank CD that pays 5.2 percent, compounded quarterly, for the next two years. How much money can you expect to earn in this period of time?

Solution: 0 2 years ├────────────────────┤ PV = -$1,000 FV2 = ?

Amount invested today = PV = $1,000 .

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Return expected from investment = i = 5.2% Duration of investment = n = 2 years Frequency of compounding = m = 4 Value of investment after 2 years = FV2 mxn

42

i   0.0 5 2 FV 2 =PV 1 +  = $1,000  1 +  4   m  =$1,000 (1.013)8 =$1,108.86

You have earned 108.86 in total compound interest.

Financial Calculator Solution: 8 N

1.3 i

-2,500 PV

0 PMT

FV 1,108.86

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.7

Multiple compounding periods: Find the future value of a five-year $100,000 investment that pays 8.75 percent and that has the following compounding periods: a.

Quarterly. b.

Monthly. c.

Daily. d.

Continuous.

Solution: 0 5 years ├────────────────────┤ PV = -$100,000 FV5 = ?

Amount invested today = PV = $100,000 Return expected from investment = i = 8.75% Duration of investment = n = 5 years a.

Frequency of compounding = m = 4 Value of investment after 5 years = FV5

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Solutions Manual mxn

45

mxn

125

mxn

3655

i   0.0875 FV 5 =PV  1+  = $100,000  1 +  4   m  =$100,000 (1.021875)20=$154,154.24 b.

Frequency of compounding = m = 12 Value of investment after 5 years = FV5

i   0.0875 FV 5 =PV  1+  = $100,000  1 +  12   m  =$100,000 (1.00729)60=$154,637.37 c.

Frequency of compounding = m = 365 Value of investment after 5 years = FV 5

i   0.0875 FV 5 =PV  1 +  = $100,000  1 +  365    m =$100,000 (1.00024)1825= $154,874.91 Frequency of compounding = m = Continuous Value of investment after 5 years = FV5 FV 5 = PV eixn=$100,000  e0.08755 = $100,0001.5488303= $154,883.03

d.

Financial Calculator Solution: a. Quarterly 20 2.1875 N I

-100,000 0 PV PMT

b. Monthly 60 0.72917 -100,000 N i PV c. Daily 1825 0.02397 -100,000 i N PV d. Continuously NA

0 PMT

0 PMT

FV 154,154.24 FV 154,637.37

FV 154,874.91

LO 2

.

SM 5-15

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.8

Growth rates: Joe Mauer, a catcher for the Minnesota Twins, is expected to hit 15 home

runs in 2018. If his home-run-hitting ability is expected to grow by 12 percent every year for the following five years, how many home runs is he expected to hit in 2023?

Solution: 0 5 years ├────────────────────┤ PV = -15 FV5 = ?

Number of home runs hit in 2018 = PV = 15 Expected annual increase in home runs hit = g= 12% Growth period = n = 5 years Expected home runs in 2023 = FV5 FV = PV(1+g) n =15 (1.12) 5 5

= 26.426 home runs

Financial Calculator Solution : 5 N

12 i

-15 PV

0 PMT

FV 26.435

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.9

Present value: Roy Gross is considering an investment that pays 7.6 percent, compounded annually. How much will he have to invest today so that the investment will be worth $25,000 in six years?

.

SM 5-16

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: 0 6 years ├────────────────────┤ PV = ?

FV6 = $25,000 Value of investment after 6 years = FV6 = $25,000 Return expected from investment = i = 7.6% Duration of investment = n = 6 years Amount to be invested today = PV FVn $25,000 = PV = (1+i)n (1.076)6

= $16,108.92

Financial Calculator Solution: 6 N

7.6 i

PV -16,108.92

0 PMT

25,000 FV

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.10 Present value: Maria Addai has been offered a future payment of $750 two years from now. If she can earn an annual rate of 6.5 percent, compounded daily, on her investment, what should she pay for this investment today?

Solution: 0 2 years x 365 days per year ├────────────────────┤ PV = ?

FV2 = $750 Value of investment after 2 years = FV2 = $750 Return expected from investment = i = 6.5%/365 = 0.065/365 = 0.00018 Duration of investment = n = 2 years × 365 days per year = 730 days Amount to be invested today = PV

.

SM 5-17

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

FV n $750 = PV = (1 + i)n (1.00018)730 = $657.66 Financial Calculator Solution:

730 N

0.018 i

PV -657.66

0 PMT

750 FV

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.11 Present value: Your brother has asked you for a loan and has promised to pay you $7,750 at the end of three years. If you normally invest to earn 6 percent per year, how much will you be willing to lend to your brother if you view this purely as a financial transaction (i.e. you don’t give your brother a special deal)?

Solution: 0 3 years ├────────────────────┤ PV = ?

FV3 = $7,750 Loan repayment amount after 3 years = FV3 = $7,750 Return expected from investment = i = 6% Duration of investment = n = 3 years Amount to be invested today = PV FV $7,750 = PV = n n (1.06)3 (1+ = i) $6,507.05 Financial Calculator Solution : 3 N

6 i

PV

0 PMT

7,750 FV

-6,507.05

LO 3 .

SM 5-18

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.12 Present value: Tracy Chapman is saving to buy a house in five years. She plans to put 20 percent down at that time, and she believes that she will need $35,000 for the down payment. If Tracy can invest in a fund that pays 9.25 percent annual interest, compounded quarterly, how much will she have to invest today?

Solution: 0 5 years ├────────────────────┤ PV = ?

FV5 = $35,000 Amount needed in the Future = $35,000 Return expected from investment = i = 9.25/4= 2.31 Duration of investment = n = 5 X 4 = 20 Amount to be invested today = PV FV $35, 000 n = PV = mxn (1.0231)4x5  i 1 +   m = $22, 166.97 Financial Calculator Solution: 20 N

2.31 i

PV -22,166.97

0 PMT

35,000 FV

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

.

SM 5-19

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

5.13 Present value: You want to buy some bonds that will have a value of $1,000 at the end of seven years. The bonds pay 4.5 percent interest annually. How much should you pay for them today?

Solution: 0 7 years ├────────────────────┤ PV = ?

FV7 = $1,000

Face value of bond at maturity = FV7 = $1,000 Appropriate discount rate = i = 4.5% Number of years to maturity = n = 7 years.

Present value of bond = PV FVn $1,000 = = PV (1+i )n (1.045)7 = $734.83 Financial Calculator Solution: 11 N

3.70 i

PV -670.55

0 PMT

1000 FV

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.14 Present value: Elizabeth Sweeney wants to accumulate $12,000 by the end of 12 years.

If the annual interest rate is 7 percent and interest compounds semiannually, how much will she have to invest today to achieve her goal?

Solution: 0 12 years × 2 periods per year ├────────────────────┤ PV = ?

FV12 = $12,000 Amount Ms. Sweeney wants at end of 12 years = FV12 = $12,000

.

SM 5-20

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Interest rate on investment = i = 7%/2 = 0.07/2 = 0.035 Duration of investment = n = 12 years × 2 periods per year = 24 periods Present value of investment = PV FV n $12,000 = PV = n (1+i) (1.035)24 = $5,255.49

Financial Calculator Solution: 24 N

3.5 i

PV -5,255.49

0 PMT

12,000 FV

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.15 Interest rate: You are in desperate need of cash and turn to your uncle, who has offered to lend you some money. You decide to borrow $1,300 and agree to pay back $1,500 in two years. Alternatively, you could borrow from your bank that is charging 6.5 percent interest annually. Should you go with your uncle or the bank?

Solution: 0 2 years ├────────────────────┤ PV = -$1,300 FV2 = $1,500 Amount to be borrowed = PV = $1,300 Amount to be paid back after 2 years = FV2 = $1,500 Interest rate on investment = i = ?

Duration of investment = n = 2 years.

Present value of investment = PV

.

SM 5-21

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

FVn PV = 1 + in )

(

$1,300= (1 + i) 2 =

$1,500 (1+i)2 $1,500

=1.1538 $1,300 i = 1.1538−1

i = 7.42% You should borrow from the bank.

Financial Calculator Solution: 2 N

i 7.42

1,300 PV

0 PMT

-1,500 FV

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.16 Number of periods: You invest $150 in a mutual fund today that pays 9 percent interest annually. How long will it take to double your money?

Solution: 0 n years ├────────────────────┤ PV = -$150 FVn = $300 Value of investment today = PV = $150 Interest on investment = n = 9% Future value of investment = FV = $300 Number of years to double investment = n

.

SM 5-22

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

FV n= PV (1+ i)n $300 = $150  (1.09)n (1.09)n=$300150=2.00 n  ln(1.09) = ln(2.00) n= ln( 2.00) 8 years ln(1.09) Financial Calculator Solution: N 8.043

9 i

-150 PV

0 PMT

300 FV

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

INTERMEDIATE 5.17 Future value: Your finance textbook sold 53,250 copies in its first year. The publishing company expects the sales to grow at a rate of 20 percent each year for the next three years and by 10 percent in the fourth year. Calculate the total number of copies that the publisher expects to sell in years 3 and 4. Draw a time line to show the sales level for each of the next four years.

Solution: Number of copies sold in its first year = PV = 53,250 Expected annual growth in the next 3 years = g = 20% Number of copies sold after 3 years = FV3 = FV n= PV(1+ ) g n

= 53, 250  (1.20)3 = 92,016 copies Financial Calculator Solution:

.

SM 5-23

Fundamentals of Corporate Finance, 4th edition

3 N

20 i

-53,250 PV

0 PMT

Solutions Manual

FV 92,016

Number of copies sold in the fourth year = FV4 FV n= PV (1+ g)n = 92,016(1.10)

=101,218 copies 0 3 4 years ├───────────┼────────┤ PV = -53,250 92,016 101,218 copies Financial Calculator Solution: 1 N

10 i

-92,016 PV

0 PMT

FV 101,218

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.18 Future Value: CelebNav, Inc., had sales last year of $700,000, and the analysts are predicting a good year for the start-up, with sales growing 20 percent a year for the next three years. After that, the sales should grow 11 percent per year for two years, at which time the owners are planning to sell the company. What are the projected sales for the last year before the sale?

Solution: 0 1 2 3 4 5 years ├───────┼────────┼───────┼────────┼───── g1 = 20% g2 = 11% PV = -$700,000

FV5=?

Sales of CelebNav last year = PV = $700,000 Expected annual growth in the next 3 years = g1 = 20%

.

SM 5-24

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Expected annual growth in years 4 and 5 = g2 = 11% Sales in year 5 = FV5 +1  g+2 ) 2 $700, = 000 (1.20)3  (1.11)2 FV 5 = PV  (1 g)3 (1 = $1, 490, 348.16 Financial Calculator Solution: 3

20

-700,000

0

N

i

PV

PMT

2 N

11 i

-1,209,600 PV

FV 1,209,600 0 PMT

FV 1,490,348.16

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.19 Future value: You decide to take advantage of the current online dating craze and start your own Web site. You know that you have 450 people who will sign up immediately and, through a careful marketing research and analysis, determine that membership can grow by 27 percent in the first two years, 22 percent in year 3, and 18 percent in year 4.

How many members do you expect to have at the end of four years?

Solution: 0 1 2 3 4 years ├───────┼────────┼───────┼────────┤ g1-2=27% g3=22% g4=18% PV = -450 FV4 = ?

Number of Web site memberships at t = 0 = PV = 450 Expected annual growth in the next 2 years = g1-2 = 27% Expected annual growth in years 3 = g3= 22% Expected annual growth in years 4 = g4= 18% Number of members in year 4 = FV4 FV4 = PV(1+ g 1)2 (1+ g3) (1+ g 4) = 450(1.27)2 (1.22) (1.18)

= 1,045 members

.

SM 5-25

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Financial Calculator Solution: 2 N

27 i

-450 PV

0 PMT

1 N

22 i

-725.805 PV

0 PMT

1 N

18 i

-885.4821 PV

0 PMT

FV 725.805 FV 885.4821 FV 1045

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.20 Multiple compounding periods: Find the future value of an investment of $2,500 made today for the following rates and periods: a.

6.25 percent compounded semiannually for 12 years b.

7.63 percent compounded quarterly for 6 years c.

8.9 percent compounded monthly for 10 years d.

10 percent compounded daily for 3 years e.

8 percent compounded continuously for 2 years Solution: 212

a.

 0.0625 FV12= PV   1 +  2   = $5,232.09

b.

FV6 = PV × ( 1 +

0.0763 4×6 4

)

= $2,500 (2.0928)

= $2,500 ×(1.5738)

= $3,934.48

.

0.089 12×10

c.

FV10 = PV × ( 1 + ) 12 = $6,067.86

d.

FV3= PV × ( 1 +

= $2,500 ×(2.4271)

0.010 365×3 = $2,500 ×(1.3498) ) 365 SM 5-26

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

= $3,374.51 FV= PV × ei x n= $3,000 ×e0.08 x 2 2 = $2,500 × 1.1735 = $2,933.78

e.

Financial Calculator Solution: a.

6.25 percent compounded semiannually for 12 years.

24 N

b.

3.125 i

-2,500 PV

0 PMT

FV 5,232.09

7.63 percent compounded quarterly for 6 years.

24 N

c.

1.9075 i

-2,500 PV

0 PMT

FV 3,934.48

8.9 percent compounded monthly for 10 years.

120

0.74166 7 i

N d.

1095 N

e.

-2,500

0

PV

PMT

FV 6,067.86

10 percent compounded daily for 3 years.

0.02739726 i

-2,500 PV

0 PMT

FV 3,374.51

NA

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

.

SM 5-27

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

5.21 Multiple compounding periods: Find the present value of $3,500 under each of the following rates and periods.

8.9% compounded monthly for five years. a.

6.6% compounded quarterly for eight years. b.

4.3% compounded daily for four years. c.

5.7% compounded continuously for three years. d.

Solution: n years 0 ├────────────────────┤ PV = ?

FV = n $3,500 a.

Return expected from investment = i = 8.9% Duration of investment = n = 5 years Frequency of compounding = m = 12 Present value of amount = PV FV 5 $3,500 = PV = 125 mn  + i   + 0.089 1 1    m 12    $3,500 = = $2,246.57 1.5579 Return expected from investment = i = 6.6% b.

Duration of investment = n = 8 years Frequency of compounding = m = 4 Present Value of amount = PV FV $3,500 = PV = 48 8 mn  + i   + 0.0 6 6 1 1     m 4    $3,500 = = $2,073.16 1.6882 Return expected from investment = i = 4.3% c.

Duration of investment = n = 4 years Frequency of compounding = m = 365 Present Value of amount = PV FV $3,500 = PV = 3654 4 mn  + i   0.043  1 1+  m   365 = $3,500 = $2,946.96 1.1877 Return expected from investment = i = 5.7% d.

Duration of investment = n = 3 years

.

SM 5-28

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Frequency of compounding = m = Continuous Present value of amount = PV FV3 $3,500 PV= = ein e0.0573

= Financial Calculator Solution: a.

$3,500 1.1865

= $2, 949.88

8.9 percent compounded monthly for five years.

60 N

b.

0.7417 i

PV -2,246.57

0 PMT

3,500 FV

6.6 percent compounded quarterly for eight years.

32 N

c.

1.65 i

PV -2,073.16

0 PMT

3,500 FV

4.3 percent compounded daily for four years.

1460 N

d.

0.011781 i

PV -2,946.96

0 PMT

3,500 FV

NA

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.22 Multiple compounding periods: Samantha plans to invest some money so that she has $5,500 at the end of three years. How much should she invest today given the following choices: a.

4.2 percent compounded daily b.

4.9 percent compounded monthly c.

5.2 percent compounded quarterly

.

SM 5-29

Fundamentals of Corporate Finance, 4th edition

d.

Solution:

a.

b.

5.4 percent compounded annually

0 3 years ├────────────────────┤ PV = ?

FV3 = $5,500 Return expected from investment = i = 4.2% Duration of investment = n = 3 years Frequency of compounding = m = 365 Present value of amount = PV FV 3 $5,500 = PV = 3653 mn  + i   0.042 1   1+  m   365 $5,500 = = $4,848.92 1.1343 Samantha should invest $4,848.92 today to reach her target of $5,500 in three years.

Return expected from investment = i = 4.9% Duration of investment = n = 3 years Frequency of compounding = m = 12 Present value of amount = PV

PV =

FV3

d.

.

𝑖mn

(1 +)m

=

c.

Solutions Manual

=

$5,500

0.049 12

×3

(1 + 12 )

$5,500 = $4,749.54 1.1580

Samantha should invest $4,749.54 today to reach her target of $5,500 in three years.

Return expected from investment = i = 5.2% Duration of investment = n = 3 years Frequency of compounding = m = 4 Present Value of amount = PV FV 3 $5,500 = PV = 43 mn  + i   +0.0 5 2 1 1     4 m    = $5,500 = $4,710.31 1.1677 Samantha should invest $4,710.31 today to reach her target of $5,500 in three years.

Return expected from investment = i = 5.4% Duration of investment = n = 3 years Frequency of compounding = m = 1 SM 5-30

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Present value of amount = PV PV=

FV 3 $5,500 = (1.054)3=$4,697.22 (1+ i)3

Samantha should invest $4,697.22 today to reach her target of $5,500 in three years.

Financial Calculator Solution : a.

4.20 percent compounded daily.

1095 N

b.

0.011507 i

PV -3526.48

0 PMT

5,500 FV

0 PMT

5,500 FV

0 PMT

5,500 FV

0 PMT

5,500 FV

4.90 percent compounded monthly.

36 N

c.

0.408333 i

PV -3454.21

5.20 percent compounded quarterly.

12 N

d.

1.30 i

PV -3425.68

5.40 percent compounded annually.

3 N

5.4 i

PV -3416.16

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

.

SM 5-31

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

5.23 Time to grow: Zephyr Sales Company has sales of $1.125 million. If the company’s management expects sales to grow 6.5 percent annually, how long will it be before sales doubles? Use a financial calculator to solve this problem.

Solution: Enter 6.5% -$1.125 $2.250 i PMT PV FV N Answer: 11 years

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.24 Time to grow: You are able to deposit $850 in a bank CD today, and you will withdraw the money only once the balance is $1,000. If the bank pays 5 percent interest, how long will it take for the balance to reach $1,000?

Solution: Amount invested today = PV = $850 Expected amount in the future = FV = $1,000 Interest rate on CD = i = 5% To calculate the time needed to reach the target FV, we set up the future value equation.

FV n = PV (1+ i)n

$1,000= $850  (1.05) n = $1,000 n (1.05) = $850 =1.1764 n  ln(1.05) ln(1.1764) ln(1.1764) n= = 3.3 years ln(1.05) Financial Calculator Solution : N 3.3

5 i

-850 PV

0 PMT

1000 FV

LO 2, 3

.

SM 5-32

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.25 Time to grow: Neon Lights Company is a private company with sales of $1.3 million a year. Management wants to take the company public but has to wait until the sales reach $2 million. If the sales are expected to grow 12 percent annually, when is the earliest that Neon Lights will go public?

Solution: Current level of sales = PV = $1,300,000 Target sales level in the future = FV = $2,000,000 Projected growth rate = g = 12% To calculate the time needed to reach the target FV, we set up the future value equation.

FV3 = PV × (1 +𝑔)

𝑛

$2,000,000= $1,300,000 × (1.12)𝑛 $2,000,000 = 1.5385 (1.12)𝑛 = $1,300,000 n × ln(1.12) = ln(1.5385) n=

ln (1.5385) = 3.8 years ln (1.12)

Financial Calculator Solution: N 3.8

12 i

-1,300,000 PV

0 PMT

2,000000 FV

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

.

SM 5-33

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

5.26 Time to grow: You have just inherited $550,000. You plan to save this money and continue to live off the money that you are earning in your current job. If you can invest the money in a bond that pays 4.6 percent interest annually, how long will it be before your inheritance is worth $1 million?

Solution: FV𝑛 = PV ×(1 +𝑖)𝑛 $1,000,000= $550,000 × (1.046)𝑛 $1,000,000= (1.046)𝑛 $550,000

ln ( $1,000,000 ) = n × ln(1.046) $550,000

$1,000,000

n=

n=

ln( $550 ,000) ln (1.046)

$0.59784 $0.04497

n = 13.29 years Financial Calculator Solution:

N 13.29

4.60 i

-550,000 PV

0 PMT

1,000,000 FV

LO 2, 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

.

SM 5-34

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

5.27 Growth rates: Xenix Corp had sales of $353,866 in 2017. If management expects its sales to be $476,450 in three years, what is the rate at which the company’s sales are expected to grow?

Solution: Sales in 2017 = PV = $353,866 Expected sales three years from now = $476,450 To calculate the expected sales growth rate, we set up the future value equation.

FV 3 = PV(1+g) 3

$476, 450= $353,866  (1 + g)3 (1 + g)3=

$476, 450 =1.3464 $353, 866 1

g = (1.3464) 3 −1 10.42% = Financial Calculator Solution : 3 N

i 10.42

-353,866 PV

0 PMT

476,450 FV

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.28 Growth rate: Infosys Technologies, Inc., an Indian technology company, reported net income of $419 million this year. Analysts expect the company’s earnings to be $1.468 billion in five years. What is the expected growth rate in the company’s earnings?

Solution: Earnings in current year = PV = $419,000,000 Expected earnings five years from now = $1,468,000,000 To calculate the expected earnings growth rate, we set up the future value equation.

.

SM 5-35

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

FV 5 = PV  (1 + g)5 $1,468,000,000= $419, 000, 000  (1 + g)5 (1 + g)5=

$1,468,000,000 =3.5036 $419, 000, 000 1

g = (3.5036) 5 −1 28.5% = Financial Calculator Solution: 5 N

i 28.5

-419,000,000 PV

0 PMT

1,468,000,000 FV

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.29 Present value: Caroline Weslin needs to decide whether to accept a bonus of $1,820 today or wait two years and receive $2,100 then. She can invest at 6 percent. What should she do?

Solution: 0 2 years ├────────────────────┤ PV = -$1,820 FV2 = ?

Amount to be received in 2 years = FV2 = $2,100 Return expected from investment = i = 6% Duration of investment = n = 2 years Present value of amount today PV = FV2 $2,100 PV= = (1+i)n (1.06)2

=$1,868.99 Since $1,869 is greater than $1,820, Caroline should wait two years unless she needs the money sooner.

LO 3 .

SM 5-36

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.30. Present value: Congress and the President have decided to increase the federal tax rate in an effort to reduce the budget deficit. Suppose that Caroline Weslin, from problem 5.29, will pay 35 percent of her bonus to the federal government for taxes if she accepts the bonus today and 40 percent if she receives her bonus in two years. Will the increase in tax rates affect her decision?

Solution: Yes. It will affect her decision.

If Caroline accepts the bonus today, after paying the taxes, she will have $1,820 × (1 - 0.35) = $1,183.00 left over.

If she waits two years and pays the high tax rate, the present value of what she will have left over is only $1,869 × (1 - 0.40) = $1,121.40.

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

ADVANCED 5.31 You have $2,500 that you want to invest in your classmate’s start-up business. You believe the business idea to be great and hope to get $3,700 back at the end of three years.

If all goes according to the plan, what will be the return on your investment?

Solution: 0 3 years ├────────────────────┤ PV = -$2,500 FV3 = $3,700 Amount invested in project = PV = $2,500 Expected return three years from now = FV =$3,700 To calculate the expected rate of return, we set up the future value equation.

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FV 3 =PV  (1+ i)3 $3,700= $2,500(1 + i = )3 3 (1 + i) =1.4800 $3,700 $2,500 1 i =(1.4800) 3 −1 = 0.1396 =13.96% Financial Calculator Solution : 3 N

-2100 PV

i 21.32

0 PMT

3750 FV

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.32 Patrick Seeley has $2,400 to invest. His brother approached him with an investment opportunity that could double his money in four years. What interest rate would the investment have to yield in order for Patrick’s brother to deliver on his promise?

Solution: 0 4 years ├────────────────────┤ PV = -$2,400 FV4 = $4,800 Amount invested in project = PV = $2,400 Expected return three years from now = FV =$4,800 Investment period = n = 4 years To calculate the expected rate of return, we set up the future value equation.

FV4= PV × (1 +𝑖)4 $4,800 = $2,400 × (1+𝑖)4 (1 +𝑖)4 =

$4,800 $2,400

= 2.0000

i = (2.000)1/4 – 1 = 0.1892 .

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= 18.92% Financial Calculator Solution : 4 N

i 18.92

-2,400 PV

0 PMT

4,800 FV

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.33 You have $12,000 in cash. You can deposit it today in a mutual fund earning 8.2 percent compounded semiannually, or you can wait, enjoy some of it, and invest $11,000 in your brother’s business in two years. Your brother is promising you a return of at least 10 percent on your investment. Whichever alternative you choose, you will need to cash in at the end of 10 years. Assume your brother is trustworthy and that both investments carry the same risk. Which one would yield the largest amount in 10 years?

Solution: Option 1: Invest in account paying 8.2 percent semiannually for 10 years.

0 10 years ├────────────────────┤ PV = -$12,000 FV10 = ?

Amount invested in project = PV = $12,000 Investment period = n = 10 years Interest earned on investment = i = 8.2% Frequency of compounding = m = 2 Value of investment after 10 years = FV10 210

 0.082  FV10= PV  1+ 2   = $26,803.77

= $12,000 (2.23365)

Financial Calculator Solution : 20 N

.

4.1 i

-12,000 PV

0 PMT

FV 26,803.77

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Option 2: Invest in brother’s business to earn 10 percent for eight years.

0 8 years ├────────────────────┤ PV = -$11,000 FV8 = ?

Amount invested in project = PV = $11,000 Investment period = n = 8 years Interest earned on investment = i = 10% Frequency of compounding = m = 1 Value of investment after 8 years = FV8 8 FV 8 = PV (1+ 0.10) =$11,000 (2.14359) = $23,579.48 You are better off investing today in the mutual fund and earn 8.2 percent semiannually for 10 years.

Financial Calculator Solution : 8 N

10 i

-11,000 PV

0 PMT

FV 23,579.48

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.34 When you were born your parents set up a bank account in your name with an initial investment of $5,000. You are turning 21 in a few days and will have access to all your funds. The account was earning 7.3 percent for the first seven years, but then the rates went down to 5.5 percent for six years. The economy was doing well from 2007 to 2009, and your account earned 8.2 percent three years in a row. Unfortunately, the next two years you earned only 4.6 percent. Finally, as the economy recovered, the return jumped to 7.6 percent for the last three years. a.

How much money was in your account at the end of Year 16? b.

How much money is in your account now, at the end of year 21? c.

What would be the balance now if your parents made another deposit of $1,200 at the end of year 7?

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Solution:

a.

0 1 7 13 14 15 16 21 years ├───┼∙∙∙∙∙∙∙∙∙∙┼∙∙∙∙∙∙∙∙∙∙∙∙────┼────┼───┼───∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙──┤ PV = -$5,000 FV21 = ? i1 = 7.3% i2 = 5.5% i3 = 8.2% i4 = 4.6% i5 = 7.6% Initial investment = PV = $5,000 Interest rate for first 7 years = i1 = 7.3% Interest rate for next 6 years = i2 = 5.5% Interest rate for next 3 years = i3 = 8.2% Investment value at age 16 years = FV16 FV 16 = PV  (1 +i7 1) (1+2) i 6 (1+3) i 3 7 = $5,000  (1 + 0.073)  (1.055)6  (1.082)3

= $5,000  (1.6376)  (1.3788)  (1.2667) =$14,300.55

b.

Interest rate for from age 17 to 18 = i4 = 4.6% Interest rate for next 3 years = i5 = 7.6% Investment at start of 16th year = PV = $14,300.95 Investment value at age 21 years = FV21 FV 21 = FV16 (1 +i 4)2 (1 +i 5)3

2 = $14,300.55 (1 + 0.046)  (1.076)3

= $14,300.55  (1.0941)  (1.2458)) =$19,492.38

c.

Additional investment at start of 8th year = $1,200 Total investment for next 7 years = $8,187.82 + $1,200 = $9,387.82 Interest rate for next 6 years (years 8–13) = i2 = 5.5% Interest rate for years 14 to 16 = i3 = 8.2% Interest rate for from age 17 to 18 = i4 = 4.6% Interest rate for next 3 years = i5 = 7.6% Investment value at age 21 = FV21 6 )3i (1 + 4 ) 2i(1 + 5)3i FV 21 = FV7  (1+ i2) (1+

3  (1.082)32  (1.046) $9,387.82  (1.055)

 (1.076)3 (1.2458) = $9387.82  (1.3788)  (1.2667)  (1.0941)

=

6

= $22, 349.16 LO 2

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Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.35 Jared Goff, the number 1 draft pick of the NFL Los Angeles Rams in 2016, and his agent are evaluating three contract options. Each option offers a signing bonus and a series of payments over the life of the contract. Goff uses a 10.25 percent rate of return to evaluate the contracts. Given the cash flows for each option, which one should he choose?

Option Year C Cash Flow Type Option A Option B 0 Signing Bonus $3,100,000 $4,000,000 $4,250,000 1 Annual Salary $ 650,000 $ 825,000 $ 550,000 2 Annual Salary $ 715,000 $ 850,000 $ 625,000 3 Annual Salary $ 822,250 $ 925,000 $ 800,000 4 Annual Salary $ 975,000 $1,250,000 $ 900,000 5 Annual Salary $1,100,000 $1,000,000 6 Annual Salary $1,250,000 Solution: To decide on the best contract from Jared Goff’s viewpoint, we need to find the present value of each option. The contract with the highest present value should be the one chosen.

Option A: Discount rate to be used = i= 10.25% Present value of contract = PVA $650,000 $715,000 $822,250 $975,000 $1,100,000 $1,250,000 + + (1.1025)3+ + + PVA = $3,100,000+ (1.1025)1 (1.1025)2 (1.1025)4 (1.1025)5 (1.1025)6 $3,100,000+$589,569 = + $588,232 + $613,576 + $659,918 + $675,305 + $696,047 $6,9 2 2,6 4 7 = Option B: Discount rate to be used = i= 10.25% Present value of contract = PVB $825,00 $850,000 $925,000 $1,250,000 + (1.1025)2 + (1.1025)3+ PVB = $4,0 0 0,0 0+0 (1.1025)4 0 = $4,0 0 0,0 0+0(1.1025) + $699,297+$690,249+$846,049

= $6,983,894 1 $748,29 Option C: 9 .

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Discount rate to be used = i= 10.25% Present value of contract = PVC $550,000 $625,000 $800,000 $900,000 $1,000,000 + + (1.1025)3+ (1.1025)4 + PVC = $4,250,00 + (1.1025)1 (1.1025)2 (1.1025)5 =0 + $498,866+$514,189+$596,972+$609,155+$613,913

= $7,083,096 $4,250,00 Option C is the best choice forJared Goff .

LO 3

0

Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.36 Surmec, Inc., reported sales of $2.1 million last year. The company’s primary business is the manufacture of nuts and bolts. Since this is a mature industry, analysts are confident that sales will grow at a steady rate of 7 percent per year. The company’s net income equals 23 percent of sales. Management would like to buy a new fleet of trucks but can only do so once the net income reaches $620,000 a year. At the end of what year will Surmec be able to buy the trucks? What will sales and net income be in that year?

Solution: Current level of sales for Surmec = PV = $2,100,000 Profit margin = 23% Net Income for the year = 0.23 x $2,100,000 = $483,000 Target profit level in the future = FV = $620,000 Projected growth rate of sales = g = 7% To calculate the time needed to reach the target FV, we set up the future value equation.

FV𝑛=PV ×(1 +g) 𝑛 $620,000 = $483,000 × (1.07)𝑛 $620,000 (1.07)𝑛 = = 1.2836 $483,000 n × ln(1.07) = ln(1.2836) ln(1.2836) n =Solution: = 3.7 years Financial Calculator ln (1.07)

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N 3.69

7 i

-483,000 PV

0 PMT

Solutions Manual

620,000 FV

The company achieves its profit target during the fourth year.

Sales level at end of year 4 = FV4 n FV n=PV(1+g) = $2,100,000 (1.07)4 = $2,752,671.62

Profit for the year = $2,752,671.62 x 0.23 = $633,114.47 Financial Calculator Solution : 4 N

7 i

-483,000 PV

0 PMT

FV 633,114.47

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.37 You will be graduating in two years and are thinking about your future. You know that you will want to buy a house five years after you graduate and that you will want to put down $60,000. As of right now, you have $8,000 in your savings account. You are also fairly certain that once you graduate, you can work in the family business and earn $32,000 a year, with a 5 percent raise every year. You plan to live with your parents for the first two years after graduation, which will enable you to minimize your expenses and put away $10,000 each year. The next three years, you will have to live on your own, as your younger sister will be graduating from college and has already announced her plan to move back into the family house. Thus, you will be able to save only 13 percent of your annual salary. Assume that you will be able to earn 7.2 percent on the savings from your salary. At what interest rate will you need to invest the current savings account balance in order to achieve your goal? Hint: Draw a time line that shows all the cash flows for years 0 through 7. Remember, you want to buy a house seven years from now and your first salary will be in Year 3.

Solution:

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0 1 2 3 4 5 6 7 ├─────┼──────┼─────┼─────┼──────┼─────┼──── $10,000 $10,000 $4,586.40 $4,815,72 $5,056.48 Starting salary in year 3 = $32,000 Annual pay increase = 5% Savings in first 2 years = $10,000 Savings rate for years 3 to 7 = 13% Year 1 2 3 4 5 6 7 Salary $0 $0 $32,000 $33,600 $35,280 $37,044 $38,896 Savings $0 $0 $10,000 $10,000 $4,586.40 $4,815.72 $5,056.48 Investment rate = i = 7.2% Future value of savings from salary = FV7 4 3 FV7 = $0 + $0 + $10,000 × (1.072) + $10,000 × (1.072) + $4,586.40 x (1.072) = $4,815.72 X (1.072)1 + $5,056.48 x (1.072)0 = $13,206.24 + $12,319.25 + $5,270.62 + $5,162.45 + $5,056.48 = $41,015.07

2

Target down payment = $60,000 Amount needed to reach target = $60,000 - $41,015.07= FV = $18,984.93 Current savings balance = PV $8,000 Time to achieve target = n = 7 years.

To solve for the investment rate needed to achieve target, we need to set up the future value equation: FV = PV × (1 +𝑖)7 $18, 984.93 = $8,000 × (1 +𝑖)7

7 $18,984.98

(1 +𝑖) +

$8,000

= 2.3731 1

i = (2.3731)7 − 1 = 1.1314 − 1 = 13.14% Financial Calculator Solution: 7 N

i 13.14

-8,000 PV

0 PMT

18,984.93 FV

LO 2

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Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

Sample Test Problems 5.1

Holding all else constant, what will happen to the present value of a future amount if you increase the discount rate? What if you increase the number of years?

Solution: Holding all else constant, both increasing the discount rate and increasing the number of years, will decrease the present value.

LO 3 Bloomcode: Comprehension AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.2

Juliette Bronson anticipates needing $500,000 to start a business. If she can earn 4.5 percent compounded annually on her investments, how much money would Juliette have to invest today to have $500,000 in three years?

Solution: 0 3 Year 1 2 ├─4─.5─%─ ────────────────┤ PV = ?

FV3 = $500,000 Amount required at end on investment period = FV3 = $500,000 Return expected from investment = i = 4.5% Duration of investment = n = 3 years Amount to be invested today = PV FV n $500,000 = PV = 1+i) n (1.045)3 ( $438,148.30 =

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Financial Calculator Solution : 3 N

4.5 i

PV -438,148.30

0 PMT

500,000 FV

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.3

Christopher Thompkins must decide how to invest $10,000 that he just inherited. What would be the future value of his investment after five years under each of the following three investment opportunities? a. 6.28% compounded quarterly. b. 6.20% compounded monthly. c. 6.12% compounded continuously.

Solution: a.

Interest rate on investment = i = 6.28% Frequency of compounding = m = 4 Value of investment after 5 years = FV5 mxn

4x5

 i  0.0628 = $10,000  1 + FV 5 =PV 1 +   4   m   =$1 0,0 00(1.01570)20= $13,655.55 Financial Calculator Solution : 20 N

1.57 i

b.

-10,000 PV

0 PMT

FV 13,655.55

Interest rate on investment = i = 6.20% Frequency of compounding = m = 12 Value of investment after 5 years = FV5 mxn 12x5  i  0.0620 = $10,000  1 + FV 5 =PV 1 +   4   m   =$1 0,0 00(1.00517)60=$13,623.37

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Financial Calculator Solution : 60 N

0.51667 i

c.

-10,000 PV

0 PMT

FV 13,623.37

Interest rate on investment = i = 6.12% Frequency of compounding = m = Continuous Value of investment after 5 years = FV5 FV5 = PV ein= $10, 000e0.06125 = $10, 000 1.358= $13, 579.82

LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.4.

Tina DeLeon deposited $2,500 today in an account paying 6 percent interest annually.

What would be the simple interest earned on this investment in five years? With annual compounding, how much interest-on-interest would Tina earn in five years?

Solution: 0 2 4 5 years 3 1 ├────────────────────┤ PV = -$2,500 FV5 = ?

Amount invested today = PV = $2,500 Return expected from investment = i = 6% Duration of investment = n = 5 years Frequency of compounding = m = 1 Value of investment after 5 years = FV5

FV 5 = PV  (1 +i ) n = $2501 ,0(.06) = $3,345.56

5

Financial Calculator Solution:

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Fundamentals of Corporate Finance, 4th edition

5 N

6 i

-2,500 PV

0 PMT

Solutions Manual

FV 3,345.56

Simple interest on investment = $2,500 × 0.06 × 5 = $750 Interest-on-interest = FV5 – PV – simple interest on investment Interest-on-interest = $3,345.56 – $2,500 – $750 = $95.56

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.5

The state of Texas had 42,725 active patient care physicians in 2013 and by 2017 this number had grown to 47,663. What was the compound annual growth rate (CAGR) in the number of active care physicians during this period?

Solution: 0 4 years 2 3 1 ├────────────────────┤ PV = -42,725 FV4 = 47,663 Number of physicians in 2013 = PV = 42,725 Number of physicians in 2017 = FV4 = 47,663 Years to maturity = n = 4 years. growth rate = i FV n PV = n i (1+)

42, 725=

47, 663 (1+i)4

$47, 663 =1.1156 $42, 725 i = (1.1156)1 4 −1

(1+i)4 =

i = 0.0277, or 2.77% The CAGR was 2.77 percent Financial Calculator Solution: .

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4 N

i 2.77

-42,725 PV

0 PMT

Solutions Manual

47,663 FV

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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Chapter 6 Discounted Cash Flows and Valuation Before You Go On Questions and Answers Section 6.1 how to calculate the future value of a stream of cash flows.

Explain 1.

It would helpful to first construct a time line so that we can identify the timing of each cash flow. Then you would calculate the future value of each individual cash flow.

Finally, you would add up the future values of all the individual cash flows to determine the future value of the cash flow stream.

2.

Explain how to calculate the present value of a stream of cash flows.

To calculate the present value of a stream of cash flows, you should first draw a time line so that you can see that each cash flow is placed in its correct time period. Then you simply calculate the present value of each cash flow for its time period, and finally you add up all the present values.

3.

Why is it important to adjust all cash flows to a common date?

When making economic decisions, we need to compare “apples to apples.” This is possible only when we bring all the cash flows to a common date, which can either be a present time or some future date. The reason is the time value of money: a dollar today is worth more than a dollar in the future. Thus, when cash flows are converted to the same time period, the time value of money concept holds true, and we can concentrate on the economic aspects of the decision.

Section 6.2 1.

How do an ordinary annuity, an annuity due, and a perpetuity differ?

Ordinary annuity assumes that the cash flows occur at the end of a period. Most types of loans are ordinary annuities. On the other hand, annuity due is an annuity whose payment is to be made immediately (or at the beginning of a period) instead of at the end of the period. For example, in many leases the first payment is due immediately, and each successive payment must be made at the beginning of the month. Perpetuity is a special case of annuity, and it refers to a constant stream of identical cash flows with no end.

2.

Give two examples of perpetuities.

The text gives the example of British government bonds called consols that have no maturity and have been traded in the markets since the end of the Napoleonic wars.

Copyright ©2015 John Wiley & Sons, Inc.

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Another example could be a preferred stock of a company that has no maturity and will pay a constant dividend forever.

3.

What is the annuity transformation method?

The annuity transformation method refers to the conversion of an ordinary annuity to annuity due. In this process, you first plot all the cash flows on a time line as if the cash flows were an ordinary annuity. Then you calculate the present or future value factor as you would with an ordinary annuity, and finally, you multiple your answer by (1 + i).

Conveniently, this relationship works for both present and future value calculations.

Section 6.3 1.

What is the difference between a growing annuity and a growing perpetuity?

A stream of cash flows that is growing at a constant rate over time can be called a growing annuity or growing perpetuity. If the cash flows extend over a finite length of time, then we call it a growing annuity and can use Equation6.5 to compute the present value. If the growth will continue for a very long time period and perhaps, forever, we refer to it as the growing perpetuity. We would then use Equation 6.6 to estimate the present value of this cash flow stream.

Section 6.4 1.

What is the APR, and why are lending institutions required to disclose this rate?

APR, or the annual percentage rate, is the annualized interest rate using simple interest. It is defined as the simple interest charged per period multiplied by the number of compounding periods per year. Lending institutions are mandated by Federal Truth-inLending Act regulations to disclose this rate to essentially make it easier for consumers to be exposed to the same kind of rate by all businesses.

2.

What is the correct way to annualize an interest rate in financial decision making?

The correct way to annualize interest rates is by computing the effective annual interest rate (EAR). This is the annual growth rate that allows for compounding, which means you earn interest on interest. To calculate the EAR, take the quoted rate and divide it by the number of compounding periods (quoted rate/m). Then take the resulting interest rate, add 1 to it, and raise it to the power equal to m. Finally, subtract 1 and the result is EAR. Show formula: 𝑟 𝑚 𝐸𝐴𝑅=(1+ ) −1 𝑚

3.

Distinguish between quoted interest rate, interest rate per period, and effective annual interest rate.

Copyright ©2015 John Wiley & Sons, Inc.

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Quoted interest rate, such as APR, is the interest rate that has been annualized by multiplying the rate per period by the number of compounding periods. Interest rate per period is the quoted rate per period. It can be stated in the form of an APR—in that case, just divide it by the number of compounding periods to obtain the interest rate per period.

Finally, EAR is the annual rate of interest that accounts for the effects of compounding.

Self-Study Problems 6.1

Kronka, Inc., is expecting cash inflows of $13,000, $11,500, $12,750, and $9,635 over the next four years. What is the present value of these cash flows if the appropriate discount rate is 8 percent?

Solution: The time line for the cash flows and their present value is as follows: 0 8% 1 2 3 4 Year ├─────────┼─────────┼─────────┼───────── $13,000 $11,500 $12,750 $9,635 $13,000 $11,500 $12,750 $9,635 + + + PV 4 = (1.08)2 (1.08)3 (1.08)4 (1.08) = $12,037.03+$9,859.40+$10,121.36+$7,082.01

= $39,099.80 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -13,000 1 1 11,500 1 2 12,750 1 3 9,635 1 4 Then solve by pressing NPV, enter the rate of 8% and compute NPV= 39,099.81 LO: 4 Level: Basic

6.2

Your grandfather has agreed to deposit a certain amount of money each year into an account paying 7.25 percent annually to help you go to graduate school. Starting

Copyright ©2015 John Wiley & Sons, Inc.

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next year, and for the following four years, he plans to deposit $2,250, $8,150, $7,675, $6,125, and $12,345 into the account. How much will you have at the end of the five years?

Solution: The time line for the cash flows and their future value is as follows:

0 7.25% 1 2 3 4 5 Year ├────────┼────────┼────────┼─────────┼──────── -$2,250 -$8,150 -$7,675 -$6,125 -$12,345 FV = [$2,250 x (1.0725)]4 + [$8,150 x (1 .0725)3] + [$7,675 x (1.0725)2] + [$6,125 x 1.0725] + 5 $12,345 = $2,976.95 + $10,054.25 + $8,828.22 + $6,569.06 + $12,345 = $40,773.48 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 2,250 1 2 8,150 1 7,675 1 3 6,125 1 4 12,345 1 5 Then solve by pressing NPV, enter the rate of 7.25% and compute NPV= 28,733.68.

Set N=5, i=7.25, PV=28,733.68, PMT=0 and solve for FV= -40,773.48 LO: 2 Level: Basic 6.3

Mike White is planning to save up for a trip to Europe in three years. He will need $7,500 when he is ready to make the trip. He plans to invest the same amount at the end of each of the next three years in an account paying 6 percent. What is the amount he will have to save every year to reach his goal of $7,500 in three years?

Solution: Amount Mike White will need in three years = FVA = $7,500 3 Number of years = n = 3

Copyright ©2015 John Wiley & Sons, Inc.

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Solutions Manual

Interest rate on investment = i = 6.0% Amount needed to be invested every year = PMT = ?

0 6% 1 2 3 Year ├─────────┼──────┼───────┤ CF=?

CF=?

CF=? FVA3 = $7,500

FVA n =CF $7, 500= CF

(1 + i) n − 1 i (1 + 0.06)3− 1 0.06

= CF  3.1836 $7, 500 3.1836 $2, = 355.82 Mike will have to invest $2,355.82 every year for the next three years.

CF =

Financial Calculator Solution : 3 N

6 I

0 PV

PMT -2,355.82

7,500 FV

LO: 5 Level: Basic 6.4

Becky Scholes has $150,000 to invest. She wants to be able to withdraw $12,500 every year forever without using up any of her principal. What interest rate would her investment have to earn in order for her to be able to do so?

Solution: Present value of Becky Scholes’s investment = $150,000 Amount needed annually = $12,500 This is a perpetuity!

CF PVP= 𝑖 CF $12,500 = PVP $150,000 𝒊=𝟖.𝟑𝟑% 𝑖=

Copyright ©2015 John Wiley & Sons, Inc.

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LO: 6 Level: Basic

6.5

Dynamo Corp. is expecting annual payments of $34,225 for the next seven years from a customer. What is the present value of this annuity if the discount rate is 8.5 percent?

Solution: The time line for Dynamo’s cash flows and their present value is as follows: 0 8.5% 1 2 3 4 5 6 7 Year

PVA = ?

$34,225

$34,225

$34,225

PVA 7 =CF

$34,225 $34,225 $34,225

$34,225

1−1 (1+ i)n i

1 − 1 (1.085)7 = $34, 225  0.085 = $34, 225  5.1185 = $175, 181.14 Financial Calculator Solution : 7 N

8.5 i

PV 175,181.14

-34,225 PMT

0 FV

LO: 2 Level: Basic

Discussion Questions 6.1

Identify the steps involved in computing the future value when you have multiple cash flows.

First, prepare a time line to identify the size and timing of the cash flows. Second, calculate the present value of each individual cash flow using an appropriate discount rate. Finally, add up the present values of the individual cash flows to obtain the present

Copyright ©2015 John Wiley & Sons, Inc.

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value of a cash flow stream. This approach is especially useful in the real world where the cash flows for each period are not the same.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.2

What is the key economic principle involved in calculating the present value or future value of multiple cash flows?

Regardless of whether you are calculating the present value or the future value of a cash flow stream, the key idea is to discount or compound the cash flows to the same point in time.

LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.3

What is the difference between a perpetuity and an annuity?

A cash flow stream that consists of the same amount being received or paid on a periodic basis for a limited time period is called an annuity. If the same payments are made periodically forever, the contract is called a perpetuity.

LO: 2 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.4

Define annuity due. Would an investment be worth more if it were an ordinary annuity or an annuity due? Explain.

When annuity cash flows occur at the beginning of each period, it is called an annuity due. Annuity due will result in a bigger investment than an ordinary annuity because each cash flow will accrue an extra interest payment.

LO: 2 Level: Basic

Copyright ©2015 John Wiley & Sons, Inc.

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Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.5

Raymond Bartz is trying to choose between two equally risky annuities, each paying $5,000 per year for five years. One is an ordinary annuity, the other is an annuity due. Which of the following statements is most correct? a. The present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due. b. The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity. c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity. d. If interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same.

The answer is c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity.

LO: 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.6

Which of the following investments will have the highest future value at the end of three years? Assume that the effective annual rate for all investments is the same. a. You earn $3,000 at the end of three years (a total of one payment). b. You earn $1,000 at the end of every year for the next three years (a total of three payments). c. You earn $1,000 at the beginning of every year for the next three years (a total of three payments).

The answer is c. Earning $1,000 at the beginning of each year for the next three years will have the highest future value as it is an annuity due.

LO: 2

Copyright ©2015 John Wiley & Sons, Inc.

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Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Explain whether or not each of the following statements is correct. a. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same amount and same interest rate. b. If an investment pays 10 percent interest compounded annually, its effective rate will also be 10 percent.

Statement A is a true statement. The 15-year mortgage will have higher monthly payments since more of the principal will have to be paid each month than in the case of a 30-year mortgage.

Statement B is true since the frequency of compounding is annual and hence the rate for a single period is the same as the rate for a year.

LO: 2, 4 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.7

6.8

When will the annual percentage rate (APR) be the same as the effective annual rate (EAR)?

The annual percentage rate (APR) will be the same as the effective annual rate only if the compounding period is annual, not otherwise.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.9

Why is the effective annual rate (EAR) superior to the annual percentage rate (APR) in measuring the true economic cost or return?

Unlike the APR, which reflects annual compounding, the EAR takes into account the actual number of compounding periods. For example, suppose there are two investment alternatives that both pay an APR of 10 percent. Assume that the first pays interest annually and that the second pays interest quarterly. It would be a mistake to assume that

Copyright ©2015 John Wiley & Sons, Inc.

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both investments will provide the same return. The real return on the first one is 10 percent, but the second investment actually provides a return of 10.38 percent because of the quarterly compounding. Thus, this is the superior investment.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.10 Suppose three investments have equal lives and multiple cash flows. A high discount rate tends to favor: a. The investment with large cash flows early. b. The investment with large cash flows late. c. The investment with even cash flows. d. None of the investments since they have equal lives.

The correct answer is .aThe investment with large cash flows early will be worth more compared to the one with the large cash flows late. The cash flows that come in later will have a heavier penalty when using a higher discount rate. Thus the investment with large cash flows early will be favored.

LO: 4 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Questions and Problems BASIC 6.1

Future value with multiple cash flows:Konerko, Inc., management expects the company to earn cash flows of $13,227, $15,611, $18,970, and $19,114 over the next four years. If the company uses an 8 percent discount rate, what is the future value of these cash flows at the end of year 4?

Solution: 0 8% 1 2 3 4 ├───────┼────────┼───────┼────────┤ Copyright ©2015 John Wiley & Sons, Inc.

SM 6-10

Fundamentals of Corporate Finance, 4th edition

$13,227

$15,611

Solutions Manual

$18,970

$19,114

FV4= [$13,227× (1.08)3 ] + [$15,611× (1.08)2 ] + [1$8,97 0× (1.08)1 ] + $19,114 = $16,662.21 + $18,208.67 + $20,487.60 + $19,114 = $74,472.48 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 13,227 1 2 15,611 1 3 18,970 1 4 19,114 1 Then solve by pressing NPV, enter the rate of 8% and compute NPV= - 54,739.50.

To get Future Value: 4 N

8 i

-54,739.50 PV

0 PMT

FV 74,472.48

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Future value with multiple cash flows: Ben Woolmer has an investment that will pay him the following cash flows over the next five years: $2,350, $2,725, $3,128, $3,366, and $3,695. If his investments typically earn 7.65 percent, what is the future value of the investment’s cash flows at the end of five years?

Solution: 0 7.65% 1 2 3 4 5 Year ├───────┼────────┼───────┼────────┼───────┤ $2,350 $2,725 $3,128 $3,366 $3,695 6.2

Copyright ©2015 John Wiley & Sons, Inc.

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+$2,725(1.0765)3 +$3,128 (1.0765)2 +$3,366 (1.0765)1+  $3,695 FV 5= $2,350(1.0765)4 = $3,155.91 + $3, 399.45 + $3, 624.89 + $3, 623.50 + $3, 695 = $17, 498.75 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 2,350 1 2 2,725 1 3 3,128 1 4 3,366 1 5 3,695 1 Then solve by pressing NPV, enter the rate of 7.65% and compute NPV= - 12,104.22.

To get Future Value: 5 N

7.65 i

12,104.22 PV

0 PMT

FV -17,498.75

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.3

Future value with multiple cash flows: You are a freshman in college and are planning

a trip to Europe when you graduate from college at the end of four years. You plan to save the following amounts annually, starting today: $625, $700, $700, and $750. If you can earn 5.75 percent annually, how much will you have at the end of four years?

Solution: 0 5.75% 1 2 3 4 Year ├───────┼────────┼───────┼────────┤ $625 $700 $700 $750 ?

Copyright ©2015 John Wiley & Sons, Inc.

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+ $750(1.0575) FV 4=$625(1.0575)4 + $700(1.0575)3 + $700(1.0575)2 = $781.63+$827.83+$782.81+793.13 = $3,185.40 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 625 -1 700 2 2 750 1 Then solve by pressing NPV, enter the rate of 5.75% and compute NPV= - 2,547.08.

To get Future Value: 4 N

5.75 i

-2,547.08 PV

0 PMT

FV 3,185.40

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.4

Present value with multiple cash flows: Saul Cervantes has just purchased some equipment for his landscaping business. For this equipment he must pay the following amounts at the end of each of the next five years: $10,450, $8,500, $9,675, $12,500, and $11,635. If the appropriate , what is the cost in today’s dollars of the equipment Saul purchased today?

Solution: 0 10.875% 1 2 3 4 5 Year ├───────┼────────┼───────┼────────┼───────┤ $10,450 $8,500 $9,675 $12,500 $11,635

Copyright ©2015 John Wiley & Sons, Inc.

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$12,500 $11,635 $9,675 $8,500 $10,450 + (1.10875)3 + + + 2 (1.10875)4 (1.10875)5 (1.10875) (1.10875) = $9,425.03+ $6,914.35+ $7,098.23 + 8,271.33 + $6,943.82 = $38,652.76

PV =

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 10,450 1 2 8,500 1 3 9,675 1 4 12,500 1 5 11,635 1 Then solve by pressing NPV, enter the rate of 10.875% and compute NPV= - 38,652.76.

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.5

Present value with multiple cash flows: Jeremy Fenloch borrowed some money from his friend and promised to repay him $1,225, $1,350, $1,500, $1,600, and $1,600 over the next five years. If the friend normally discounts investments at 8 percent annually, how much did Jeremy borrow?

Solution: 0 8% 1 2 3 4 5 Year ├───────┼────────┼───────┼────────┼───────┤ $1,225 $1,350 $1,500 $1,600 $1,600 $1,225 $1,350 $1,500 $1,600 $1,600 + + (1.08)3 + + (1.08)4 (1.08)5 (1.08) (1.08)2 = $1,134.26+$1,157.41+$1,190.75+$1,176.05+$1,088.93 = $5,747.40

PV =

Financial Calculator Solution:

Copyright ©2015 John Wiley & Sons, Inc.

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Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 Frequency (F) 1,225 1,350 -1112 0 1,500 1,600 1 2 3 4 Then solve by pressing NPV, enter the rate of 8% and compute NPV= 5,747.40.

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.6

Present value with multiple cash flows: Biogenesis Inc. management expects the following cash flow stream over the next five years. They discount all cash flows using a 23 percent discount rate. What is the present value of this cash flow stream?

1 2 3 4 5 Year ┼────────┼───────┼────────┼───────┤ -$1,133,676 -$978,452 $275,455 $878,326 $1,835,444 Solution: 0 23% 1 2 3 4 5 ├───────┼────────┼───────┼───── ───┼───────┤ -$1,133,676 -$978,452 $275,455 $878,326 $1,835,444

Year

− $1,133,676 − $978,452 $275,455 $878,326 $1,835,444 + + + + PV = (1.23)2 (1.23)3 (1.23)4 (1.23)5 (1.23) =− $921,687.80− $646,739.37+$148,025.09+$383,738.43.+$651,951.94 = −$384,711.72

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 -1,133,676 1

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2 -978,452 1 3 275,455 1 4 878,326 1 5 1,835,444 1

Then solve by pressing NPV, enter the rate of 23% and compute NPV= - 384,711.72.

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.7

Present value of an ordinary annuity: An investment opportunity requires a payment of $750 for 12 years, starting a year from today. If your required rate of return is 8 percent, what is the value of the investment to you today?

Solution: 0 8% 1 2 3 11 12 Year ├───────┼────────┼───────┼………………┼───────┤ $750 $750 $750 $750 $750 Annual payment = PMT = $750 No. of payments = n = 12 Required rate of return = 8% Present value of investment = PVA12 1 1− (1+i)n PVA n =PMT  i

1− = $750

1 (1.08)12 = $750 7.5361 0.08

= $5, 652.06 Financial Calculator Solution : 12 N

8 i

PV

750 PMT

0 FV

-5,652.06

Copyright ©2015 John Wiley & Sons, Inc.

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LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.8

Present value of an ordinary annuity: Dynamics Telecommunications Corp. has made an investment in another company that will guarantee it a cash flow of $22,500 each year for the next five years. If the company uses a discount rate of 15 percent on its investments, what is the present value of this investment?

Solution: 0 15% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ $22,500 $22,500 $22,500 $22,500 $22,500 Annual payment = PMT = $22,500 No. of payments = n = 5 Required rate of return = 15% Present value of investment = PVA5 1 1− (1+i)n PVA n =PMT  i − 1 1 (1.15)5 = $22, 500 3.3522 = $22, 500 0.15

= $75, 423.49 Financial Calculator Solution : 5 N

15 i

PV

22,500 PMT

0 FV

-75,423.49 LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Copyright ©2015 John Wiley & Sons, Inc.

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Future value of an ordinary annuity: Robert Hobbes plans to invest $25,000 a year at the end of each year for the next seven years in an investment that will pay him a rate of return of 11.4 percent. How much money will Robert have at the end of seven years?

Solution: 0 11.4% 1 2 3 6 7 Year ├───────┼────────┼───────┼………………┼───────┤ $25,000 $25,000 $25,000 $25,000 $25,000 6.9

Annual investment = PMT = $25,000 No. of payments = n = 7 Investment rate of return = 11.4% Future value of investment = FVA7 (1 + i) n − 1 FVA n = PMT  i = $25, 000

(1.114)7− 1 = $25, 000 9.9044 0.114

= $247, 609.95

Financial Calculator Solution : 7 N

11.4 i

0 PV

25,000 PMT

FV -247,609.95

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.10 Future value of an ordinary annuity: Cecelia Thomas is a sales executive at a Baltimore firm. She is 25 years old and plans to invest $3,000 every year in an IRA account, beginning at the end of this year until she reaches the age of 65. If the IRA investment will earn 9.75 percent annually, how much will she have in 40 years, when she turns 65?

Solution: 0 9.75% 1 2 3 39 40 Year ├───────┼────────┼───────┼………………┼───────┤ $3,000 $3,000 $3,000 $3,000 $3,000

Copyright ©2015 John Wiley & Sons, Inc.

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Annual investment = PMT = $3,000 No. of payments = n = 40 Investment rate of return = 9.75% Future value of investment = FVA40 (1+i)n−1 FVA = PMT n i

= $3,000

(1.0975)40 −1 =$3,000 413.5588 0.0975

= $1, 240, 676.41 Financial Calculator Solution : 40 N

9.75 i

0 PV

3,000 PMT

FV -1,240,676.41

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.11 Future value of an annuity due: Refer to Problem 6.10. If Cecelia Thomas invests at the beginning of each year, how much will she have at age 65?

Solution: 0 9.75% 1 2 3 39 40 Year ├───────┼────────┼───────┼………………┼───────┤ $3,000 $3,000 $3,000 $3,000 $3,000 Annual investment = PMT = $3,000 No. of payments = n = 40 Type of annuity = Annuity due Investment rate of return = 9.75% Future value of investment = FVA40

Copyright ©2015 John Wiley & Sons, Inc.

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FVA n = PMT 

(1+ i )n − 1

= $3,000

i

Solutions Manual

 (1 + i )

(1.0975)40− 1  (1.0975) = $3,000 413.55881.0975 0.0975

= $1, 361, 642.36

Financial Calculator Solution : BGN Mode 40 N

9.75 i

0 PV

3,000 PMT

FV -1,361,642.36

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.12 Computing annuity payment: Kevin Winthrop is saving for an Australian vacation in three years. He estimates that he will need $5,000 to cover his airfare and all other expenses for a week-long holiday in Australia. If he can invest his money in an S&P 500 equity index fund that is expected to earn an average annual return of 10.3 percent over the next three years, how much will he have to save every year if he starts saving at the end of this year?

Solution: 0 10.3% 1 2 3 Year ├───────┼────────┼───────┤ PMT PMT PMT FVAn = $5,000 Future value of annuity = FVA = $5,000 Return on investment = i = 10.3% Payment required to meet target = PMT Using the FVA equation:

Copyright ©2015 John Wiley & Sons, Inc.

SM 6-20

Fundamentals of Corporate Finance, 4th edition

FVA n = PMT

(1+ i) n − 1 i

$5,000 = PMT 

(1.103)3 − 1 0.103

PMT=

Solutions Manual

$5,000 $5,000 = (1.103)3 −1 3.3196 0.103 = $1, 506.20

Kevin has to save $1,506.20 every year for the next three years to reach his target of $5,000.

Financial Calculator Solution : 3 N

10.3 i

0 PV

PMT 1,506.20

-5,000 FV

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.13 Computing annuity payment: The Elkridge Bar & Grill has a seven-year loan of $23,500 with Bank of America. It plans to repay the loan in seven equal installments starting today. If the rate of interest is 8.4 percent, how much will each payment be?

Solution: 0 1 2 3 6 7 Year ├───────┼────────┼───────┼………………┼───────┤ PMT PMT PMT PMT PMT PVAn = $23,500 n = 7; i = 8.4% Present value of annuity = PVA = $23,500 Return on investment = i = 8.4% Payment required to meet target = PMT Type of annuity = Annuity due Using the PVA equation:

Copyright ©2015 John Wiley & Sons, Inc.

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Fundamentals of Corporate Finance, 4th edition

PVA n = PMT PMT=

1 1− (1+i)n i

Solutions Manual

(1+i )

$23, 500 $23, 500 = 5.13591.084 1 1− (1.084)7  (1.084) 0.084

= $4, 221.07 Each payment made by Elkridge Bar & Grill will be $4,221.07, starting today.

Financial Calculator Solution : 7 N

8.4 i

0 PV

PMT -4,221.07

23,500 FV

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.14 Perpetuity: Your grandfather is retiring at the end of next year. He would like to ensure that his heirs receive payments of $10,000 a year forever, starting when he retires. If he can earn 6.5 percent annually, how much does your grandfather need to invest to produce the desired cash flow?

Solution: Annual payment needed = PMT = $10,000 Investment rate of return = i = 6.5% Term of payment = Perpetuity Present value of investment needed = PV PMT $10,000 = 0.065 PV of Perpetuity = i = $153,846.15 LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Copyright ©2015 John Wiley & Sons, Inc.

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6.15 Perpetuity: Calculate the annual cash flows for each of the following investments: a. $250,000 invested at 6% b. $50,000 invested at 12% c. $100,000 invested at 10% Solution: a.

Annual payment = PMT Investment rate of return = i = 6% Term of payment = Perpetuity Present value of investment needed = PV = $250,000 PMT PV of Perpetuity = i PMT = PV i=$250,0000.06 = $15,000 Annual payment = PMT b.

Investment rate of return = i = 12% Term of payment = Perpetuity Present value of investment needed = PV = $50,000

PMT i PMT = PV i=$50,0000.12 = $6,000

PV of Perpetuity =

c.

Annual payment = PMT Investment rate of return = i = 10% Term of payment = Perpetuity Present value of investment needed = PV = $100,000

PMT i PMT = PV  i = $100,0000.10 = $10,000

PV of Perpetuity =

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.16. Effective annual interest rate: Marshall Chavez bought a Honda Civic for $17,345. He put down $6,000 and financed the rest through the dealer at an APR of 4.9 percent for four years. What is the effective annual interest rate (EAR) if the loan payments are made monthly?

Solution:

Copyright ©2015 John Wiley & Sons, Inc.

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Loan amount = PV = $11,345 Interest rate on loan = i = 4.9% Frequency of compounding = m = 12 Effective annual rate = EAR m1

12

i   0.0 4 9 −1 EAR = 1+  −1= 1+ 12   m  =1.05−1=5% LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.17 Effective annual interest rate: Cyclone Rentals borrowed $15,550 from a bank for three years. If the quoted rate (APR) is 6.75 percent, and the compounding is daily, what is the effective annual interest rate (EAR)?

Solution: Loan amount = PV = $15,550 Interest rate on loan = i = 6.75% Frequency of compounding = m = 365 Effective annual rate = EAR m1

365

i   0.0675 EAR = 1 + m  − 1 =1 + 365     = 1.0698− 1=6.98%

−1

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.18 Growing perpetuity: You are evaluating a growing perpetuity investment from a large financial services firm. The investment promises an initial payment of $20,000 at the end of this year and subsequent payments that will grow at a rate of 3.4 percent annually. If you use a 9 percent discount rate for investments like this, what is the present value of this growing perpetuity?

Solution: Cash flow at t = 1 = CF1 = $20,000 Annual growth rate = g = 3.4% Discount rate = i = 9%

Copyright ©2015 John Wiley & Sons, Inc.

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Solutions Manual

Present value of growing perpetuity = PVA∞ CF1 $20,000 PVA = = (i−g) (0.09−0.034) = $357,142.86 LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

INTERMEDIATE

Future value with multiple cash flows:Trigen Corp. management will invest $331,000, $616,450, $212,775, $818,400, $1,239,644, and $1,617,848 in research and development over the next six years. If the appropriate interest rate is 6.75 percent, what is the future value of these investments eight years from today?

Solution: 0 6.75% 1 2 3 4 5 6 ├───────┼────────┼───────┼────────┼───────┼─── $331,000 $616,450 $212,775 $818,400 $1,239,644 $1,617,848 6.19

$331, 000  (1.0675)5  +$616, 450  (1.0675)4  + $212, 775  (1.0675)3    =  FV 8   (1.0675)2  +$1,239,644(1.0675)1+$1,617,848   + $818,  400  (1.0675)2

+ $1,617,848 = $458,846.49 + $800, 514.85 + $258,835.74 + $932, 612.84  (1.0675)2 + $1, 323, 319.97 = $5,391,977.89(1.0675)2 $6, 144, 462.11 =

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 0 1 331,000 2 616,450 3 212,775 4 818,400

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Frequency (F) -1 1 1 1

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1,239,644 1,617,848

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1 1

Then solve by pressing NPV, enter the rate of 6.75% and compute NPV=3,643,684.79.

Set N=8, i =6.75, PV=-3,643,684.79, PMT=0 and solve for FV= 6,144,462.10 LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.20 Future value with multiple cash flows: Stephanie Watson is 20 years old and plans to make the following investments beginning next year. She will invest $3,125 in each of the next three years and will then make investments of $3,650, $3,725, $3,875, and $4,000 over the following four years. If the investments are expected to earn 11.5 percent annually, how much will Stephanie have when she turns 30?

Solution: Expected rate of return = i = 11.5% Investment period = n = 7 years Future value of investment = FV 6 5 4 $3,125(1.115) +$3,125(1.115)+$616,450(1.115)     =  +$4,000 (1.115)3 FV 7 2 (1.115)+$3,875 (1.115)3 +    (1.115)1 $3,650 $3,725  +  

+ = $6,004.81 $5,385.48+ $4,830.03+ $5,059.61+ $4,631.01+ $4,320.63+ $4,0 =$34, 231.57 ( 1. 115)3  = $47, 451.66

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 3,125 3 2 3,650 1 3 3,725 1 4 3,875 1 5 4,000 1

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Then solve by pressing NPV, enter the rate of 11.5% and compute NPV=15,977.28.

Set N=10, i =11.5, PV=-15,977.28, PMT=0 and solve for FV= 47,451.66 LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.21 Present value with multiple cash flows: Carol Jenkins, a lottery winner, will receive the following payments over the next seven years. She has been approached by an investor who will pay Carol a lump sum today for the rights to those future cash flows. If she can invest her cash flows in a fund that will earn 10.5 percent annually, how much should Carol require the investor to pay for the cash flows?

0 1 2 3 4 5 6 7 Year ├────┼─────┼─────┼──────┼─────┼──────┼───── $200,000 $250,000 $275,000 $300,000 $350,000 $400,000 $550,000 Solution: Expected rate of return = i = 10.5% Investment period = n = 7 years Future value of investment = FV $200,000 $250,000 $275,000 $300,000 $350,000 $400,000 $550,000 + + + + + + FV 7= (1.105)1 (1.105)2 (1.105)3 (1.105)4 (1.105)5 (1.105)6 (1.105)7 = $180,995.48+$204,746.01+$203,819.56+$201,220.46+$212,449.96

+ $219,728.47+$273,417.77 = $1,496,377.71 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -0 200,000 1 1 250,000 1 2 275,000 1 3 300,000 1 4 350,000 1 5

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400,000 550,000

1 1

Then solve by pressing NPV, enter the rate of 10.5% and compute NPV=.

Set N=7, i =10.5, PV=-, PMT=0 and solve for FV= 1,496,377.71 LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.22 Computing annuity payment: Gary Whitmore is a high school sophomore. He currently has $7,500 in a savings account that pays 5.65 percent annually. Gary plans to use his current savings plus what he can save over the next four years to buy a car. He estimates that the car will cost $12,000 in four years. How much money should Gary save each year if he wants to buy the car?

Solution: Cost of car in four years = $12,000 Amount invested in money market account now = PV = $7,500 Return earned by investment = i = 5.65% Value of current investment in 4 years = FV4 FV=PV(1+i)4=$750106)4 ,0(.55 4 = $9,344.14 Balance of money needed to buy car = $12,000 – $9,344.14 = $2,655.86 = FVA Payment needed to reach target = PMT + i) n − 1 FVA= PMT (1 i

PMT=

$2, 655.86 $2, 655.86 FVA = = 4.351949 1−(1+i)n (1.0565)4 −1 0.0565 i = $610.27

Financial Calculator Solution : 4 N

5.65 i

-7,500 PV

Copyright ©2015 John Wiley & Sons, Inc.

0 PMT

FV 9,344.14

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4 N

5.65 i

0 PV

PMT -610.27

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2,655.86 FV

LO 1 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.23 Growing annuity: Modern Energy Company owns several gas stations. Management is looking to open a new station in the western suburbs of Baltimore. One possibility that managers at the company are evaluating is to take over a station located at a site that has been leased from the county. The lease, originally for 99 years, currently has 73 years before expiration. The gas station generated a net cash flow of $92,500 last year, and the current owners expect an annual growth rate of 6.3 percent. If Modern Energy uses a discount rate of 14.5 percent to evaluate such businesses, what is the present value of this growing annuity?

Solution: Time for lease to expire = n = 73 years Last year’s net cash flow = CF0 = $92,500 Expected annual growth rate = g = 6.3% Firm’s required rate of return = i = 14.5% Expected cash flow next year = CF1 = $92,500(1 + g) = $92,500(1.063) = $98,327.50 Present value of growing annuity = PVAn CF  1+gn   1.0 673  $98,327.50 1−   = (0.145−0.063)   1 −  PVA n = (i−g)   1+i    3 1.1  45  =$1,199,115.850.995593 =$1,193,831.54 LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.24 Future value of an annuity due: Jeremy Denham plans to save $5,000 every year for the next eight years, starting today. At the end of eight years, Jeremy will turn 30 years

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old and plans to use his savings toward the down payment on a house. If his investment in a mutual fund will earn him 10.3 percent annually, how much will he have saved in eight years when he buys his house?

Solution: 0 10.3% 1 2 3 7 8 Year ├───────┼────────┼───────┼………………┼───────┤ $5,000 $5,000 $5,000 $5,000 $5,000 Annual investment = PMT = $5,000 No. of payments = n = 8 Type of annuity = Annuity due Investment rate of return = 10.3% Future value of investment = FVA8 (1+ i )n − 1  (1+i) FVAn =PMT     i  (1.103)8 − 1 = $5,000 = $5,00011.56121.103  0.103 (1.103)  = $63,760.19 Financial Calculator Solution : BGN Mode 8 N

10.3 i

0 PV

5,000 PMT

FV -63,760.19

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.25 Present value of an annuity due: Grant Productions borrowed some money from the California Finance Company at a rate of 17.5 percent for a seven-year period. The loan calls for a payment of $1,540,862.19 each year beginning today. How much did Grant borrow?

Solution: 0 17.5% 1 2 3 6 7 ├───────┼────────┼───────┼………………┼───────┤ PMT =$1,540,862.19 at the beginning of each year

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Annual payment = PMT = $1,540,862.19 Type of annuity = Annuity due No. of payments = n = 7 Required rate of return = 17.5% Present value of investment = PVA8 1 1− (1+i)n (1+i) PVA n =PMT  i

= $1,540,862.19

1−

1 (1.175)7  (1.175) = $1,540,862.19 3.86631.175 0.175

= $6, 999, 999.98$7,  000, 000 Financial Calculator Solution : BGN Mode 7 N

i 17.6

0 PV

1,540,862.19 PMT

FV -6,999,999.98

LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.26 Present value of an annuity due: Sharon Kabana has won a state lottery and will receive a payment of $89,729.45 every year, starting today, for the next 20 years. If she invests the proceeds at a rate of 7.25 percent, what is the present value of the cash flows that she will receive? Round to the nearest dollar.

Solution: 0 7.25% 1 2 3 19 20 ├───────┼────────┼───────┼………………┼───────┤ PMT = $89,729.45 at the beginning of each year Annual payment = PMT = $89,729.45 Type of annuity = Annuity due No. of payments = n = 20 Required rate of return = 7.25% Present value of investment = PVA20

Copyright ©2015 John Wiley & Sons, Inc.

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PVA n =PMT 

1−

Solutions Manual

1 (1+i)n (1+i) i

= $89, 729.45

1−

1 (1.0725)20  (1.0725) = $89,729.4510.39121.0725 0.0725

= $999, 999.95$1,  000, 000 Financial Calculator Solution : BGN Mode 20 N

7,25 i

0 PV

89,729.45 PMT

FV -999,999.95

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.27 Present value of an annuity due: You wrote a piece of software that does a better job of allowing computers to network than any other program designed for this purpose. A large networking company wants to incorporate your software into its systems and is offering to pay you $500,000 today, plus $500,000 at the begining of each of the following six years, for permission to do this. If the appropriate interest rate is 6 percent, what is the present value of the cash flow stream that the company is offering you?

Solution: You are being offered a seven year annuity due. You can solve this problem several different ways. First, you can calculate the present value of each of the individual cash flows and then add the present values together. Second, you can use the annuity transformation method discussed in the chapter. Third, you can calculate the present value of an ordinary six-year annuity and then add $500,000 to that value. Of course you can also use your calculator or Excel to do the calculations for you. Below are the calculations for the annuity transformation method.

PVA7 = CF × PV annuity factor = $500,000 × 5.5824 = $2,791,190.72 Annuity value due

= PVA7 × (1 + i)

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= $2,791,190.72 × 1.06 = $2,958,662.16 Financial Calculator Solution : BGN Mode 7 N

6 i

PV -2,958,662.16

500,000 PMT

0 FV

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.28 Present value of an annuity: Suppose that the networking company in problem 6.27 will not start paying you until the first of new systems that uses your software is sold in two years. What is the present value of that annuity? Assume that the appropriate interest rate is still 6 percent.

Solution: Since the first cash flow will not be received for two years, the present value will be less than in problem 6.27. All you have to do to solve this problem is to discount the answer from problem 6.27 for two years.

Annuity value = value of annuity value due/(1 + i)2 = $2,958,662/(1.06)2 = $2,633,198.79 This is also equal to the value of the regular annuity in problem 6.27, PVA7, discounted one year at 6 percent.

Financial Calculator Solution: BGN Mode 2 N

6 i

PV -2,633,198.79

0 PMT

2,958,662.16 FV

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Copyright ©2015 John Wiley & Sons, Inc.

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6.29 Perpetuity: Calculate the present value of the following perpetuities: a. $1,250 discounted to the present at 7percent b. $7,250 discounted to the present at 6.33percent c. $850 discounted to the present at 20 percent Solution: a.

Annual payment = PMT =$1,250 Investment rate of return = i = 7% Term of payment = Perpetuity Present value of investment needed = PV PMT $1,250 PV of Perpetuity = = i 0.07 =$17,857.14 b.

c.

Annual payment = PMT =$7,250 Investment rate of return = i = 6.33% Term of payment = Perpetuity.

Present value of perpetuity = PV PMT $7,250 PV of Perpetuity = = 0.0633 i = $114,533.97 Annual payment = PMT =$850 Investment rate of return = i = 20% Term of payment = Perpetuity.

Present value of investment needed = PV

PMT $850 = i 0.20 = $4,250

PV of Perpetuity = LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.30 Effective annual interest rate: Find the effective annual interest rate (EAR) on each of the following: a. 6 percent compounded quarterly. b. 4.99 percent compounded monthly. c. 7.25 percent compounded semiannually. d. 5.6 percent compounded daily.

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Solution: Interest rate = i = 6% a.

Frequency of compounding = m = 4 Effective annual rate = EAR m1

b.

c.

d.

4

i   0.06 EAR = 1 + m  − 1 =1 +  −1 4     = 1.06136− 1 = 6.14% Interest rate = i = 4.99% Frequency of compounding = m = 12 Effective annual rate = EAR m1

12

m1

2

m1

365

i   0.0499 EAR = 1 + m  −1= 1+  −1 12     = 1.0511−1=5.11 % Interest rate = i = 7.25% Frequency of compounding = m = 2 Effective annual rate = EAR i   0.0725 EAR = 1 + m  −1= 1+  −1 2     = 1.0738− 1=7.38 % Interest rate = i = 5.6% Frequency of compounding = m = 365 Effective annual rate = EAR i   0.0 5 6 EAR = 1 + m  −1= 1+ 365    = 1.0576− 1=5.76%

−1

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.31 Effective annual interest rate: Which of the following investments has the highest effective annual interest rate (EAR)? a. A bank CD that pays 8.25 percent compounded quarterly. b. A bank CD that pays 8.25 percent compounded monthly. c. A bank CD that pays 8.45 percent compounded annually. d. A bank CD that pays 8.25 percent compounded semiannually. e. A bank CD that pays 8 percent compounded daily (on a 365-day per year basis).

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Solution: a.

b.

c.

d.

e.

Solutions Manual

Interest rate on CD = i = 8.25% Frequency of compounding = m = 4 Effective annual rate = EAR m1

4

m1

12

m1

1

m1

2

i   0.0825 EAR = 1 + m  − 1 =1 +  −1 4     = 1.08509− 1 = 8.51% Interest rate on CD = i = 8.25% Frequency of compounding = m = 12 Effective annual rate = EAR

i   0.0825 EAR = 1 + m  −1= 1+  −1 12     = 1.0857− 1=8.57 % Interest rate on CD = i = 8.45% Frequency of compounding = m = 12 Effective annual rate = EAR i   0.0845 EAR = 1 + m  −1= 1+  −1 1     = 1.0845− 1=8.45 % Interest rate on CD = i = 8.25% Frequency of compounding = m = 2 Effective annual rate = EAR i   0.0825 EAR = 1 + m  −1= 1+  −1 2     = 1.0842− 1=8.42 % Interest rate on CD = i = 8% Frequency of compounding = m = 365 Effective annual rate = EAR m 1

365

i   0.08 EAR = + 1 m  −1= 1+  − 1  365   = 1.0833−1=8.33 % Investment b. (8.25% monthly) has the highest EAR. LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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6.32 Effective annual interest rate: You are considering three alternative investments: (1) a three-year bank CD paying 7.5 percent compounded quarterly; (2) a three-year bank CD paying 7.3 percent compounded monthly; and (3) a three-year bank CD paying 7.75 percent compounded annually. Which investment has the highest effective annual interest rate (EAR)?

Solution: (1) Interest rate on CD = i = 7.5% Frequency of compounding = m = 4 Effective annual rate = EAR m1

4

m1

12

 i   0.075  −1 EAR = 1 + m  −1= 1+ 4     = 1.0771−1=7.71 % (2) Interest rate on CD = i = 7.3% Frequency of compounding = m = 12 Effective annual rate = EAR i    0.0 7 3 −1 EAR = 1 + m  −1= 1+  12     = 1.0755− 1=7.55 % Interest rate on CD = i = 7.75% (3) Frequency of compounding = m = 1 Effective annual rate = EAR m1

1

i   0.0775 EAR = 1 + m  −1= 1+  −1 1     = 1.0775− 1=7.75 % Investment (3) The three-year bank CD paying 7.75 percent interest compounded annually has the highest effective yield.

LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

ADVANCED 6.33 You have been offered the opportunity to invest in a project which is expected to provide you with the following cash flows: $4,000 in one year, $12,000 in two years, and $8,000 in three years. If the appropriate interest rates are 6 percent for the first year, 8 percent for

Copyright ©2015 John Wiley & Sons, Inc.

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the second year, and 12 percent for the third year, what is the present value of these cash flows?

Solution: The answer is $20,495.15. Calculated as follows: $4,000 $12,000 $8,000 PV= + + 1.06 (1.06)(1.08) (1.06)(1.08)(1.12)

= $3, 773.58 + $10, 482.18 + $6, 239.39 = $20, 495.15 If the interest rate is different each year, then you must perform the calculation in this way. What you are effectively doing here is discounting each cash flow one year at a time using the appropriate rate. For example, you discount the year three cash flow of $8,000 for one year at 12 percent: $8,000/1.12 = $7,142.86 You then discount this result for one year at 8 percent: $7,142.86/1.08 = $6,613.76 Finally, you get the present value of the $8,000 by discounting the above result by 6 percent: $6,613.76/1.06 = $6,239.40 The one cent difference from the number above is due to rounding.

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.34 Tirade Owens, a professional athlete, currently has a contract that will pay him a large amount in the first year of his contract and smaller amounts thereafter. He and his agent have asked the team to restructure the contract. The team, though reluctant, obliged.

Tirade and his agent came up with a counteroffer. What are the present values of each of the three alternatives below using a 14 percent discount rate? Which of the three has the highest present value?

Team’s Offer Year Current Contract Counteroffer 1 $8,125,000 $4,000,000.00 $5,250,000.00 2 $3,650,000 $3,825,000.00 $7,550,000.00 3 $2,715,000 $3,850,000.00 $3,625,000.00 4 $1,822,250 $3,925,000.00 $2,800,000.00 Solution: Current Contract

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$8,125,000 $3,650,000 $2,715,000 $1,822,250 + + + (1.14)2 (1.14)3 (1.14)4 (1.14) = $7,127,192.98+$2,808,556.48+$1,832,547.67+$1,078,918.29 = $12,847,215.41

PV =

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 $8,125,000 1 2 $3,650,000 1 3 $2,715,000 1 4 $1,822,250 1 Then solve by pressing NPV, enter the rate of 14% and compute NPV=12,847,215.41.

Team’s Offer $4,000,000 $3,825,000 $3,850,000 $3,925,000 + + + PV = (1.14)2 (1.14)3 (1.14)4 (1.14) = $3,508,771.93+$2,943,213.30+ $2,598,640.34+ $2,323,915.09 = $11,374,540.65 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 1 $4,000,000.00 2 1 $3,825,000.00 3 1 $3,850,000.00 4 1 $3,925,000.00 Then solve by pressing NPV, enter the rate of 14% and compute NPV=11,374,540.65.

Counteroffer $5,250,000 $7,550,000 $3,625,000 $2,800,000 + + + PV = (1.14)2 (1.14)3 (1.14)4 (1.14) = $4,605,263.16+$5,809,479.84+$2,446,771.75+$1,657,824.78 = $14,519,339.52 Financial Calculator Solution:

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Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -1111 0 1 $5,250,000.00 2 $7,550,000.00 3 $3,625,000.00 4 $2,800,000.00 Then solve by pressing NPV, enter the rate of 14% and compute NPV=14,519,339.52.

The counteroffer has the best value for the player.

LO 1 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.35 Gary Kornig is 30 years old and wants to retire when he is 65. So far he has saved (1) $6,950 in an IRA account in which his money is earning 8.3 percent annually and (2) $5,000 in a money market account in which he is earning 5.25 percent annually. Gary wants to have $1 million when he retires. Starting next year, he plans to invest a fixed amount every year until he retires in a mutual fund in which he expects to earn 9 percent annually. How much will Gary have to invest every year to achieve his savings goal?

Solution: Investment (1) Balance in IRA investment = PV = $6,950 Return on IRA account = i = 8.3% Time to retirement = n = 35 years Value of IRA at age 65 = FVIRA FV IRA = PV (1+ i)n = $6,950(1.083)35

= $113, 235.03 Financial Calculator Solution: 35

8.3

0

6,950

N

i

PV

PMT

FV -113,235.03

Investment (2) Balance in money market investment = PV = $5,000

Copyright ©2015 John Wiley & Sons, Inc.

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Return on money market account = i = 5.25% Time to retirement = n = 35 years Value of money market at age 65 = FVMMA FV MMA = PV (1+ i)n = $5,000(1.0525)35

=$29,973.93 Financial Calculator Solution : 35

8.3

0

5,000

N

i

PV

PMT

FV -29,973.93

Target retirement balance = $1,000,000 Future value of current savings = $113,235.03 + $29,973.93 = $143,208.96 Amount needed to reach retirement target = FVA = $856,774.04 Annual payment needed to meet target = PMT Expected return from mutual fund = i = 9% (1+ i) n − 1  FVA= PMT    i 

PMT =

=

FVA $856, 791.04 $856, 791.04 = = 215.711  (1+ i)n − 1  (1.09)35−1     i   0.09   $3, 971.94

Financial Calculator Solution : 35 N

9 i

0 PV

PMT -3,971.94

856,792.04 FV

LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.36 The top prize for the state lottery is $100,000,000. You have decided it is time for you to take a chance and purchase a ticket. Before you purchase the ticket, you must decide whether to choose the cash option or the annual payment option. If you choose the annual

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payment option and win, you will receive $100,000,000 in 25 equal payments of $4,000,000─one payment today and one payment at the end of each of the next 24 years.

If you choose the cash payment, you will receive a one-time lump sum payment of $59,194,567.18. If you can invest the proceeds and earn 6 percent, which option should you choose?

Solution: You should choose the lump sum option. To see this, all you have to do is calculate the present value of the cash flows from the annual payment option using the 6 percent discount rate. Since the annual payment option is like a 25- year annuity due, this value is: PVA25 = CF × PV annuity factor = $4,000,000 × 12.7834 = $51,133,424.63Annuity value due = PVA25 × (1 + i) = $51,133,424.63 × 1.06 = $54,201,430.11 Since this is less than the $59,194,567.18 lump sum, you are better off taking the lump sum.

Financial Calculator Solution: BGN Mode 25 N

6 i

PV 54,201.430.11

-4,000,000 PMT

0 FV

LO 2 Bloomcode: Anlysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.37 At what interest rate would you be indifferent between the cash and annual payment options in problem 6.36?

Solution: You would be indifferent if you could only earn 5 percent from your investments. With this discount rate, the present value of the cash flows from the annual payment option equals the $59,194,567.18 lump sum.

PVA25 = CF × PV annuity factor = $4,000,000 × 14.0949 = $56,375,778.26

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Annuity value due

= PVA25 × (1 + i) = $56,376,000 × 1.05 = $59,194,567.18 If you use your calculator or Excel to calculate the present value of the cash flows from the annual payment option you will get exactly $59,194,567.18.

Financial Calculator Solution : BGN Mode 4 N

5 i

PV 59,194,567.18

-4,000,000 PMT

0 FV

LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.38 Babu Baradwaj is saving for his son’s college tuition. His son is currently 11 years old and will begin college in seven years. Babu has an index fund investment of $7,500 that is earning 9.5 percent annually. Total expenses at the University of Maryland, where his son says he plans to go, currently total $15,000 per year, but are expected to grow at roughly 6 percent each year. Babu plans to invest in a mutual fund that will earn 11 percent annually to make up the difference between the college expenses and his current savings. In total, Babu will make seven equal investments with the first starting today and with the last being made a year before his son begins college. a. What will be the present value of the four years of college expenses at the time that Babu’s son starts college? Assume a discount rate of 5.5 percent. b. What will be the value of the index mutual fund when his son just starts college? c. What is the amount that Babu will have to have saved when his son turns 18 if Babu plans to cover all of his son’s college expenses? d. How much will Babu have to invest every year in order to have enough funds to cover all his son’s expenses?

Solution: Annual cost of college tuition today (t = 0) = $15,000 Expected increase in annual tuition costs = g = 6% Four-year tuition costs (t = 7 to t = 10) a.

Years from now Future value calculation Tuition costs $15,000(1.06)7 7 $22,554.45 $15,000(1.06)8 8 $23,907.72

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$15,000(1.06)9 9 $15,000(1.06)10 10 Discount rate = i = 5.5% Present value of tuition costs = PV $22,554.45 $23,907.72 $25,342.18 $26,862.72 + + + PV = (1.055)2 (1.055)3 (1.055)4 (1.055) = $21,378.63+$21,479.95+$21,581.75+$21,684.03 = $86,124.36

$25,342.18 $26,862.72

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 $22,554.45 1 2 $23,907.72 1 $25,342.18 1 3 $26,862.72 1 4 Then solve by pressing NPV, enter the rate of 5.5% and compute NPV=86,124.36 b.

Future value of the index mutual fund at t = 7 Present value of index fund investment = PV = $7,500 Return on fund = i = 9.5% Future value of investment = FV FV = PV (1+ i)n = $7,500(1.095)7

= $14, 156.64 Financial Calculator Solution : 7 N

9.5 i

c.

d.

7,500 PV

0 PMT

FV -14,156.64

Target savings needed at t = 7 PV of tuition costs – Future value of investment

= $86,124.36 – $14,156.64 = $71,967.72

Annual savings needed Return on fund = i = 11%

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Amount that needs to be saved = FVA = $71,967.72 Annuity payment needed = PMT + n− FVA= PMT (1 i) 1  (1+ i) i

PMT=

FVA $71,967.72 $71,967.72 = = 9.7833  1.11 (1+ i)n −1 (1.11)7 − 1 0.11  (1.11) (1+i) i = $6, 627.21

Financial Calculator Solution : 4 N

11 i

0 PV

0 PMT -6,627.21

71,967.72 FV

LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.39 You are now 50 years old and plan to retire at age 65. You currently have a stock portfolio worth $150,000, a 401(k) retirement plan worth $250,000, and a money market account worth $50,000. Your stock portfolio is expected to provide annual returns of 12 percent, your 401(k) investment will earn 9.5 percent annually, and the money market account earns 5.25 percent, compounded monthly. a. If you do not save another penny, what will be the total value of your investments when you retire at age 65? b. Assume you plan to invest $12,000 every year in your 401(k) plan for the next 15 years (starting one year from now). How much will your investments be worth when you retire at age 65? c. Assume that you expect to live 25 years after you retire (until age 90). Today, at age 50, you take all of your investments and place them in an account that pays 8 percent (use the scenario from part b in which you continue saving). If you start withdrawing funds starting at age 66, how much can you withdraw every year (e.g., an ordinary annuity) and leave nothing in your account after a 25th and final withdrawal at age 90? d. You want your current investments, which are described in the problem statement, to support a perpetuity that starts a year from now. How much can you withdraw each year without touching your principal?

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Solution: a.

Solutions Manual

Stock Portfolio Current value of stock portfolio = $150,000 Expected return on portfolio = i = 12% Time to retirement = n = 15 years Expected value of portfolio at age 65 = FV Stock FV St oc k = PV  (1+ i ) 15= $150, 000 (1.12)15 = $821,034.86 410(k) Investment Current value of 410(k) portfolio = $250,000 Expected return on portfolio = i = 9.5% Time to retirement = n = 15 years Expected value of portfolio at age 65 = FV401k FV 401k = PV  (1+ i ) 15= $250, 000 (1.095)15 = $975,330.48 Money market account Current value of savings = $50,000 Expected return on portfolio = i = 5.25% Time to retirement = n = 15 years Frequency of compounding = m = 12 Expected value of portfolio at age 65 = FV MMA m n

i  FV MMA = P V   1 +   m

1215

 0.0525 =$50,0001+ 12   

= $50, 000  2.1941 = $109, 706.14 Total value of all three investments = $821,034.86 + $975,330.48 + $109,706.14 = $1,906,071.48

b.

Planned annual investment in 401k plan = $12,000 Future value of annuity = FVA (1+ i) n − 1  FVAn =PMT     i 

(1.095)15 − 1   = $12,000 30.5402  0.0 9 5   = $366,482.77

= $1 2,0 0 0

Financial Calculator Solution:

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15 N

9.5 i

0 PV

Solutions Manual

12,000 PMT

FV -366,482.77 Total investment amount at retirement = $1,906,071.48 + $366,482.77 = $2,272,554.25

c.

Amount available at retirement = PVA = $2,272,554.25 Length of annuity = n = 25 Expected return on investment = i = 8% Annuity amount expected = PMT Using the PVA equation:  1  1− (1 + i)n   PVAn =PMT   i      $2,272,554.25 $2,272,554.25  = 10.6748 PMT = 1   1 − (1.08) 25    0.08    = $212,889.63 Each payment received for the next 25 years will be $212,889.63.

Financial Calculator Solution : 8 i

25 N

d.

-2,272,554.25 PV

0 PMT 212,889.63

0 FV

Type of payment = Perpetuity Present value of perpetuity = PVA = $2,272,554.25 Expected return on investment = i = 8% PMT PV of Perpetuity = i PMT $2,272,553.75= 0.08

PMT = $2,272,554.250.08 = $181,804.34 You could receive an annual payment of $181,804.34 forever.

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LO 1, LO 2, LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.40 Trevor Diaz wants to purchase a Maserati Qattroporte sedan, which has an invoice price of $121,737 and a total cost of $129,482. Trevor plans to put down $20,000 and will pay the rest by taking on a 5.75 percent five-year bank loan. What is the monthly payment on this auto loan? Prepare an amortization table using Excel.

Solution: Cost of new car = $129,482 Down payment = $20,000 Loan amount = $129,482 – $20,000 = $109,482 Interest rate on loan = i = 5.75% Term of loan = n = 5 years Frequency of payment = m = 12 Monthly payment on loan = PMT 1 1− (1+i)n PVA n = PMT  i PMT=

$109, 482 $109, 482 = 52.0379 1 1− 125  0575  1+  12  0.0575 12 = $2, 103.89

Financial Calculator Solution : 60 N

5.75/12 i

109,482 PV

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0 PMT 2,103.89

0 FV

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Show a portion of an Excel amortization table for this loan as follows:

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.41 The Yan family buying a new 3,500-square-foot house in Muncie, Indiana, and will borrow $237,000 from Bank One at a rate of 6.375 percent for 15 years. What will be their monthly loan payment? Prepare an amortization schedule using Excel.

Solution: Home loan amount = $237,000 Interest rate on loan = i = 6.375% Term of loan = n = 15 years Frequency of payment = m = 12 Monthly payment on loan = PMT

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PVA n = PMT  PMT=

=

Solutions Manual

1 1− (1+i)n i

$237, 000 1 1− 1215  0.06375  1+ 12   0.06375 12 $237, 000 = $2, 048.27 115.7072

Financial Calculator Solution : 60 N

6.375/12 i

-237,000 PV

PMT 2,048.27

0 FV

Show a portion of an Excel amortization table for this loan as follows:

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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6.42 Assume you are now 21 years old and will start working as soon as you graduate from college. You plan to start saving for your retirement on your 25th birthday and retire on your 65th birthday. After retirement, you expect to live at least until you are 85. You wish to be able to withdraw $40,000 (in today’s dollars) every year from the time of your retirement until you are 85 years old (i.e., for 20 years). The average inflation rate is likely to be 5 percent. a. Calculate the lump sum you need to have accumulated at age 65 to be able to draw the desired income. Assume that your annual return on your investment is likely to be 10 percent. b. What is the dollar amount you need to invest every year, starting at age 26 and ending at age 65 (i.e., for 40 years, to reach the target lump sum at age 65? c. Now answer questions a. and b. assuming the rate of return to be 8 percent per year, then again at 15 percent per year. d. Now assume you start investing for your retirement when you turn 30 years old and analyze the situation under rate of return assumptions of (i) 8 percent, (ii) 10 percent, and (iii) 15 percent. e. Repeat the analysis by assuming that you start investing only when you are 35 years old.

Solution: Provide more guidance here. If the student is 21, then the first withdrawal will be 40,000(1+.05)45=$359,400. Then, withdrawals grow at 5% per year thereafter (a spreadsheet is helpful here).

Next, find the NPV of the anticipated retirement withdrawals at each anticipated interest rate. This is the lump sum needed at retirement. This can be done with a spreadsheet or alternatively, with the formula for the present value of a growing annuity as follows to find the present value of withdrawals: 𝟏.𝟎𝟓𝟐𝟎 𝟑𝟓𝟗,𝟒𝟎𝟎.𝟑𝟏𝟐 𝒙[𝟏−( ) ]=𝟒,𝟑𝟓𝟑,𝟎𝟖𝟔.𝟕𝟗 𝑷𝑽𝑨𝒏= .𝟏−.𝟎𝟓 𝟏.𝟏 Finally, find the annuity payment that will generate that lump sum at the end of the student’s working life. Assume 40 years of saving, 35 years of saving and finally 30 years of saving.

RETIREMENT ANALYSIS SUMMARY INVESTMENT AGE = 25 INVESTMENT AGE = 30 Rate of Return

8%

10%

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15%

8%

10%

INVESTMENT AGE = 35 15%

8%

10%

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Fundamentals of Corporate Finance, 4th edition Inflation rate Retirement Income Level Lump sum needed at age $5,160,266 65 Annuity payment $19,919 needed

Solutions Manual 5% $40,000

$4,353,087

$3,011,353

$5,160,266

$4,353,087

$3,011,353

$5,160,266

$4,353,087

$3,011,353

$9,835

$1,693

$29,946

$16,062

$3,417

$45,552

$26,463

$6,927

LO 1, LO 2, LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Sample Test Problems 6.1

Freisinger, Inc., is expecting a new project to start paying off, beginning at the end of next year. It expects cash flows to be as follows: 0 7.8% 1 2 3 4 5 ├───────┼────────┼───────┼───── ───┼───────┤ $433,676 $478,452 $475,455 $478,326 $535,444

If Freisinger can reinvest these cash flows to earn a return of 7.8 percent, what is the future value of this cash flow stream at the end of five years? What is its present value?

Solution:  (1.078) +$478,452 (1.078)+$475,455 (1.078)  +$478, 326 (1.078)   FV 5 =$433,676  4

3

2

1

+$535, 444 = $585, 653.08 + $599, 369.52 + $552, 518.65 + $515, 635.43 + $535, 444 $2, 788, 620.68 =

 +  455 / (1.078)3 $475, $478, 326 / (1.078)4 / (1.078)2 452 + $478, + PV= $433, 676 / 1.078  + [$535, 444 / (1.078)5 ] + 200.32+ $367, 807.22 = $402, 296.85 + $411, 718.95 + $379, 536.14 $354, = $1,915,559.47

Financial Calculator Solution:

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Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 Frequency (F) 433,676 -11111 0 478,452 1 475,555 2 478,326 3 535,444 4 5 Then solve by pressing NPV, enter the rate of 7.8% and compute NPV=1,915,559.47.

Set N=5, i =7.8, PV=-1,915,559.47, PMT=0 and solve for FV=2,788,620.68 Spreadsheet Solution: Using a spreadsheet, use the formula =NPV(0.078,433676,478452,475555,478326,535444) to find the present value, and then use the formula =FV(0.078,5,0, -1915559.47)= 2,788,620.68.

LO: 1 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Compare an annuity due with an ordinary annuity. The payments for both are made annually and are of the same dollar amounts. The two annuities also have the same duration in years and the same discount rate. Which of the following statements is /are correct? a. The present value of the ordinary annuity is greater. b. The present value of the annuity due is greater. c. The future value of the ordinary annuity is greater. d. The future value of the annuity due is greater.

Solution: b and d are both correct The cash flows of the annuity due are received at the beginning of the period, resulting in less discounting and a higher PV and more compounding and a higher FV. LO: 2 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.2

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You plan to set up an endowment at your alma mater that will fund $200,000 of scholarships each year indefinitely. If the principal (the amount you donate) can be invested at 5.5 percent, compounded annually, how much do you need to donate to the university today, so that the first scholarships can be awarded beginning one year from now?

Solution: Annual payment needed = PMT = $200,000 Investment rate of return = i = 5.5% Term of payment = Perpetuity PMT $200,000 = PV of Perpetuity = Present value of investment needed = 0.055 i = $3,636,363.64 LO: 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.3

6.4

Annalise Genric wants to open a restaurant in a historic building. The property can be leased for 20 years, but not purchased. She believes her restaurant can generate a net cash flow of $76,000 the first year and expects an annual growth rate of 4 percent thereafter. If a discount rate of 15 percent is used to evaluate this business, what is the present value of the cash flows that it will generate?

Solution: Length of lease = n = 20 years Next year’s net cash flow = CF1 = $76,000 Expected annual growth rate = g = 4% Required rate of return = i = 15% Present value of growing annuity = PVAn

CF 1  1+g n  $7 6,0 0 0 1−   = PVA n = ( i − g )   1 + i  (0.15−0.04) = $690,9090.86612 =$598,410.10

  1.0 20    1 −    4   1.1  5

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Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.5

A credit card offers financing at an APR of 18 percent, with monthly compounding on outstanding charges. What is the effective annual rate (EAR)?

Solution: Interest rate = i = 18% Frequency of compounding = m = 12 Effective annual rate = EAR 

12 i m1    0.18 EAR=  1 +  − 1 =  1 +  − 1  m  12 = 1.1956 − 1 = 0.1956, or 19.56 percent

LO: 5 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Thomas Nguyen currently has $10,000 in the bank earning interest of 6 percent per year, compounded monthly. If he needs $25,000 to purchase a car and can save an additional $100 a month stating at the end of this month, how long will it take him to accumulate the $25,000?

Solution: months 0 5% 1 2 3 4 ? ├───────┼────────┼───────┼────────┤……………. $10,000 $100 $100 $100 $100 $100 $25,000 Monthly payment = CF = $100 Present Value = PV = 10,000 Future Value = FV = 25,000 Annual rate of return = i = 6% Payments per year = m = 12 Type of annuity = Ordinary Annuity Using the FVA equation and the equation for the FV of a single amount: 6.6

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 i nm    1 +  −1 nm   i   m     + PV   1 +  = FV = C F   i m    m   0.06nm  1+  −1 nm   0.06 = $ 1 0 0    12  + 1   0.06 $25,000 + $ 10, 000    12 12       nm

nm

 0.06   0.06 $25, 000 = $20, 000  1+ 1+ − $20, 000 + $10, 000    12 12   0.06 12 nm  $45,000=$30,000 1+ +    $45,000   0.06 ln n m ln 1   $30,000 =  12  nm=

ln (1.5)=81.3months ln (1.005)

Solving for n × m yields: n × m = 81.3 months It will take Shannon 81.3 months or 6.8 years to save the $25,000.

Financial Calculator Solution: Alternatively, a financial calculator can be used to find the time required to save: i=6/12=0.5; PV=-10,000; PMT=-100; FV=25,000 – solve for N=81.296 or 6.8 years.

Spreadsheet Solution: Using a spreadsheet, enter the formula =NPER(0.06/12,-100,-10000,25000).

LO: 2 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Appendix: Deriving the Formula for the Present Value of an Ordinary Annuity In this chapter we showed that the formula for a perpetuity can be obtained from the formula for the present value of an ordinary annuity if n is set equal to ∞. It is also possible to go the other way.

In other words, the present value of an ordinary annuity formula can be derived from the formula for a perpetuity. In fact, this is how the annuity formula was originally obtained. To see how this was done, assume that someone has offered to pay you $1 per year forever, beginning next year, but that, in return, you will have to pay that person $1 per year forever, beginning in year n + 1.

Solution: In this problem, you will receive an annual payment that grows at a rate of g forever. In return, you will have to pay that person $1(1 + g)n each year forever, beginning in year n + 1. The cash flows that you will receive can be represented as in the following time line. ∞

0 1 2 3 n-1 n n+1 n+2

Receive $1 $1(1+g) $1(1+g)2……$1(1+g)n-2 $1(1+g)n-1 $1(1+g)n Pay $0 $0 $0 $0 $0 $1(1+g)

n

The first time line shows the cash flows for the perpetuity that you will receive. This perpetuity is worth: $1 CF PVReceive=(i−g)= (i−g) The second time line shows the cash flows for the perpetuity that you will pay. The present value of what you owe is:

$1(1+g) n CF(1+g) n (-g) i (i - g) = PV Owe = n (1+)i n (1+ i) Notice that if you subtract, year-by-year, the cash flows you would pay from the cash flows you would receive, you get the cash flows for an n-year annuity.

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0123

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n –1 n

n+1 n+2

∞

+ g)n-2 $1(1 + g)n-1 $0 Difference $1 $1(1 + g) $1(1 +)2………$1(1 g Therefore, the value of the offer equals the value of an n-year growing annuity. Solving for the difference between PVOwe from PV Re ceive ,we see that this is the same as Equation 6.5.

CF(1 + g) n n CF CF  1 + g  i   1 − − = PV Re ceive −PV Owe =  (i - g) (i - g)   1 + i  (1+i)n

Problem 6A.1 In the chapter text, you saw that the formula for a growing perpetuity can be obtained from the formula for the present value of a growing annuity if n is set equal to ∞. It is also possible to go the other way. In other words, the present value of a growing annuity formula can be derived from the formula for a growing perpetuity. In fact, this is how Equation 6.5 was actually derived. Show how Equation 6.5 can be derived from Equation 6.6.

Solution: The limit of [(1+g)/(1+i)]^n will be zero. The growth rate in perpetuity must always be less that the interest rate which makes intuitive sense. The numerator therefore will always be less than the denominator and when n is set to infinity the numerator divided by the denominator will tend to zero. Therefore as n tends to infinity the resultant limit of Equation 6.5 is Equation 6.6.

LO: 4 Level: Advanced

Copyright ©2015 John Wiley & Sons, Inc.

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Chapter 7 Risk and Return Before You Go On Questions and Answers Section 7.1 Note to instructor: There are no questions for this section.

Section 7.2are the two components of a total holding period return?

What 1.

Capital appreciation and income. This can be seen in Equation 7.1.

2.

How is the expected return on an investment calculated?

The expected return is calculated as a weighted-average of the possible returns on an investment (outcomes) where the weights are the probabilities that each of the possible returns will be realized.

Section 7.3 1.

What is the relation between the variance and the standard deviation?

The standard deviation is the square root of the variance. Alternatively, the variance equals the standard deviation squared.

2.

What relation do we generally observe between risk and return when we examine historical returns?

Investments with higher risks tend to have higher returns. This is illustrated in Exhibit 7.3.

3.

What type of return tells you the average compounded return earned by an investor?

The geometric average return.

Section 7.4 1.

.

What does the coefficient of variation tell us, and how is it related to the Sharpe Ratio?

The coefficient of variation is a measure of risk per unit of return. It tells us the amount of risk, defined as the standard deviation of returns, associated with each 1 percent of

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expected return for an asset. A larger coefficient of variation indicates greater risk for each 1 percent of return.

The Sharpe ratio differs from the coefficient of variation in two ways. First, instead of using the total return in the calculation, with the Sharpe ratio we use the difference between the total return and the risk free rate. Second, the Sharpe ratio is the inverse of the coefficient of variation ratio that would be calculated using this adjusted return. Computing the inverse of the coefficient of variation yields a measure of return per unit of risk, which some investors find more intuitive than a measure of risk for each 1 percent of return.

2.

What are the two components of total risk?

The two components of total risk are unsystematic risk and systematic risk. Unsystemtic risk is risk that is unique to a particular asset. This is the risk that can be eliminated through diversification. Systematic risk is risk that is common to all assets and cannot be diversified away.

3.

Why does the total risk of a portfolio not approach zero as the number of assets in a portfolio becomes very large?

Because the systematic risk associated with the individual assets cannot be diversified away. With a very large number of assets, the total risk of a portfolio will approach the weighted average (where the weights are the fractions of total portfolio value represented by each asset) of the systematic risks associated with each asset.

Section 7.5 1.

Why are returns on the stock market used as a benchmark in measuring systematic risk?

Because the stock market portfolio is the most diversified portfolio for which good return data are available and it is the portfolio that both comes closest to eliminating all unique risk. This makes the returns on the stock market a practical choice as a benchmark for measuring the systematic risk of individual assets.

2.

How is beta estimated?

Beta is estimated using regression analysis in which returns on an individual asset are regressed against returns on the market. Beta is the slope of the regression line. This is illustrated in Exhibit 7.10.

3.

How would you interpret a beta of 1.5 for an asset? A beta of 0.75?

A beta of 1.5 indicates that the asset has 1.5 times as much systematic risk as the market.

A beta of 0.75 indicates that the asset has 75 percent as much systematic risk as the market.

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Section 7.6 Note to instructor: There are no questions for this section.

Section 7.7 How is the expected return on an asset related to its systematic risk?

1.

CAPM tells us that there is a linear relation between expected return and systematic risk.

With zero systematic risk, the expected return equals the risk-free rate. For systematic risk greater than zero, the expected return on an asset increases as its systematic risk increases and this increase is linear. This relation is illustrated in Equation 7.12.

2.

What name is given to the relation between risk and expected return implied by the CAPM? This plot is called the Security Market Line, or SML, and is illustrated in Exhibit 7.11.

3.

If an asset’s expected return does not plot on the line in question 2 above, what does that imply about its price?

If the expected return on an asset does not plot on the SML, then this indicates that the expected return on the asset is either too low or too high in view of its systematic risk. If the asset plots below the SML, the expected return is too low and its price is too high. If the asset plots above the SML, the expected return is too high and its price is too low.

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Self-Study Problems 7.1

Kaaran made a friendly wager with a colleague that involves the result from flipping a coin. If heads comes up, Kaaran must pay her colleague $15; otherwise, her colleague will pay Kaaran $15. What is Kaaran’s expected cash flow, and what is the variance of that cash flow if the coin has an equal probability of coming up heads or tails? Suppose Kaaran’s colleague is willing to handicap the bet by paying her $20 if the coin toss results in tails. If everything else remains the same, what are Kaaran’s expected cash flow and the variance of that cash flow?

Solution: Part 1: E(cash flow) = (0.5 × –$15) + (0.5 × $15) = 0 σ2cash flow = [0.5 × (–$ 15 - $0)]2 + [0.5 × ($15 – $0)] =2 $225 Part 2: E(cash flow) = (0.5 × –$15) + (0.5 × $20) = $2.50 2 2 σ2cash flow = [0.5 × (–$15 – $2.50)] + [0.5 × ($20 – $2.50)] = $306.25

7.2

You know that the price of CFI, Inc., stock will be $12 exactly one year from today.

Today the price of the stock is $11. Describe what must happen to the price of CFI, Inc., today in order for an investor to generate a 20 percent return over the next year. Assume that CFI does not pay dividends.

Solution: The expected return for CFI based on today’s stock price is ($12 – $11)/$11 = 9.09 percent, which is lower than 20 percent. Since the stock price one year from today is fixed, then the only way that you will generate a 20 percent return is if the price of the stock drops today. Consequently, the price of the stock today must drop to $10. It is found by solving the following: 0.2 = ($12 – x)/ x, or x = $10.

7.3

The expected value of a normal distribution of prices for a stock is $50. If you are 90 percent sure that the price of the stock will be between $40 and $60, then what is the variance of the prices for the stock?

Solution: Since you know that 1.645 standard deviations around the expected return captures 90 percent of the distribution, you can set up either of the following equations: $60 = $50 + 1.645σ $40 = $50 – 1.645σ or and solve for σ. Doing this with either equation yields σ = $6.079 and σ2 = 36.954

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7.4

During the period from 2011 through 2015 the annual returns on small U.S. stocks were -3.26 percent, 18.23 percent, 45.07 percent, 2.92 percent, and -3.60 percent, respectively. What would a $1 investment, made at the beginning of 2011, have been worth at the end of 2015? What average annual return would have been earned on this investment?

Solution: The value in 2015 is: V2015 = $1 × (1 + −0.0326) × (1 + 0.1823) × (1 + 0.4507) × (1 + 0.0292) × (1 + −0.0360) $1.646 Substituting into Equation 7.5 and solving for the geometric average yields: R Geometric average = [(1 + R1) × (1 + R2) × … × (1 + Rn)] – 1/n 1 = [$1.646]1/5 - 1 = 0.1048, or 10.48% per year

7.5

You must choose between investing in stock A and stock B. You have already used CAPM to calculate the rate of return you should expect to receive for each stock given their systematic risk and decided that the expected return for both exceeds that predicted by CAPM by the same amount. In other words, both are equally attractive investments for a diversified investor. However, since you are still in school and do not have a lot of money, your investment portfolio is not diversified.

You have decided to invest in the stock that has the highest expected return per unit of total risk. If the expected return and standard deviation of returns for stock A are 10 percent and 25 percent, respectively, and the expected return and standard deviation of returns for stock B are 15 percent and 40 percent, respectively, which should you choose? Assume that the risk free rate is 5 percent.

Solution: A comparison of the Sharpe ratios for the two stocks will tell you which has the highest expected return per unit of total risk.

E(R)A -Rrf 0.10− 0.05 = = 0.20 SA= σRA 0.25

SB =

E(R B ) - R r f 0.15 − 0.05 = = 0.25 0.40 σR B

Stock B has the highest expected return per unit of risk.

7.6 CSB, Inc., has a beta of 1.35. If the expected market return is 14.5 percent and the risk-free rate is 5.5 percent, what is the appropriate required return of CSB (using the CAPM)?

Solution: .

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E(R CSB ) = Rrf + CSB[E(RM) - Rrf] = 0.055 +[1.35 × (0.145 - 0.055)] = 0.1765 or, 17.65%

Discussion Questions 7.1

Suppose that you know the risk and the expected return for two stocks. Discuss the process you might utilize to determine which of the two stocks is a better buy. You may assume that the two stocks will be the only assets held in your portfolio.

You should be looking to maximize your expected return on an investment given the level of risk that such an investment requires the investor to bear. Therefore, you should compare the expected return and risk associated with each of the two stocks. If the stocks have the same expected return, then choose the stock with the lower risk. If the stocks have the same risk, then choose the stock with the greatest expected return. If the expected return and risk of the two assets have no common level, perhaps you should compare the ratio of the risk/expected return to see which stock contains the least risk per unit of expected return.

LO: 1 Level: Basic 7.2

What is the difference between the expected rate of return and the required rate of return? What does it mean if they are different for a particular asset at a particular point in time?

The required rate of return is the rate of return that investors require to compensate them for the risk associated with an investment. The expected return will not necessarily equal the required rate of return. The expected return can be lower, in which case the return will not be sufficient to compensate the investor for the risk associated with the investment if the expected return is realized. It can also be higher, in which case the expected return will be greater than that necessary to compensate the investor for the riskiness of the asset.

LO: 7 Level: Basic 7.3

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Suppose that the standard deviation of the returns on the shares of stock at two different companies is exactly the same. Does this mean that the required rate of return will be the same for these two stocks? How might the required rate of return on the stock of a third company be greater than the required rates of return on the stocks of the first two companies even if the standard deviation of the returns of the third company’s stock is lower?

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No. Because some risk can be diversified away, it is possible that two stocks with the same standard deviation of returns can have different required rates of return. One of these stocks can have a higher systematic risk than the other stock and, therefore, a higher required rate of return. The third stock can have a higher required rate of return if its systematic risk is greater than the systematic risk of the stock in the other two companies.

LO: 4 Level: Basic 7.4

The correlation between stocks A and B is 0.50, while the correlation between stocks A and C is –0.5. You already own stock A and are thinking of buying either stock B or stock C. If you want your portfolio to have the lowest possible risk, would you buy stock B or C? Would you expect the stock you choose to affect the return that you earn on your portfolio?

You would buy stock C because it would result in your portfolio having a lower beta. If you buy stock C, the required return for your portfolio would be lower than the required return would be if you bought stock B. If the expected returns on stocks C and B equal their required returns, then you would expect your portfolio to earn less with stock C.

LO: 6 Level: Basic 7.5

The idea that we can know the return on a security for each possible outcome is overly simplistic. However, even though we cannot possibly predict all possible outcomes, this fact has little bearing on the risk-free return. Explain why.

The risk-free security delivers the same return in all states of the world. Even though we do not know all of the possible states of the world in future periods, we do know that the U.S. government will be able to repay its borrowing in every state of the world.

Therefore, the shortcoming of the model does not affect the risk-free security’s return.

LO: 7 Level: Basic 7.6

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Which investment category included in Exhibit 7.3 has shown the greatest degree of risk in the United States since 1926? Explain why that makes sense in a world where the value of an asset in this investment category is likely to be more sensitive to changes in market conditions than is the price of a corporate bond.

Small stocks have generally been riskier than large stocks, long-term corporate bonds, long-term government bonds, intermediate government bonds, and short-term government bonds. The explanation for this can be best understood if we realize that small stocks will be affected to a greater extent than the list of investments above by

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either good or bad states of the world. These good and bad effects translate into a distribution with greater spread or greater risk than the other investments.

LO: 4 Level: Intermediate 7.7

You are concerned about one of the investments in your fully diversified portfolio.

You just have an uneasy feeling about the CFO, Iam Shifty, of that particular firm.

You do believe, however, that the firm makes a good product and that it is appropriately priced by the market. Should you be concerned about the effect on your portfolio if Shifty embezzles a portion of the firm’s cash?

The risk of Shifty embezzling is a nonsystematic risk that will most likely be offset by a more fortunate event affecting another holding in your portfolio. Therefore, Shifty’s actions should not affect the risk that you bear by investing in your diversified portfolio (systematic risk).

LO: 6, 7 Level: Basic 7.8

The CAPM is used to price the risk (estimate the expected return) for any asset. Our examples have focused on stocks, but we could also use CAPM to estimate the expected rate of return for bonds. Explain why.

A firm’s ability to repay its debt obligations will be affected in a very similar, and yet lessened, way than the firm’s stock will be affected. That is, systematic and nonsystematic factors will also affect returns for debt securities. However, if held in a diversified portfolio, then only the systematic risk component will be borne and then compensated for bearing. Therefore, we can use the CAPM to price debt securities.

LO: 8 Level: Intermediate 7.9

In recent years, investors have agreed that the market portfolio consists of more than just a group of U.S. stocks and bonds. If you are an investor who invests in only U.S. stocks and bonds, describe the effects on the risk in your portfolio.

If the market portfolio is composed of all assets, then the U.S.-only portfolio will probably have a small amount of unsystematic risk that is not providing return compensation for that risk. Therefore, the portfolio is bearing too much risk given its expected returns.

LO: 6, 7 Level: Basic 7.10 You may have heard the statement that you should not include your home as an asset in your investment portfolio. Assume that your house will comprise up to 75

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percent of your assets in the early part of your investment life. Evaluate the implications of omitting it when calculating the risk of your overall investment portfolio.

From a systematic risk measurement perspective, omitting the beta of your real estate investment, which does not have a beta equal to zero, could have a serious impact on your portfolio’s perceived systematic risk. In a volatile real estate market, you could be understating the risk in your portfolio, and in a flat real estate market, you could be overestimating the risk in your portfolio.

LO: 8 Level: Intermediate

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Questions and Problems BASIC 7.1

Returns: Describe the difference between a total holding period return and an expected return.

LO 2, LO 3 Solution: A holding period return is the total return over some investment or “holding” period. It consists of a capital appreciation component and an income component. A holding period return reflects past performance. An expected return is a return that is based on the probability-weighted average of the possible returns from an investment. It describes a possible return (or even a return that may not be possible) for a yet- to-occur investment period.

7.2

Expected returns: John is watching an old game show rerun on television called Let’s Make a Deal in which the contestant chooses a prize behind one of two curtains. Behind one of the curtains is a gag prize worth $150, and behind the other is a round-the-world trip worth $7,200. The producer of the game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. What is the expected value of the selection, and what is the standard deviation of that selection?

LO 3 Solution: E(prize) = (0 .75 × $150) + (0.25 × $7,200) = $1,912.50 σ2prize = (0.75 × ($150 – $1,912.50))2 + (0.25 × ($7,200 – $1,912.50) )2 = $9,319,218.75 prize = ($9,319,218.75)1/2 = $3,052.74 σ

7.3

Expected returns: You have chosen biology as your college major because you would like to be a medical doctor. However, you find that the probability of being accepted to medical school is about 10 percent. If you are accepted to medical school, then your starting salary when you graduate will be $300,000 per year. However, if you are not accepted, then you would choose to work in a zoo, where you will earn $40,000 per year. Without considering the additional years you would spend in school if you study medicine or the time value of money, what is your expected starting salary as well as the standard deviation of that starting salary?

LO 3

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Solution: E(salary) = 0.9($40,000) + (0.1) ($300,000) = $66,000 σ2salary =0.9($40,000 – $66,000)2+ (0.1) ($300,000 – $66,000) 2= $6,084,000,000 ($6,084,000,0001/2 ) = $78,000 σsalary =

Historical market: Describe the general relation between risk and return that we observe in the historical bond and stock market data.

LO 3, LO 4 7.4

Solution: The general axiom that the greater the risk, the greater the return describes the historical returns of the bond and stock market. If we look at Exhibit 7.3 in the text, we see that small stocks have averaged the greatest returns but that they also have the greatest standard deviation for the returns. When compared to large stocks, the average return and standard deviation of the small stocks are greater. Large stock average returns and standard deviation numbers are larger than those of long-term government bonds, which are larger than those of intermediate-term government bonds, which in turn are larger than those of U.S. Treasury bills. The comparison shows that the riskier the investment category, the greater the average return as well as standard deviation of returns.

7.5

Single-asset portfolios: Stocks A, B, and C have expected returns of 15 percent, 15 percent, and 12 percent, respectively, while their standard deviations are 45 percent, 30 percent, and 30 percent, respectively. If you were considering the purchase of each of these stocks as the only holding in your portfolio and the risk free rate is 0 percent, which stock should you choose?

LO 4 Solution: Since the holding will be made in a completely undiversified portfolio, then we can calculate the risk per unit of return for each stock, the coefficient of variation, and choose the stock with the lowest value.

CV(RA) = 0.45/0.15 = 3.0 CV(RB) = 0.30/0.15 = 2.0===> Choose B CV(RC) = 0.30/0.12 = 2.5 Alternatively, we could have noted that the expected return for A and B was the same, with A having a greater degree of risk. B and C have the same degree of risk, but B has a greater expected return. This would lead you to the conclusion, just as our coefficient of variation calculations did, that Stock B is superior.

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Arithmetic average: Tanner invested $1,000 in large U.S. stocks at the beginning of 2012. This investment earned 15.98 percent in 2012, 32.41 percent in 2013, 13.69 percent in 2014, and 1.41 percent in 2015. What return did he earn in the average year during the 2012 to 2015 period?

LO 5 Solution: The answer is the arithmetic average of the four returns, which is calculated using Equation 7.4. n

Ri 15.98%+32.41%+13.69%+1.41% i=1

RArithmetic average =

7.7

n

=

4

=15.87%

Geometric average: What was the average annual return that Tanner earned over the 2012 through 2015 period (see problem 7.6).

LO 5 Solution: The answer is the geometric average of the four returns, which is calculated using equation 7.5. × (1 + R)]1/nn R Geometric average = [(1 + R1) × (1 +…R2)× –1 = [(1 + 0.1598) × (1 + 0.3241) × (1 + 0.1369) × (1 + 0.0141]1/4 – 1 = 0.1535, or 15.35% 7.8

Diversification: Describe how investing in more than one asset can reduce risk through diversification.

LO 6 Solution: An investor can reduce the risk of his or her investments by investing in two or more assets whose values do not always move in the same direction at the same time. This is because the movements in the values of the different investments will partially cancel each other out.

7.9 Systematic risk: Define systematic risk.

LO 7 Solution:

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Risk that cannot be diversified away is systematic risk. It is the only type of risk that exists in a diversified portfolio, and it is the only type of risk that is rewarded in asset markets.

7.10 Measuring systematic risk: Susan is expecting the returns on the market portfolio to be negative in the near term. Since she is managing a stock mutual fund, she must remain invested in a portfolio of stocks. However, she is allowed to adjust the beta of her portfolio. What kind of beta would you recommend for Susan’s portfolio?

LO 7 Solution: If we confine our analysis to portfolios with positive beta values, and since beta describes how much and what direction our portfolio is expected to vary with the market portfolio, then Susan should construct a very low beta portfolio. In that case, Susan’s portfolio is not expected to have losses quite as large as that of the market portfolio. A large beta portfolio would have larger losses than that of the market portfolio. If Susan could construct a negative beta portfolio, then she would like to construct as negative a portfolio beta as possible.

7.11 Measuring systematic risk: Describe and justify what the value of the beta of a U.S. Treasury bill should be.

LO 7 Solution: Since the beta of any asset is the slope of the line of best fit for the plot of an asset against that of the market return, then we can use that logic to help us understand the beta of a Tbill. If we purchased a T-bill five years ago and held the same T-bill through each of the last 60 months, then the return for each of those 60 months would be exactly the same.

Therefore, the vertical axis coordinates of each of the monthly returns would have the same value and the slope (beta) of the line of best fit would be zero. The meaning of a beta of zero means that our T-bill has no systematic risk. That is logically given that we know that a T-bill has no risk at all since it is a riskless asset.

7.12 Measuring systematic risk: If the expected rate of return for the market is not much greater than the risk-free rate of return, what does this suggest about the general level of compensation for bearing systematic risk?

LO 7 Solution:

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Such a situation suggests that return compensation for investing in an asset is determined more by the risk-free return than by the market’s compensation for bearing systematic risk. This means that the price for bearing systematic risk is very low. This may be caused by a very low perceived level of risk in the market or by an abundance of funds in the market seeking to be invested in risky assets.

7.13 CAPM: Describe the Capital Asset Pricing Model (CAPM) and what it tells us.

LO 8 Solution: The CAPM describes the relation between systematic risk and the expected return. The model tells us that the expected return on an asset with no systematic risk equals the riskfree rate. As systematic risk increases, the expected return increases linearly with beta.

The CAPM is written as E(Ri) = Rrf + β i(E(Rm) – Rrf) .

7.14The Security Market Line: If the expected return on the market is 10 percent and the risk-free rate is 4 percent, what is the expected return for a stock with a beta equal to 1.5?

What is the market risk premium?

LO 8 Solution: Following the CAPM prediction: E(Ri) = Rrf + β (E(Rm) – Rrf) = 0.04 + 1.5 × (0.1 – 0.04) = 0.13 The market risk premium is (E(Rm) – Rrf) = 0.06

INTERMEDIATE 7.15 Expected returns: Jose is thinking about purchasing a soft drink machine and placing it in a business office. He knows that there is a 5 percent probability that someone who walks by the machine will make a purchase from the machine, and he knows that the profit on each soft drink sold is $0.10. If Jose expects a thousand people per day to pass by the machine and requires a complete return of his investment in one year, then what is the maximum price that he should be willing to pay for the soft drink machine? Assume 250 working days in a year, and ignore taxes and the time value of money.

LO 3 Solution: E(Revenue) = 1,000 × 0.05 x $.10 × 250 days = $1,250 Therefore, the most Jose should pay for the machine is $1,250.

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7.16 Interpreting the variance and standard deviation: The distribution of grades in an introductory finance class is normally distributed, with an expected grade of 75. If the standard deviation of grades is 7, in what range would you expect 95 percent of the grades to fall?

LO 4 Solution: 95% is 1.960 standard deviations from the mean.

Thus, the range can be determined as: 75 ±(1.960 ×(7)) So, the lower end is: 75 – (1.960 × (7)) = 61.28 And the upper end is: 75 + (1.960 × (7)) = 88.72 So, 95 percent of the grades should fall between 61.28 and 88.72.

7.17 Calculating the variance and standard deviation: Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.4, 0.5, and 0.1, respectively, then what are the expected return and LO 4 the standard deviation of the return on Kate’s investment?

Solution: E(Ri) = (0.4)(0.3) + (0.5) (0.1) + (0.1) (–.25) = 0.145 σ2return = (0.4)(0.3 – 0.145)2 + (0.5) (0.1 – 0.145)2 + (0.1) (–0.25 – 0.145)2 = 0.02623 = (0.02623)1/2= 0.16194 rounded to 0.162 σreturn

7.18 Calculating the variance and standard deviation: Barbara is considering investing in a company’s stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find the expected return and the standard deviation of the return on Barbara’s investment.

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Probability 0.1 0.4 0.3 0.2

Return 25.00% 15.00% 10.00% -5.00%

LO 4 Solution: E(R)i = 0.1 × (0.25) + (0.4) × (0.15) + (0.3) × (0.1) + (0.2) (–0.05) = 0.105 2 σ2return = 0.1 × (0.25 – 0.105)2 + (0.4) ×(0.15 – 0.105)+ (0.3) × (0.1 – 0.105)2+ (0.2) × (–0.05 – 0.105)2

= 0.00773 σreturn = (0.00773)1/2 = 0.08789

7.19 Calculating the variance and standard deviation: Ben would like to invest in gold and is aware that the returns on such an investment can be quite volatile. Use the following table of states, probabilities, and returns to determine the expected return and the standard deviation of the return on Ben’s gold investment.

Probability Return 0.1 Boom 40.00% 0.2 Good 30.00% 0.3 OK 15.00% 0.2 Level 2.00% 0.2 Slump -12.00% LO 4 Solution E(R)i = 0.1 × (0.4) + (0.2) × (0.3) + (0.3) × (0.15) + (0.2) × (0.02) + (0.2) × (–0.12) = 0.125 2 σ2return = 0.1 × (0.4 – 0.125)2+ (0.2) × (0.3 – 0.125)+ 2(0.3) × (0.15 – 0.125) + (0.2) × (0.02 – 0.125)2 + (0.2) × (–0.12 – 0.125)2 = 0.02809 ) = 0.16759 rounded to 0.168 σreturn = (0.028091/2

7.20 Single-asset portfolios:Using the information from Problems 7.17, 7.18, and 7.19, calculate the coefficient of variation for each of the investments in those problems.

LO 3, LO 4 Solution: Coefficient of variation = σReturn / E(Ri) Problem 17: 0.16194/0.145 = 1.11684 (using the exact values rather than the printed) Problem 18: 0.08789/0.105 = 0.83707 (using the exact values rather than the printed) Problem 19: 0.16759/0.125 = 1.34069 (using the exact values rather than the printed) .

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7.21 Portfolios with more than one asset: Emmy is analyzing a two-stock portfolio that consists of a utility stock and a commodity stock. She knows that the return on the utility stock has a standard deviation of 40 percent and the return on the commodity stock has a standard deviation of 30 percent. However, she does not know the exact covariance in the returns of the two stocks. Emmy would like to plot the variance of the portfolio for each of three cases—covariance of 0.12, 0, and –0.12—in order to understand what the variance of the portfolio would be for a range of covariances. Do the calculation for all three cases (0.12, 0 and –0.12), assuming an equal proportion of each stock in the portfolio.

LO 6 Solution:

Var(Rassetport)=x22+x22 22+2x1x21,2 2 11 Case 1, σ1,2 = 0.12: (0.5)2 × (0.4)2 + (0.5)2 × (0.3)2 + 2 × (0.5) × (0.5) × (0.12) = 0.1225 Case 2, σ1,2 = 0.0: (0.5)2 × (0.4)2 + (0.5)2 × (0.3)2 + 2 × (0.5) × (0.5) × (0.0) = 0.0625 Case 3, σ1,2 = -0.12: (0.5)2 × (0.4)2 + (0.5)2 × (0.3)2 + 2 × (0.5) × (0.5) × (-0.12) = 0.0025

7.22Portfolios with more than one asset: Given the returns and probabilities for the three possible states listed below, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 11.75 percent and 18 percent, respectively.

Probability Return on A Return on B Good 0.35 0.30 0.50 OK 0.50 0.10 0.10 Poor 0.15 -0.25 -0.30 LO 6 Solution:

=  AB = 0.35  (0.3 − 0.1175)  (0.5 − 0.18) + 0.5  (0.10−.1175) (0.1 − 0.18) + Cov(R ,R A ) B 0.15 ( −0.25−0.1175)(−0.3−0.18)=0.0476 7.23 Compensation for bearing systematic risk: You have constructed a diversified portfolio of stocks such that there is no unsystematic risk. Explain why the expected return of that portfolio should be greater than the expected return of a risk-free security.

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LO 7 Solution: Your portfolio contains no unsystematic risk but it does contain systematic risk.

Therefore, the market should compensate the holder of this portfolio for the systematic risk that the investor bears. A risk-free security has no risk and therefore requires no compensation for risk bearing. The expected return of your portfolio should therefore be greater than the return of the risk-free security.

7.24 Compensation for bearing systematic risk: Write out the equation for the covariance in the returns of two assets, Asset 1 and Asset 2. Using that equation, explain the easiest way for the two asset returns to have a covariance of zero.

LO 7 Solution:

Cov ( Return1,Return2)=R12

  −E(Return 1) ( Return − E(Return 2) ) =  (ip(Return1,i n

i=1

2,i

We know that all state probabilities must be greater than zero, and thus the source of a zero covariance cannot be from the state probabilities. The easiest way for the entire probability weighted sum to equal zero is for one of the assets, say Number 1(2), to have a value in all states that is equal to the expected return of Number 1(2). Another way of saying that is for one of the assets to have a constant return in all states. If that occurs, then the second term in the equation will always be equal to zero, causing the sum, or covariance, to be zero.

7.25 Compensation for bearing systematic risk: Evaluate the following statement: “By fully diversifying a portfolio, such as by buying every asset in the market, we can completely eliminate all types of risk, thereby creating a synthetic Treasury bill.”

LO 7 Solution: The statement is false. A portfolio of all assets would only eliminate unsystematic risk.

The systematic risk would remain. If you could eliminate both systematic and unsystematic risk, the expected rate of return on the market portfolio would be equal to the risk-free rate of return, and we know that this is not true.

7.26 CAPM: Damien knows that the beta of his portfolio is equal to 1, but he does not know the risk-free rate of return or the market risk premium. He also knows that the expected return on the market is 8 percent. What is the expected return on Damien’s portfolio?

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LO 8 Solution: Following the CAPM prediction: E(Ri) = Rrf + β (E(Rm) – Rrf) = Rrf + E(Rm) – Rrf = E(Rm) = 0.08 = 8.0%

7.27 CAPM: In February 2017 the risk free rate was 2.97 percent, the market risk premium was 6 percent and the beta for Twitter stock was 0.99. What is the expected return that was consistent with the systematic risk associated with the returns on Twitter stock?

LO 8 Solution: From Equation 7.12: E(RTwitter stock) = Rrf + βTwitter stock[E(Rm) - Rrf] E(RTwitter stock) = 0.0297 + 0.99[0.06] E(RTwitter stock) = 0.0297 + 0.0594 = 0.0891, or 8.91% 7.28 CAPM: The market risk premium is 6 percent, and the risk-free rate is 5 percent. If the expected return on a bond is 6.5 percent, what is its beta?

LO 8 Solution: From Equation 7.12, we can calculate the beta of the bond as: E(Rbond) = Rrf + β bond × [E(Rm) - Rrf] 0.065 = 0.050 + β bond × 0.06 β bond = (0.065 – 0.050)/0.060 = 0.25

ADVANCED

7.29 David is going to purchase two stocks to form the initial holdings in his portfolio. Iron stock has an expected return of 15 percent, while Copper stock has an expected return of 20 percent. If David plans to invest 30 percent of his funds in Iron and the remainder in Copper, what will be the expected return from his portfolio? What if David invests 70 percent of his funds in Iron stock?

LO 3 Solution: Part 1: E(Rport) = (0.3) × (0.15) + (0.7) × (0.2) = 0.185 = 18.5% Part 2: E(Rport) = (0.7) × (0.15) + (0.3) × (0.2) = 0.165 = 16.5%

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7.30 Peter knows that the covariance in the return on two assets is –0.0025. Without knowing the expected return of the two assets, explain what that covariance means.

LO 3, LO 6 Solution: The covariance measure is dependent on the expected return of the two assets but without knowing the expected return of the two assets, it is difficult to characterize the scale of the covariance. However, since the covariance is negative, we can say that generally the two assets move in opposite directions, with respect to their own means, from each other in given states of nature.

7.31 In order to expect that it will fund her retirement, Glenda needs her portfolio to have an expected return of 12 percent per year over the next 30 years. She has decided to invest in Stocks 1, 2, and 3, with 25 percent in Stock 1, 50 percent in Stock 2, and 25 percent in Stock 3. If Stocks 1 and 2 have expected returns of 9 percent and 10 percent per year, respectively, then what is the minimum expected annual return for Stock 3 that is likely to enable Glenda to achieve her investment requirement?

LO 3, LO 6 Solution: The formula for the expected return of a three-stock portfolio is: E(R3assetport)=x1E(R1)+x2E(R2)+x3E(R3) Therefore, we can solve as in the following: 0.12 = 0.25 × (0.09) + 0.5 × (0.1) + 0.25 × E(R3) E(R3) = 0.19 or 19.0%

7.32 Tonalli is putting together a portfolio of 10 stocks in equal proportions. What is the relative importance of the variance for each stock versus the covariance for the pairs of stocks in her portfolio? For this exercise, ignore the actual values of the variance and covariance terms and explain their importance conceptually.

LO 4, LO 6 Solution: The variance of the portfolio will be composed of 10 (n = 10) individual stock variance terms and 45 ((n2 –n)/2) covariance terms. Therefore, the vast majority of the portfolio variance calculation will be determined by the covariance terms of the portfolio in most cases.

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7.33 Explain why investors who have diversified their portfolios will determine the price and, consequently, the expected return on an asset.

LO 3, LO 6 Solution: If all investors require returns that compensate them for the level of risk that they bear, then undiversified investors will require a greater return for a given investment than diversified investors will. In other words, diversified investors will be willing to pay a higher price for an asset than will undiversified investors. Therefore, a diversified investor is the marginal investor whose purchase will determine the price, and therefore the expected return for an asset.

7.34 Brad is about to purchase an additional asset for his well-diversified portfolio. He notices that when he plots the historical returns of the asset against those of the market portfolio, the line of best fit tends to have a large amount of prediction error for each data point (the scatter plot is not very tight around the line of best fit). Do you think that this will have a large or a small impact on the beta of the asset? Explain your opinion.

LO 6 Solution: It will have no effect on the beta of the asset. The beta measures only the systematic risk or variation in the returns of the asset. The prediction error reflects the unsystematic risk inherent in the returns of the asset and will consequently not affect the beta of the asset.

7.35 Draw the Security Market Line (SML) for the case where the market risk premium is 5 percent and the risk-free rate is 7 percent. Now suppose an asset has a beta of –1.0 and an expected return of 4 percent. Plot it on your graph. Is the security properly priced? If not, explain what we might expect to happen to the price of this security in the market. Next, suppose another asset has a beta of 3.0 and an expected return of 20 percent. Plot it on the graph. Is this security properly priced? If not, explain what we might expect to happen to the price of this security in the market.

LO 8 Solution: The Security Market Line (SML) shows the relationship between an asset’s expected return and its beta. We know the market has a beta of one, and we know the risk-free rate has a beta of zero. The risk-free rate of return is 7 percent, and the market is expected to return 5 percent more than this. Therefore, the expected rate of return for the market (a beta one asset) is 12 percent. To draw this SML, we need only connect the dots:

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Expected Return

18% 15% 12% 9% 6% 3% 0% 1

0

2

Beta

We can see from the following diagram that an asset with expected return of 4 percent and a beta of –1.0 is underpriced (its expected return is too high). As the market becomes aware of this underpricing, investors will purchase the asset, bidding up its price until its expected return falls on the SML. (Recall that as the initial purchase price of an asset increases, the expected return from purchasing the asset will decrease because you are paying a higher initial cost for the asset.)

18%

Expected Return

15%

The investment will fall here in this plot

12%

9%

6%

3%

0% -1

0

1

2

Beta

As we can see from the following diagram, an asset with a beta of 3.0 should have an expected return of 7% + (3)(5%) = 22%. The asset only has an expected return of 20 percent. Therefore, this asset is overpriced. Demand for this asset will be low, driving down its market price, until the asset’s expected return falls on the SML.

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23%

Expected Return

18%

14%

9%

The investment will fall here in this plot

5%

0% 0

1

2

3

Beta

7.36 If the CAPM describes the relation between systematic risk and expected returns, can both an individual asset and the market portfolio of all risky assets have negative expected real rates of return? Why or why not?

LO 8 Solution: A negative expected real rate of return implies that the expected total rate of return is less than the risk-free rate.

1) It is possible for the beta of an individual stock to be negative. Therefore, from CAPM, E[Ri] = Rrf + βi × [E(Rm) - Rrf)], it is also possible for a share of stock to have a negative expected real rate of return.

2) It is not possible for the market portfolio to have a negative expected real rate of return since the beta for the market equals 1.

7.37 You have been provided the following data on the securities of three firms and the market: σRi Security E[Ri] βi  Stock A

0.15

1.0

1.5

0.18 Stock B 0.15 0.5 0.02 0.5 Stock C 0.10 0.04 Market portfolio 0.10 0 Treasury bills 0.05 Assume the CAPM and SML are true and fill in the missing values in the table. Would you invest in the stock of any of the three firms? If so, which one(s) and why?

LO 8 Solution:

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1) The missing values in the table are:  A = RA,M (  RA )  RM = 1.0( RA ) (0.04)

 RA = 0.06  B = RB,M (  RB )  RM = 0.5(0.18) (0.04) = 2.25  C = RC,M ( RC )  RM = RC,M ( 0.04) 0.02



RC,M

= 1.00

 R M ,M = 1.00;  M = 1.00

 RT−bill,M = 0;  T−bill = 0 2) Using Equation 7.12 you can calculate the expected returns for the different shares: E(RA) = 0.05 + [1.5 × (0.10 - 0.05)] = 0.125, or 12.5% E(RB) = 0.05 + [2.25 × (0.10 - 0.05)] = 0.1625, or 16.25% E(RC) = 0.05 + [0.5 × (0.10 - 0.05)] = 0.075, or 7.5% A comparison of the expected returns that are given in the table above,with the returns that CAPM predicts (which are calculated above), indicates that you should buy stocks A and C and avoid stock B.

Sample Test Problems INTERMEDIATE Given the following information from Capstone Corporation, what price would CAPM predict that the company’s stock will trade for 1 year from today. Assume that the risk free rate is 3 percent and that the market risk premium is 8 percent?

Beta: 0.65 Current stock price: $64.61 Annual dividend: $1.92 LO 2, LO 8 Solution: Using CAPM, we find: E(RCapstone) = Rrf + ßCapstone × (E(Rm) – Rrf) 7.1

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= 0.03 + (0.65 × 0.08) = 0.082 or 8.2 percent Using the total holding period return formula (Equation 7.1) we can solve for the stock price in one year:

P RT=1

7.2.

P0−+ CF 1 0.082= P0

P1 −$64.61+1.92 P1=$67.99 $6 4.6 1

You are considering investing in a mutual fund. The fund is expected to earn a return of 15 percent in the next year. If its annual return is normally distributed with a standard deviation of 6.5 percent, what return can you expect the fund to beat 95 percent of the time?

LO 4 Solution: Since the annual returns earned by the mutual fund are normally distributed, a 95 percent confidence level corresponds to 1.96 standard deviations from the mean.

Therefore, 95 percent of the time you would expect the annual return for next year to be in the range: 0.15 + (1.96× 0.065).

The lower end of this range is: 0.15 – (1.96 × 0.065) = 0.0226, or 2.61%, which is the return that you can expect the fund to beat 95 percent of the time.

7.3

You have just invested in a portfolio of three stocks. The amount of money that you invested in each stock and its beta are summarized below. Calculate the beta of the portfolio and use the capital asset pricing model (CAPM) to compute the expected rate of return for the portfolio. Assume that the expected rate of return on the market is 15 percent and that the risk-free rate is 7 percent.

Stock Investment Beta A $ 200,000 1.50 B 300,000 0.65 C 500,000 1.25

LO 3, LO 8 Solution:

Portfolio Beta = p=

N



wii

i=1

A

$200,000

20%

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B $300,000 30% C 50% $500,000 100% Total $1,000,000  p = (0.20 × 1.50) + (0.30 × 0.65) + (0.50 × 1.25) = 1.12 E(RPortfolio) = Rrf + βPortfolio (E(RM) – Rrf) = 0.07 + [1.12 × (0.15 - 0.07)] = 0.1596, or 15.96%

7.4

What would you recommend to an investor who is considering making an investment in a stock which plots below the security market line (SML)? Explain.

LO 8 Solution: You should recommend that the investor not make this investment. An investment that plots below the SML has an expected return that is too low to fully compensate the investor for its systematic risk. In other words, its price is so high that it is not expected to yield a sufficiently high return to compensate for its risk. If investors in the market as a whole realize this, they will sell the stock in question and its price will be driven down by such sales to the point where the expected return fully compensates them for the risk. If the investor you are advising buys the stock now and its price subsequently declines, he or she will bear the cost of that decline.

7.5 Why does an investor want a diversified portfolio? Can an investor eliminate all risk?

LO 6, LO 7 Solution: An investor of a diversified portfolio reduces total risk by investing in two or more assets whose values do not always move in the same direction at the same time. With enough diversification, the investor can eliminate unsystematic or unique risk, but, by definition, will not be able to eliminate systematic, or market risk.

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CHAPTER 8 Bond Valuation and the Structure of Interest Rates Before You Go On Questions and Answers Section 8.1 1.

What are the main differences between the corporate bond markets and stock markets?

The market for corporate bonds is very large, but smaller than the corporate equity market in the U.S. Most secondary market transactions involving corporate bonds take place in the over-the-counter market, making the corporate bond market thin relative to the more organized equity markets. Prices in the corporate bond market also tend to be more volatile than prices of securities sold in markets with greater trading volumes. This is because a few large trades can have a larger impact on a security’s price than numerous trades of various sizes. The biggest investors in corporate bonds are mutual funds, life insurance companies, and pension funds, and given the size of these investors, the trades are conducted in much larger blocks than in the stock market.

2.

A bond has a 7 percent coupon rate, a face value of $1,000, and a maturity of four years.

On a time line, lay out the cash flows for the bond.

The annual payments for the bond will be $70 ($1,000 x 7%); thus the time line for cash inflows would be as follows: 0

3.

1

_2

_______3

$70

$70

$70

_____4 $1,070 ($1,000 + $70)

Explain what a convertible bond is.

Convertible bonds are bonds that can be converted into shares of common stock at some predetermined ratio at the discretion of the bondholder. The convertible feature allows

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the bondholder to take advantage of the firm’s prosperity if the share prices rises above a certain value.

Section 8.2 1.

Explain conceptually how bonds are priced.

The current price of a bond is equal to the present value of all the cash flows that will be received from the investment. There are two sets of cash flows from a bond investment.

First, there are the coupon payments to be received either annually or semiannually throughout the life of the bond. Second, there is the principal or face value of $1,000 that will be received when the bond matures. In order to find the price of the bond, we must find the present value of the coupons and the present value of the face value. We do this by discounting the entire cash flow stream at the current market rate and adding them up.

This gives us the current price of the bond. Recognize that the coupons represent an annuity and that we can use the equation for the present value of an annuity from Chapter 6 to calculate the present value of this cash flow stream.

2.

What is the compounding period for most bonds sold in the United States?

Most bonds sold in the United States pay interest semiannually, whereas European bonds typically only pay interest once a year.

3.

What are zero coupon bonds, and how are they priced?

Zero coupon bonds are debt instruments that do not pay coupon interest but promise a single payment (interest earned plus principal) paid at maturity. The price of a zero coupon bond can be calculated using the same equation as used for coupon bonds, but setting the coupon payments to zero. The resulting formula is as follows: PB = Fmn/(1 + i/m)mn Because zero coupon bonds offer the entire payment at maturity, for a given change in interest rates, their price fluctuates more than coupon bonds with a similar maturity.

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Section 8.3 1.

Explain how bond yields are calculated.

A bond’s yield is calculated by finding the interest rate that equates the bond’s price to the present value of its interest payments and principal amount. The calculation of a bond’s yield, or its yield to maturity, takes into account the bond’s time to maturity, the coupon rate, and face value.

Section 8.4 1.

What is interest rate risk?

Bond prices are negatively related to interest rate movements. As interest rates rise, bond prices fall, and vice versa. Interest rate risk simply recognizes the fact that bond prices fluctuate as interest rates change, and, if you sell a bond before maturity, you may sell the bond for a price other than what you paid for it. The greater the fluctuation in bond prices due to changes in interest rates, the greater the interest rate risk.

2.

Explain why long-term bonds with zero coupons are riskier than short-term bonds that pay coupon interest.

According to bond theorems number two and three, for a given change in interest rates, longer-term bonds with low coupon rates have greater price changes than shorter-term bonds with higher coupon rates. The likelihood of interest rates changing during the long run is higher than the short term. Thus, long-term zero coupon bonds have greater interest rate risk—greater price swings—than short-term bonds that pay coupon payments.

Section 8.5 1.

.

What are default risk premiums, and what do they measure?

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Default risk premiums are the amount of return that investors must be paid to purchase a security that possesses default risk compared to a similar risk-free investment. Default risk premiums, at any point in time, represent compensation for the expected financial injury for owning a bond plus some additional premium for bearing risk.

2.

Describe the three most prominent bond rating systems.

Default risk premiums tend to increase during periods of economic decline and to narrow during periods of economic expansion. This phenomenon is due to changes in investors’ willingness to own bonds with different credit ratings over the business cycle, the socalled flight to quality argument. Specifically, during periods of expansion when few defaults take place, investors are willing to invest in bonds with low credit quality (these bonds typically pay higher interest rates) to gain higher yields. In contrast, during tough economic times when many businesses fail, investors are concerned with safety.

Accordingly, they adjust their portfolios to include more high-quality credits and sell off bonds with low credit ratings. The three most prominent credit rating agencies are Moody’s Investors Service (Moody’s), Standard & Poor’s (S&P) and Fitch. Exhibit 8.4 describes the corporate bond rating systems used by the three rating agencies.

3.

What are the key factors that most affect the level and shape of the yield curve?

The key factors that most affect the shape of the yield curve are the real rate of interest, the expected rate of inflation, and interest rate risk. If the future real rate of interest is expected to rise, it will result in an upward slope of the real rate of interest and consequently in an upward bias to the market yield curve. Similarly, increasing the expected rate of inflation will result in an upward-sloping yield curve, because long-term interest rates will contain a larger inflation premium than short-term interest rates. If these two variables are expected to decline in the future, the result will be a downward bias to the yield curve. In contrast, the longer a bond’s maturity, the greater the bond’s interest rate risk. Thus, interest rate risk premium always adds an upward bias to the

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slope of the yield curve, since the longer the maturity of a security, the greater its interest rate risk.

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Self-Study Problems 8.1

Calculate the price of a five-year bond that has a coupon of 6.5 percent paid annually.

The current market rate is 5.75 percent.

Solution: 0 5.75%

1

2

3

4

5 Year

├───────┼────────┼───────┼────────┼───── $65

PB = =

$65

$65

$65

$1,065

C+F C3 C1 C C4 + +2 + + + 5 5 (1 i)2 (1+ i)3 (1+ i)4 (1+i)5 1+i $65 ($65 + $1, 000) $65 $65 $65 + + + + (1.0575)5 (1+ 0.0575)1 (1.0575)2 (1.0575)3 (1.0575)4

= $61.47+ $58.12+$54.96+$51.95+$805.28 = $1, 031.81 Financial Calculator Solution: Enter

5

5.75

N

i

Answer 8.2

PMT

65

1000

PV

FV

-1,031.81

Bigbie Corp. issued a five-year bond a year ago with a coupon of 8 percent. The bond pays interest semiannually. If the yield to maturity on this bond is 9 percent, what is the price of the bond?

Solution: 0 9% 1

2

3

4

5

6

7

8 Semiannual Period

├───┼───┼───┼────┼───┼───┼───┼────┤ PB =? $40

.

$40

$40

$40

$40

$40

$40

$1,040

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PB =

C 8 + 8F C2 / m C3 / m C1 / m + + +..........+ (1+ i / m)1 (1+ i / m)2 (1+ i / m)3 (1+ i / m)8

=

($40+$1,000) $40 $40 + + +........+ (1.045)8 (1+ 0.09 / 2)1 (1.045)2 (1.045)3 $80/2

+ = $38.28 + $36.63 + $35.05 + $33.54 + $32.10 + $30.72 + $29.39 $731.31 = $967.02 Alternatively, we can use the present value annuity factor (in Equation 5.5) and the present value equation (Equation 5.4) from Chapter 5 to solve for the price of the bond:  1−  C = PB  m   

1

(1+i m)

mn

i m

= $263.84 + $703.19

 1    8  1−  (1 + 0.045) Fn = $40   + mn i m   (1 + 0.045 ) +       

$1,000

(1.045) 8

= $967.03

Financial Calculator Solution: Enter

8

4.5

40

N

i

PMT

PV

FV

-967.03

Answer 8.3

1000

Rockwell Industries has a three-year bond outstanding that pays a 7.25 percent coupon and is currently priced at $913.88. What is the yield to maturity of this bond? Assume annual coupon payments.

Solution: 0

1

2

3

├───────┼────────┼───────┤ PB = $913.88

.

$72.50

$72.50

$1,072.50

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Solutions Manual

Use the trial-and error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate.

Try YTM = 10%.

PB = =

C 3 + 3F C1 C2 3 + 2 + (1+i) 1 + i ( 1+ i ) $72.50 1.10

+

$72.50 (1.10)2

+

$72.50+$1,000 (1.10)3

= $65.91 + $59.92+$805.79  $931.61

Try a higher rate, say YTM = 11%.

PB = =

C 3 + 3F C1 C2 3 + 2 + (1+i) 1 + i ( 1+ i ) $72.50 $72.50 $72.50+$1,000 + + (1.11)3 1.11 (1.11)2

= $65.32 + $58.84+$784.20  $908.36

Since this is less than the price of the bond, we know that the YTM is between 10 and 11 percent and closer to 11 percent.

Try YTM = 10.75%.

PB = =

C + F C1 C2 + + 3 33 2 1 + i ( 1+ i ) ( 1 + i ) $72.50 $72.50 $72.50+$1,000 + + 1.1075 (1.1075)2 (1.1075)3

= $65.46+ $59.11+$789.53  $914.09 Alternatively, we can use Equation 5.5 and the present value equation (Equation 5.4) from Chapter 5 to solve for the price of the bond:

.

SM 8-8

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

1    1(1+i)n −  Fn + PB = C   i   (1+i)n     1  1 − (1.1075)3 $1,000  $913.88= $72.50  0.1075 + (1.1075)3     = $177.94+ $736.15 $914.09 Thus, the YTM is approximately 10.75 percent. Using a financial calculator provided an exact YTM of 10.7594 percent.

Financial Calculator Solution : Enter

3 N

-913.88

1,000

PMT

PV

FV

i

Answer 8.4

72.50 10.7594

Hindenberg, Inc., has a 10-year bond that is priced at $1,100.00. It has a coupon of 8 percent paid semiannually. What is the yield to maturity on this bond?

Solution: 0

1

2

3

4

5

6

19

20

├───┼────┼───┼───┼───┼────┼── ─┼────┤ $40

$40

$40

$40

$40

$40

$40

$40 $1,000

The easiest way to calculate the yield to maturity is with a financial calculator. The inputs are as follows: Enter

20 N

Answer

.

i

40

−1,100

1,000

PMT

PV

FV

3.31

SM 8-9

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

The answer we get is 3.31 percent, which is the semiannual interest rate. To obtain an annualized yield to maturity, we multiply this by two: YTM = 3.31%  2 YTM = 6.62% 8.5

Highland Corp., a U.S. company, has a five-year bond whose yield to maturity is 6.5 percent. The bond has no coupon payments. What is the price of this zero coupon bond?

Solution: You have the following information: YTM = 6.5% No coupon payments Most U.S. bonds pay interest semiannually. Thus m x n = 5 × 2 = 10 and i/2 = 0.065/2 = 0.0325. Using Equation 7.3, we obtain the following:

PB = =

Fmn

(1+i m) mn

$1,000 (1.0325)10

= $726.27 Financial Calculator Solution: Enter

10

3.25

N

i

Answer

0 PMT

1,000 PV

FV

-726.27

Discussion Questions

.

SM 8-10

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

8.1 Because the conversion feature in a convertible bond is valuable to bondholders, convertible bond issues have lower coupon payments than otherwise similar bonds that are not convertible. Does this mean that a company can lower its cost of borrowing by selling convertible debt? Explain.

No. The interest (coupon) payments can be reduced by the company but the company cannot reduce the overall cost of borrowing by selling convertible debt. The reduction in the value of the interest payments is offset by the value of the conversion feature. If the company’s stock price goes above the price implied by the conversion ratio, the existing stockholders must share some of their gains with the bondholders. Investors are going to look for a required rate of return that compensates them for the risk that they are bearing. The only difference with a convertible bond is that some of that compensation comes in the form of the ability to benefit from appreciation in the company’s stock price.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.2

What economic conditions would prompt investors to take advantage of a bond’s convertibility feature?

A bond’s convertibility feature becomes attractive when the company’s stock price rises above the bond’s price. This usually happens in times of economic expansion when the stock market is booming and interest rates are increasing, hence lowering the bond’s price.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-11

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

8.3 We know that a vanilla bond with a coupon rate below the market rate of interest will sell for a discount and that a vanilla bond with a coupon rate above the market rate of interest will sell for a premium. What kind of bond or loan will sell at its par value regardless of what happens to the market rate of interest?

A bond (or a loan) that pays a variable coupon (interest) rate that moves up and down with the market rate of interest will sell at its par value regardless of what happens in the market.

While corporate bonds in the U.S. do not have variable coupon payments, bank loans often have variable rates which adjust frequently enough so that the value of the loans remains relatively constant as interest rates move up and down over time.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.4

Define yield to maturity. Why is it important?

Yield to maturity (YTM) is the rate of return earned by investors if they buy a bond today at its market price and hold it to maturity. It is important because it represents the opportunity cost to the investor or the discount rate that makes the present value of the bond’s cash flows (i.e., its coupons and its principal payments) equal to the market price. So, YTM is also referred to as the going market rate or the appropriate discount rate for a bond’s cash flows.

It is important to understand that any investor who buys a bond and holds it to maturity will have a realized gain equal to the yield to maturity. If the investor sells before the maturity date, then realized gain will not be equal to the YTM, but will only be based on cash flows earned to that point. Similarly, for callable bonds, investors are guaranteed a gain to the point in time when the bond is first called, but they cannot be assured of the yield to maturity because the issuer could call the bond before maturity.

LO: 3 Level: Basic

.

SM 8-12

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.5

Define interest rate risk. How can the CFOs manage this risk?

The change in a bond's prices caused by changes in interest rates is called interest rate risk.

In other words, we can measure the interest rate risk to a bond’s investor by measuring the percentage change in the bond’s price caused by a 1 percent change in the market interest rates.

The key to managing interest rate risk is to understand the relationships between interest rates, bond prices, the coupon rate, and the bond’s term to maturity. Portfolio managers need to understand that as interest rates rise bond prices decline, and it declines more for low-coupon bonds and longer-term bonds than for the others. In such a scenario, bond portfolio managers can reduce the size and maturity of their portfolio to reduce the impact of interest rate increases. When interest rates decline, bond prices increase and rise more for longer-term bonds and higher coupon bonds. At such times, CFOs can increase the size and maturity of their portfolios to take advantage of the inverse relationship between interest rates and bond prices.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Risk Analysis

8.6

Explain why bond prices and interest rates are negatively related. What are the roles of the coupon rate and the term to maturity in this relation?

Bond prices and interest rates are negatively related because the market rate varies, while the coupon rate and face value are constant over the life of the bond. Thus, as rates increase, of the present value of the interest and principle payments from existing bonds declines.

.

SM 8-13

Fundamentals of Corporate Finance, 4th edition

o

Solutions Manual

For a given change in interest rates, longer-term bonds experience greater price changes (price volatility) than shorter-term bonds. Longer-term bonds have a larger proportion of their cash flows farther in the future, and the change in the present value of those longer-term cash flows will be greater when interest rates change because they are more heavily discounted. In addition, the longer it takes for investors to receive the cash flows, the more uncertainty they have to deal with and hence the more price-volatile the bond will be.

o

Lower coupon bonds are more price volatile than higher coupon bonds. The same argument used above also explains this relationship. The lower the coupon on a bond, the greater the proportion of cash flows that investors receive at maturity, as opposed to the higher coupon bonds which give the investors cash flow in higher amounts before maturity.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.7

If interest rates are expected to increase, should investors look to long-term bonds or short-term securities? Explain.

As interest rates increase, bond prices decrease with longer-term bonds, experiencing a bigger decline than shorter-term securities. So, investors expecting an increase in interest rates should choose short-term securities over long-term securities and reduce their interest rate risk.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.8

Explain what you would assume the yield curve would look like during economic expansion and why.

.

SM 8-14

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

At the beginning of an economic expansion, the yield curve tends to be rather steep as the rates begin to rise once the demand for capital is beginning to pick up due to growing economic activity. The yield curve will retain its positive slope during the economic expansion, which reflects the investors’ expectations that the economy will grow in the future and that the inflation rates will also rise in the future.

LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.9

An investor holds a 10-year bond paying a coupon rate of 9 percent. The yield to maturity of the bond is 7.8 percent. Would you expect the investor to be holding a par-value, premium, or discount bond? What if the yield to maturity were 10.2 percent? Explain.

Since the bond’s coupon of 9 percent is greater than the yield to maturity, the bond will be a premium bond. As market rates of interest drop below the coupon rate of the 9 percent bond, demand for the bond increases, driving up the price of the bond above face value.

If the yield to maturity is at 10.2 percent, then the bond is paying a lower coupon than the going market rate and will be less attractive to investors. The demand for the 9 percent bond will decline, driving its price below the face value. This will be a discount bond.

LO: 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-15

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

8.10 a. Investor A holds a 10-year bond, while investor B holds an 8-year bond. If interest rate increases by 1 percent, which investor has the higher interest rate risk? Explain.

Since A holds the longer-term bond, he or she will face the higher interest rate risk.

Longer-term bonds are more price volatile than shorter-term bonds. b. Investor A holds a 10-year bond paying 8 percent a year, while investor B also has a 10-year bond that pays a 6 percent coupon. Which investor has the higher interest rate risk? Explain.

Investor B will have the higher interest rate risk since lower coupon bonds have a higher interest rate risk than higher coupon bonds of the same maturity.

LO: 4 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Questions and Problems BASIC 8.1

Bond price: BA Corp is issuing a 10-year bond with a coupon rate of 8 percent. The interest rate for similar bonds is currently 6 percent. Assuming annual payments, what is the value of the bond?

Solution: Years to maturity = n = 10 Coupon rate = C = 8%

.

SM 8-16

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Annual coupon = $1,000 × 0.08 = $80 Current market rate = i = 6% Present value of bond = PB 0 6% 1

2

3

4

5

10 Years

6

─────┤ ├───┼────┼───┼───┼───┼────┼── $80

$80

$80

$80

$80

$80

$80 + $1,000

PB=

C3 C10+ F 10 C1 C + + + +2 + (1 i )2 (1+ i)3 (1 + i )10 i (1 +)1

 1  1  1−  Fn (1 + i )n  (1.06)10  $1,000   = C 1 − = $80 (1.06)10  + + i)n  0.06 + i   (1          = $1,147.20 $558.39 = $588.81+ 

Financial Calculator Solution : Enter

10

6

80

N

i

PMT

1000

FV

PV -1,147.20

Answer LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.2

Bond price: Pierre Dupont just received a cash gift from his grandfather. He plans to invest in a five-year bond issued by Venice Corp. that pays an annual coupon rate of 5.5 percent. If the current market rate is 7.25 percent, what is the maximum amount Pierre should be willing to pay for this bond?

Solution: 0

7.25%

1

2

3

4

5 Years

.

SM 8-17

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

├───────┼────────┼───────┼────────┼───────┤ $55

$55

$55

$55

$1,055

Coupon rate = C = 5.5% Annual coupon = $1,000 × 0.055 = $55 Current market rate = i = 7.25% Present value of bond = PB

1    1  1−  1−(1+ i)n   (1.0725)5 Fn   $1,000 = $55   PB= C   + i (1+ i)n  0.0725 + (1.0725)5            = $224.01+ $704.72= $928.72 Financial Calculator Solution: Enter

5

7,25

55

N

i

PMT

Answer

1000 PV

FV

-928.72

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.3

Bond price: Knight, Inc., has issued a three-year bond that pays a coupon rate of 6.10 percent. Coupon payments are made semiannually. Given the market rate of interest of 5.80 percent, what is the market value of the bond?

Solution: Years to maturity = n = 3 Coupon rate = C = 6.1% Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.061/2) = $30.50 Current market rate = i = 5.8% Present value of bond = PB

.

SM 8-18

Fundamentals of Corporate Finance, 4th edition

0 5.8% 1

2

3

4

Solutions Manual

5

6

Periods

├───┼────┼───┼───┼───┼────┤ $30.50 $30.50 $30.50 $30.50 $30.50 $30.50 + $1,000

1  1   2 n  1− i   (1.029)6 $1,000 F2n 2  = $3 0.5 0    + 2n i  0.0 2 9 + (1.029)6  1+ i 2 2        = $165.77+ $842.38= $1,008.15

 1 − PB= C    2  

(1+)

(

)

Financial Calculator Solution: Enter

6

2.9

30.50

N

i

PMT

Answer

1,000 PV

FV

-1,008.15

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.4

Bond price: Regatta, Inc., has seven-year bonds outstanding that pay a 12 percent coupon rate. Investors buying these bonds today can expect to earn a yield to maturity of 8.875 percent. What is the current value of these bonds? Assume annual coupon payments.

Solution: Years to maturity = n = 7 Coupon rate = C = 12% Annual coupon = $1,000 x 0.12 = $120 Current market rate = i = 8.875% Present value of bond = PB

.

SM 8-19

Fundamentals of Corporate Finance, 4th edition

08.875%1

2

3

4

Solutions Manual

5

6

7

Years

├───┼────┼───┼───┼───┼────┼───┤ $120 $120 $120 $120 $120 $120

$120+ $1,000

   1  1 1−  1−(1 + i)n  (1.08875)7 Fn $1,000   = $120   PB= C   + n i   0.08875 + (1.08875)7  (1 + i)         = $606.50+ $551.44 = $1,157.94 Financial Calculator Solution: Enter

7

8.875

N

i

Answer

120 PMT

1,000 PV

FV

-1,157.94

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.5

Bond price: You are interested in investing in a five-year bond that pays a 7.8 percent coupon rate with interest to be received semiannually. Your required rate of return is 8.4 percent. What is the most you would be willing to pay for this bond?

Solution: Years to maturity = n = 5 Coupon rate = C = 7.8% Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.078/2) = $39.00 Current market rate = i = 8.4% Present value of bond = PB

.

SM 8-20

Fundamentals of Corporate Finance, 4th edition

0 8.4% 1

2

3

4

Solutions Manual

5

10 Periods

6

├───┼────┼───┼───┼───┼────┼── ─────┤ $39

$39

$39

$39

$39

$39+

$39

$1,000

1  1   2 n  i 1−  10 F2n (1.042)  $1,000 2 =   $39  + 2n i  0.0 4 2 + (1.042)10  1+ i 2 2        = $313.20+ $662.71= $975.91

 1 − PB= C    2  

(1+)

(

)

Financial Calculator Solution: Enter

10

4.2

39

N

i

PMT

Answer

1,000 PV

FV

-975.91

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.6

Zero coupon bonds: Diane Carter is interested in buying a five-year zero coupon bond with a face value of $1,000. She understands that the market interest rate for similar investments is 9 percent. Assume annual coupon payments. What is the current value of this bond?

Solution: Years to maturity = n = 5 Coupon rate = C = 0% Current market rate = i = 9% 0 9% 1

.

2

3

4

5 Years

SM 8-21

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

├───┼────┼───┼───┼───┤ $0

$0

$0

$0

$0+ $1,000

PB =

Fmn

(1 +i m)

mn

=

$1,000 =$649.93 (1.09)5

Financial Calculator Solution: Enter

5

9

0

N

i

PMT

1,000 PV

FV

-649.93

Answer LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.7

Zero coupon bonds: Ten-year zero coupon bonds issued by the U.S. Treasury have a face value of $1,000 and interest is compounded semiannually. If similar bonds in the market yield 10.5 percent, what is the value of these bonds?

Solution: Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i = 10.5% 010.5% 1

2

3

4

5

6

20 Periods

├───┼────┼───┼───┼───┼────┼── ─────┤ $0

$0

$0

$0

$0

$0

$0 + $1,000

PB =

.

Fmn

=

$1,000 = $359.38 (1.0525)20

)mn (1+i m

SM 8-22

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Financial Calculator Solution: Enter

20

5.25

0

N

i

PMT

1,000 PV

FV

-359.38

Answer LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.8

Zero coupon bonds: Northrop Real Estate Company management is planning to fund a development project by issuing 10-year zero coupon bonds with a face value of $1,000.

Assuming semiannual compounding, what will be the price of these bonds if the appropriate discount rate is 14 percent?

Solution: Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i = 14% 014% 1

2

3

4

5

6

20 Periods

this ├───┼────┼───┼───┼───┼────┼── ─────┤ $0

$0

$0

$0

$0

$0

$0 + $1,000

PB =

Fmn

=

$1,000 = $258.42 (10 . 7)20

)mn (1+i m

Financial Calculator Solution:

.

SM 8-23

Fundamentals of Corporate Finance, 4th edition

Enter

Solutions Manual

20

7

0

N

i

PMT

Answer

1,000 PV

FV

-258.42

LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.9

Yield to maturity: Ruth Hornsby is looking to invest in a three-year bond that makes semiannual coupon payments at a rate of 5.875 percent. If these bonds have a market price of $981.13, what yield to maturity can she expect to earn?

Solution: Years to maturity = n = 3 Coupon rate = C = 5.875% Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.05875/2) = $29.375 Yield to maturity = i Present value of bond = PB = $981.13 Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate.

Try YTM = 6%.

.

SM 8-24

Fundamentals of Corporate Finance, 4th edition

 1−  PB = C   2   

1

(1+i 2) i

2n

2

   +   

Solutions Manual

F2n

( 1 +) i 2 2n

1   6   1 − (1 + 0.03) $1,000  (1.03)6 $981.13  $29.375   0.03  +       $159.13 + $837.48  $996.61

Try a higher rate, say YTM = 6.6%.  1−  PB = C   2   

1

   F2n 2 + 2n i  2      + 1  6  1 − (1 + 0.033)  $1,000 $981.13  $29.375    0.033 (1.033)6     $157.56 + $823.00

(1+i)

2n

( 1 +) i 2

 $980.56

The YTM is approximately 6.6 percent. Using a financial calculator provided an exact YTM of 6.58 percent Enter

6

$29.375 -$981.13 $1,000 N

Answer

i%

PMT

PV

FV

3.29 x 2 = 6.58%

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-25

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

8.10 Yield to maturity: Rudy Sandberg wants to invest in four-year bonds that are currently priced at $868.43. These bonds have a coupon rate of 6 percent and make semiannual coupon payments. What is the current market yield on this bond?

Solution: Years to maturity = n = 4 Coupon rate = C = 6% Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.06/2) = $30 Yield to maturity = i Present value of bond = PB = $868.43 Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate.

Try YTM = 10%.  1−  PB = C   2   

1

(1+ i 2) i

2

2n

   +   

F2n

(1 ) + i2

2n

=

1   8 (1 0.05) + − 1   $1,000 $868.43  $30    + (1.05)8 0.05       $193.90 + $676.84  $870.74

Try a higher rate, say YTM = 10.1%.

.

SM 8-26

Fundamentals of Corporate Finance, 4th edition

 1−  PB = C   2   

1

(1 + i 2 ) i

2n

2

   +   

Solutions Manual

F2n

(1+ i2 )

2n

1   1− 8  (1 + 0.0505)  $1,000 $868.43  $30*  8 +  0.0505 (1.0505)        $193.51 + $674.27  $867.78

The YTM is approximately 10.1 percent. Using a financial calculator provided an exact YTM of 10.08 percent.

Enter

8 N

Answer

i%

$30

-$868.43

$1,000

PMT

PV

FV

5.04 x 2 =10.08%

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.11 Realized yield: Josh Kavern bought 10-year, 12 percent coupon bonds issued by the U.S. Treasury three years ago at $913.44. If he sells these bonds, for which he paid the face value of $1,000, at the current price of $804.59, what is his realized yield on the bonds?

Assume similar coupon-paying bonds make annual coupon payments.

Solution: Purchase price of bond = $913.44 Years investment held = n = 3 Coupon rate = C = 12% Frequency of payment = m = 1

.

SM 8-27

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Annual coupon = $1,000 × (0.12) = $120 Realized yield = i Selling price of bond = PB = $804.59 To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has declined, market rates must have increased.

So, the realized return is going to be less than the bond’s coupon. Try rates lower than the coupon rate.

Try i = 10%.

 1  1−(1+ i)n  Fn  PB= C   + i (1+ i) n        1  1 − (1.10)3 $804.59 $913.44= $120   +  0.10  (1.10)3     = $298.42+ $604.50 $902.92 Try a lower rate, i = 9.5%.

 1  1−(1+ i)n  Fn  PB= C   + i (1+ i) n         1 1 − (1.095)3 $804.59 $913.44= $120   +  0.095  (1.095)3    = $301.07+ $612.82=$913.89 The realized rate of return is approximately 9.5 percent. Using a financial calculator provided an exact yield of 9.52 percent.

Enter

3 N

Answer

i%

$120

-$913.44

$804.59

PMT

PV

FV

9.52%

LO 3 Bloomcode: Application

.

SM 8-28

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.12 Realized yield: Four years ago, Lisa Stills bought six-year, 5.5 percent coupon bonds issued by the Fairways Corp. for $947.68. If she sells these bonds at the current price of $894.52, what will be her realized yield on the bonds? Assume similar coupon-paying bonds make annual coupon payments.

Solution: Purchase price of bond = $947.68 Years investment held = n = 4 Coupon rate = C = 5.5% Frequency of payment = m = 1 Annual coupon = $1,000 × (0.055) = $55 Realized yield = i Selling price of bond = PB = $894.52 To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has declined, market rates must have increased.

So, the realized return is going to be less than the bond’s coupon. Try rates lower than the coupon rate.

Try i = 5%.

 1  1−(1+ i)n  Fn  PB= C   + (1+ i) n i        1  1 − (1.05)4 $894.52 $947.68= $55   +  0.05  (1.05)4      $930.95 = $195.03+ $735.92 Try a lower rate, i = 4.5%.

.

SM 8-29

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

 1  1−(1+ i)n  Fn  PB= C   +  i (1+ i) n       1  1 − (1.045)4 $894.52 $947.68= $55   0.045  + (1.045)4      = $197.31+ $750.11 $947.42  The realized rate of return is approximately 4.5 percent. Using a financial calculator provided an exact yield of 4.49 percent.

Enter

4 N

Answer

i%

$55

-$947.68

$894.52

PMT

PV

FV

4.49%

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

INTERMEDIATE 8.13 Bond price: The International Publishing Group is raising $10 million by issuing 15-year bonds with a coupon rate of 8.5 percent. Coupon payments will be made annually.

Investors buying the bonds today will earn a yield to maturity of 8.5 percent. At what price will the bonds sell in the marketplace? Explain.

Solution: Years to maturity = n = 15 Coupon rate = C = 8.5% Annual coupon = $1,000 × 0.085 = $85 Current market rate = i = 8.5% Present value of bond = PB

.

SM 8-30

Fundamentals of Corporate Finance, 4th edition

0 8.5% 1

2

3

Solutions Manual

15

4

Year

─────┤ ├───┼────┼───┼───┼─── $85

$85

$85

$85+

$85

$1,000 n = 15;

C = 8.5%;

i = YTM = 8.5%

   1  1 1−  1−(1+ i)n  Fn (1.085)15  $1,000  = $85   PB= C   + (1+ i)n  0.0 8 5 + (1.085)15 i            = $705.86+ $294.14 = $1,000.00 This answer should have been intuitive. Since the bond is paying a coupon equal to the going market rate of 8.5 percent, the bond should be selling at its par value of $1,000.

Enter 15 8.5% $85 $1,000 N Answer

i%

PMT

PV

FV

-$1,000

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.14 Bond Price: Lopez Information Systems management is planning to issue 10-year bonds. The going market yield for such bonds is 8.125 percent. Assume that coupon payments will be made semiannually. Management is trying to decide between issuing an 8 percent coupon bond or a zero coupon bond. Lopez needs to raise $1 million. What will the price of an 8 percent coupon bond be, and how many 8 percent coupon bonds will have to be issued?

What will the price of a zero coupon bond be, and how many zero coupon bonds will have to be issued?

.

SM 8-31

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: 8 percent coupon bonds Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 8.00% Semiannual coupon = $1,000 × (0.08/2) = $40 Current market rate = i = 8.125% Present value of bond = PB 0

8.125%

1

2

3

20

├───────┼────────┼────────┼── ─────────┤ $40

$40

$40

$40+ $1,000

1  mn  i F 2n 2   i + 1+ i 2 2    = $540.62+ $450.94= $991.56

 1 − PB= C    2  

(1+)

(

1   1−(1.040625)20  $1,000  = $40    0.040625 + (1.040625)20     

)mn

The firm can sell these bonds at $991.56 .

Enter

20

4.0625%

N

i%

Answer

$40 PMT

$1,000 PV

FV

-$991.55

Amount to be raised = $1,000,000 Number of bonds sold = $1,000,000 / $991.55 = 1,009 bond contracts Zero coupon bonds Years to maturity = n = 10 Coupon rate = C = 0%

.

SM 8-32

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Current market rate = i = 8.125% 0 8.125%

1

2

3

4

5

20

6

─────┤ ├───── ┼────┼───┼───┼───┼────┼── $0

$0

$0

$0

$0

$0+

$0

$1,000

PB =

Fmn

=

$1,000

= $450.94

)20 )mn(1.040625 (1+i m

Enter

20

4.0625%

N

i%

Answer

$0

$1,000

PMT

PV

FV

-$450.94

Amount to be raised = $1,000,000 Number of bonds sold = $1,000,000 / $450.94 = 2,218 bond contracts (Rounded) LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.15 Bond price: Marshall Company is issuing eight-year bonds with a coupon rate of 6.5 percent and semiannual coupon payments. If the current market rate for similar bonds is 8 percent, what will be the bond price? If company management wants to raise $1.25 million, how many bonds does the firm have to sell?

Solution: Years to maturity = n = 8 Frequency of payment = m = 2 Coupon rate = C = 6.5% Semiannual coupon = $1,000 × (0.065/2) = $32.50 .

SM 8-33

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Current market rate = i = 8% Present value of bond = PB 0 8% 1

2

3

16

4

Period

─────┤ ├───┼────┼───┼───┼─── $32.50

$32.50+

$32.50………..$32.50

$1,000

1  mn  i F 2n 2   i + 1+ i 2 2   = $378.70+ $533.91=$912.61

 1 − PB= C    2  

(1+)

(

1   1−(1.04)16  $1,000  = $3 2.5 0   0.04 + (1.04)16     

)mn

To raise $1.25 million, the firm would have to sell: Number of bonds = $1,250,000 / $912.61 = 1,370 bond contracts Enter

16

4%

$32.50

N

i%

PMT

Answer

$1,000 PV

FV

-$912.61

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.16 Bond price: Rockne, Inc., has outstanding bonds that will mature in six years and pay an 8 percent coupon semiannually. If you paid $1036.65 today and your required rate of return was 6.6 percent, did you pay the right price for the bond?

Solution: Years to maturity = n = 6 Frequency of payment = m = 2

.

SM 8-34

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Coupon rate = C = 8% Semiannual coupon = $1,000 × (0.08/2) = $40 Current market rate = i = 6.6% Present value of bond = PB 0 6.6%

1

2

12

3

─────────┤ ├───────┼────────┼────────┼── $40

$40

$40+

$40

$1,000

1  1   mn  i 1−  12 F 2n (1.033)  $1,000 2  = $40    i  0.0 3 3 + (1.033)12 + 1+ i 2 2         = $391.12+ $677.32= $1,068.45

 1 − PB= C    2  

(1+)

(

)mn

You paid less than what the bond is worth. That was a good price.

Enter

12

3.3%

N

i%

Answer

$40 PMT

$1,000 PV

FV

-$1,068.45

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.17 Bond price: Nanotech, Inc., has a bond issue maturing in seven years that is paying a coupon rate of 9.5 percent (semiannual payments). Management wants to retire a portion of the issue by buying the securities in the open market. If it can refinance at 8 percent, how much will Nanotech pay to buy back its current outstanding bonds?

Solution: Years to maturity = n = 7 Frequency of payment = m = 2

.

SM 8-35

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Coupon rate = C = 9.5% Semiannual coupon = $1,000 × (0.095/2) = $47.50 Current market rate = i = 8%

Present value of bond = PB 0 8%

1

2

14

3

├───────┼────────┼────────┼── ──────┤ $47.50

$47.50

$47.50 +

$47.50

$1,000

1  1   mn  i 1− F 2n (1.04)14  $1,000 2    = $4 7.5 0  i  0.04 + (1.04)14 + 1+ i 2 2        = $501.75+ $577.48=$1,079.22

 1 − PB= C    2  

(1+)

(

)mn

The firm will be willing to pay no more than $1,079.22 for their bond.

Enter

14 N

Answer

4%

$47.50 i%

PMT

$1,000 PV

FV

-$1,079.22

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.18 Zero coupon bonds: Kintel, Inc., management wants to raise $1 million by issuing six- year zero coupon bonds with a face value of $1,000. The company’s investment banker states that investors would use an 11.4 percent discount rate to value such bonds. At what price would these bonds sell in the marketplace? How many bonds would the firm have to issue to raise $1 million? Assume semiannual coupon payments.

.

SM 8-36

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: Years to maturity = n = 6 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i = 11.4% Assume semiannual coupon payments.

5 0 11.4% 1

2

3

4

12 Period

6

─────┤ ├───┼────┼───┼───┼───┼────┼── $0

$0

$0

$0

$0

$0

$0

$1,000

PB =

Fmn

=

$1,000 = $514.16 (.0 1 57)12

)mn (1+i m

Financial Calculator Solution: Enter

12

5.7

0

N

i

PMT

Answer

1,000 PV

FV

514.16

At the price of $514.16, the firm needs to raise $1 million. To do so, the firm will have to issue: Number of bonds

= $1,000,000 / $514.16 = 1,945 bond contracts

LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.19 Zero coupon bonds: Rockinghouse Corp. management plans to issue seven-year zero coupon bonds. It has learned that these bonds will sell today at a price of $439.76.

Assuming annual coupon payments, what is the yield to maturity on these bonds?

.

SM 8-37

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: Years to maturity = n = 7 Coupon rate = C = 0% YTM = i Present value of bond = PB = $439.76 0i=?1

2

3

4

5

6

7

├───┼────┼───┼───┼───┼────┼───┤ $0

$0

$0

$0

$0

$0

$0+ $1,000

To solve for the YTM, a trial-and-error approach has to be used.

Try YTM = 10%.

F $1,000 = n (1+i)n (1.10)7 $439.76$513.16 PB=

Try a higher rate, YTM = 12%.

PB =

Fn $1,000 = + (1 i )n (1.12)7

$439.76 $452.35 Try YTM=12.5%.

PB=

F

n

=

$1,000

7 (1+i) (1.125) n

$439.76$438.46 The YTM is approximately 12.5 percent.

Enter

7 N

Answer

i%

$0

-$439.76

$1,000

PMT

PV

FV

12.453%

LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-38

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

8.20 Yield to maturity: Electrolex, Inc., has four-year bonds outstanding that pay a coupon rate of 6.6 percent and make coupon payments semiannually. If these bonds are currently selling at $914.89, what is the yield to maturity that an investor can expect to earn on these bonds? What is the effective annual yield?

Solution: Years to maturity = n = 4 Frequency of payment = m = 2Coupon rate = C = 6.6% YTM = i Semiannual coupon payments = $1,000 × (0.066/2) = $33 Present value of bond = PB = $914.89 0i=?

1

2

3

8

├───────┼────────┼────────┼── ─────────┤Yrs. $33

$33

$33

$33+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Since this is a discount bond, the market rate should be higher than 6.6 percent.

Try i = 8% or i/2 = 4%.

1   1 −   (1 + i)n  Fn  PB = C  + i + (1 i)n  

 1  1 − (1.04)8   $1,000 $914.89 = $33    + (1.04)8 0.04     = $222.18+ $730.69  $952.87 

Try a higher rate, i = 9%, i/2 = 4.5%.

.

SM 8-39