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SOLUTIONS MANUAL for Fundamentals of Corporate Finance 13th Edition by Ross

Solutions Manual Fundamentals of Corporate Finance 13th edition Ross, Westerfield, and Jordan Prepared by Brad Jordan University of Florida Joe Smolira Belmont University

CHAPTER 1 INTRODUCTION TO CORPORATE FINANCE Answers to Concepts Review and Critical Thinking Questions 1.

Capital budgeting (deciding whether to expand a manufacturing plant), capital structure (deciding whether to issue new equity and use the proceeds to retire outstanding debt), and working capital management (modifying the firm‘s credit collection policy with its customers).

Disadvantages: unlimited liability, limited life, difficulty in transferring ownership, difficulty in raising capital funds. Some advantages: simpler, less regulation, the owners are also the managers, sometimes personal tax rates are better than corporate tax rates.

The primary disadvantage of the corporate form is the double taxation to shareholders of distributed earnings and dividends. Some advantages include: limited liability, ease of transferability, ability to raise capital, and unlimited life.

In response to Sarbanes-Oxley, small firms have elected to go dark because of the costs of compliance. The costs to comply with Sarbox can be several million dollars, which can be a large percentage of a small firm‘s profits. A major cost of going dark is less access to capital. Since the firm is no longer publicly traded, it can no longer raise money in the public market. Although the company will still have access to bank loans and the private equity market, the costs associated with raising funds in these markets are usually higher than the costs of raising funds in the public market.

The treasurer‘s office and the controller‘s office are the two primary organizational groups that report directly to the chief financial officer. The controller‘s office handles cost and financial accounting, tax management, and management information systems, while the treasurer‘s office is responsible for cash and credit management, capital budgeting, and financial planning. Therefore, the study of corporate finance is concentrated within the treasury group‘s functions.

To maximize the current market value (share price) of the equity of the firm (whether it‘s publicly traded or not).

In the corporate form of ownership, the shareholders are the owners of the firm. The shareholders elect the directors of the corporation, who in turn appoint the firm‘s management. This separation of ownership from control in the corporate form of organization is what causes agency problems to exist. Management may act in its own or someone else‘s best interests, rather than those of the shareholders. If such events occur, they may contradict the goal of maximizing the share price of the equity of the firm.

A primary market transaction.

2 SOLUTIONS MANUAL 9.

In auction markets like the NYSE, brokers and agents meet at a physical location (the exchange) to match buyers and sellers of assets. Dealer markets like NASDAQ consist of dealers operating at dispersed locales who buy and sell assets themselves, communicating with other dealers either electronically or literally over-the-counter.

10. Such organizations frequently pursue social or political missions, so many different goals are conceivable. One goal that is often cited is revenue minimization; that is, provide whatever goods and services are offered at the lowest possible cost to society. A better approach might be to observe that even a not-for-profit business has equity. Thus, one answer is that the appropriate goal is to maximize the value of the equity. 11. Presumably, the current stock value reflects the risk, timing, and magnitude of all future cash flows, both short-term and long-term. If this is correct, then the statement is false. 12. An argument can be made either way. At the one extreme, we could argue that in a market economy, all of these things are priced. There is thus an optimal level of, for example, ethical and/or illegal behavior, and the framework of stock valuation explicitly includes these. At the other extreme, we could argue that these are noneconomic phenomena and are best handled through the political process. A classic (and highly relevant) thought question that illustrates this debate goes something like this: ―A firm has estimated that the cost of improving the safety of one of its products is $30 million. However, the firm believes that improving the safety of the product will only save $20 million in product liability claims. What should the firm do?‖ 13. The goal will be the same, but the best course of action toward that goal may be different because of differing social, political, and economic institutions. 14. The goal of management should be to maximize the share price for the current shareholders. If management believes that it can improve the profitability of the firm so that the share price will exceed $35, then they should fight the offer from the outside company. If management believes that this bidder or other unidentified bidders will actually pay more than $35 per share to acquire the company, then they should still fight the offer. However, if the current management cannot increase the value of the firm beyond the bid price, and no other higher bids come in, then management is not acting in the interests of the shareholders by fighting the offer. Since current managers often lose their jobs when the corporation is acquired, poorly monitored managers have an incentive to fight corporate takeovers in situations such as this. 15. We would expect agency problems to be less severe in countries with a relatively small percentage of individual ownership. Fewer individual owners should reduce the number of diverse opinions concerning corporate goals. The high percentage of institutional ownership might lead to a higher degree of agreement between owners and managers on decisions concerning risky projects. In addition, institutions may be better able to implement effective monitoring mechanisms on managers than can individual owners, based on the institutions‘ deeper resources and experiences with their own management. The increase in institutional ownership of stock in the United States and the growing activism of these large shareholder groups may lead to a reduction in agency problems for U.S. corporations and a more efficient market for corporate control.

CHAPTER 2 - 3 16. How much is too much? Who is worth more, Mark Parker or LeBron James? The simplest answer is that there is a market for executives just as there is for all types of labor. Executive compensation is the price that clears the market. The same is true for athletes and performers. Having said that, one aspect of executive compensation deserves comment. A primary reason executive compensation has grown so dramatically is that companies have increasingly moved to stock-based compensation. Such movement is obviously consistent with the attempt to better align stockholder and management interests. In recent years, stock prices have soared, so management has cleaned up. It is sometimes argued that much of this reward is due to rising stock prices in general, not managerial performance. Perhaps in the future, executive compensation will be designed to reward only differential performance, that is, stock price increases in excess of general market increases.

CHAPTER 2 FINANCIAL STATEMENTS, TAXES, AND CASH FLOW Answers to Concepts Review and Critical Thinking Questions 1.

Liquidity measures how quickly and easily an asset can be converted to cash without significant loss in value. It‘s desirable for firms to have high liquidity so that they have a large factor of safety in meeting short-term creditor demands. However, since liquidity also has an opportunity cost associated with it—namely that higher returns can generally be found by investing the cash into productive assets—low liquidity levels are also desirable to the firm. It‘s up to the firm‘s financial management staff to find a reasonable compromise between these opposing needs.

The recognition and matching principles in financial accounting call for revenues, and the costs associated with producing those revenues, to be ―booked‖ when the revenue process is essentially complete, not necessarily when the cash is collected or bills are paid. Note that this way is not necessarily correct; it‘s the way accountants have chosen to do it.

Historical costs can be objectively and precisely measured whereas market values can be difficult to estimate, and different analysts would come up with different numbers. Thus, there is a trade-off between relevance (market values) and objectivity (book values).

Depreciation is a noncash deduction that reflects adjustments made in asset book values in accordance with the matching principle in financial accounting. Interest expense is a cash outlay, but it‘s a financing cost, not an operating cost.

Market values can never be negative. Imagine a share of stock selling for –$20. This would mean that if you placed an order for 100 shares, you would get the stock along with a check for $2,000. How many shares do you want to buy? More generally, because of corporate and individual bankruptcy laws, net worth for a person or a corporation cannot be negative, implying that liabilities cannot exceed assets in market value.

4 SOLUTIONS MANUAL 6.

For a successful company that is rapidly expanding, for example, capital outlays will be large, possibly leading to negative cash flow from assets. In general, what matters is whether the money is spent wisely, not whether cash flow from assets is positive or negative.

It‘s probably not a good sign for an established company, but it would be fairly ordinary for a startup, so it depends.

For example, if a company were to become more efficient in inventory management, the amount of inventory needed would decline. The same might be true if it becomes better at collecting its receivables. In general, anything that leads to a decline in ending NWC relative to beginning would have this effect. Negative net capital spending would mean that more long-lived assets were liquidated than purchased. If a company raises more money from selling stock than it pays in dividends in a particular period, its cash flow to stockholders will be negative. If a company borrows more than it pays in interest, its cash flow to creditors will be negative.

10. The adjustments discussed were purely accounting changes; they had no cash flow or market value consequences unless the new accounting information caused stockholders to revalue the derivatives. 11. Enterprise value is the theoretical takeover price. In the event of a takeover, an acquirer would have to take on the company's debt but would pocket its cash. Enterprise value differs significantly from simple market capitalization in several ways, and it may be a more accurate representation of a firm's value. In a takeover, the value of a firm's debt would need to be paid by the buyer. Thus, enterprise value provides a much more accurate takeover valuation because it includes debt in its value calculation. 12. In general, it appears that investors prefer companies that have a steady earnings stream. If true, this encourages companies to manage earnings. Under GAAP, there are numerous choices for the way a company reports its financial statements. Although not the reason for the choices under GAAP, one outcome is the ability of a company to manage earnings, which is not an ethical decision. Even though earnings and cash flow are often related, earnings management should have little effect on cash flow (except for tax implications). If the market is ―fooled‖ and prefers steady earnings, shareholder wealth can be increased, at least temporarily. However, given the questionable ethics of this practice, the company (and shareholders) will lose value if the practice is discovered. Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1.

To find owners‘ equity, we must construct a balance sheet as follows:

CA NFA TA

Balance Sheet $ 5,400 CL 28,100 LTD OE $33,500 TL & OE

$ 4,100 10,600 ?? $33,500

CHAPTER 2 - 5

We know that total liabilities and owners‘ equity (TL & OE) must equal total assets of $33,500. We also know that TL & OE is equal to current liabilities plus long-term debt plus owners‘ equity, so owners‘ equity is: Owners‘ equity = $33,500 – 10,600 – 4,100 Owners‘ equity = $18,800 And net working capital (NWC) is: NWC = CA – CL NWC = $5,400 – 4,100 NWC = $1,300 2.

The income statement for the company is: Income Statement Sales $742,000 Costs 316,000 Depreciation 39,000 EBIT $387,000 Interest 34,000 EBT $353,000 Taxes (21%) 74,130 Net income $278,870

One equation for net income is: Net income = Dividends + Addition to retained earnings Rearranging, we get: Addition to retained earnings = Net income – Dividends = $278,870 – 125,000 = $153,870

EPS = Net income/Shares

= $278,870/75,000

= $3.72 per share

DPS = Dividends/Shares

= $125,000/75,000

= $1.67 per share

Taxes = .10($9,875) + .12($40,125 – 9,875) + .22($85,525 – 40,125) + .24($163,300 – 85,525) + .32($189,000 – 163,300) Taxes = $41,495.50 The average tax rate is the total tax paid divided by taxable income, so: Average tax rate = $41,495.50/$189,000 Average tax rate = .2196, or 21.96% The marginal tax rate is the tax rate on the next $1 of earnings, so the marginal tax rate is 32 percent.

To calculate OCF, we first need the income statement:

6 SOLUTIONS MANUAL Income Statement Sales $49,800 Costs 23,700 Depreciation 2,300 EBIT $23,800 Interest 1,800 Taxable income $22,000 Taxes (22%) 4,840 Net income $17,160 OCF = EBIT + Depreciation – Taxes OCF = $23,800 + 2,300 – 4,840 OCF = $21,260 7.

Net capital spending = NFAend – NFAbeg + Depreciation Net capital spending = $3,100,000 – 2,300,000 + 327,000 Net capital spending = $1,127,000

Change in NWC = NWCend – NWCbeg Change in NWC = (CAend – CLend) – (CAbeg – CLbeg) Change in NWC = ($5,970 – 3,240) – ($5,320 – 2,510) Change in NWC = $2,730 – 2,810 Change in NWC = –$80

Cash flow to creditors = Interest paid – Net new borrowing Cash flow to creditors = Interest paid – (LTDend – LTDbeg) Cash flow to creditors = $305,000 – ($2,660,000 – 2,250,000) Cash flow to creditors = –$105,000

10.

Cash flow to stockholders = Dividends paid – Net new equity Cash flow to stockholders = Dividends paid – [(Commonend + APISend) – (Commonbeg + APISbeg)] Cash flow to stockholders = $654,000 – [($965,000 + 5,040,000) – ($780,000 + 4,780,000)] Cash flow to stockholders = $209,000 Note, APIS is the additional paid-in surplus.

11.

Cash flow from assets = Cash flow to creditors + Cash flow to stockholders = –$105,000 + 209,000 = $104,000 Cash flow from assets = $104,000 = OCF – Change in NWC – Net capital spending = $104,000 = OCF – (–$55,000) – 1,500,000 Operating cash flow Operating cash flow

= $104,000 – 55,000 + 1,500,000 = $1,549,000

Intermediate 12.

To find the book value of current assets, we use: NWC = CA – CL. Rearranging to solve for current assets, we get: CA = NWC + CL

CHAPTER 2 - 7 CA = $275,000 + 945,000 CA = $1,220,000 The market value of current assets and fixed assets is given, so: Book value CA = $1,220,000 Book value NFA = 3,500,000 Book value assets = $4,720,000 13.

Market value NWC = $1,250,000 Market value NFA = 5,400,000 Total = $6,650,000

To find the OCF, we first calculate net income. Income Statement Sales $336,000 Costs 194,700 Other expenses 9,800 Depreciation 20,600 EBIT $110,900 Interest 14,200 Taxable income $96,700 Taxes 21,275 Net income $ 75,425 Dividends Additions to RE

$21,450 $53,975

a. OCF = EBIT + Depreciation – Taxes OCF = $110,900 + 20,600 – 21,275 OCF = $110,225 b. CFC = Interest – Net new LTD CFC = $14,200 – (–5,400) CFC = $19,600 Note that the net new long-term debt is negative because the company repaid part of its longterm debt. c. CFS = Dividends – Net new equity CFS = $21,450 – 7,100 CFS = $14,350 d. We know that CFA = CFC + CFS, so: CFA = $19,600 + 14,350 CFA = $33,950 CFA is also equal to OCF – Net capital spending – Change in NWC. We already know OCF. Net capital spending is equal to: Net capital spending = Increase in NFA + Depreciation Net capital spending = $53,200 + 20,600 Net capital spending = $73,800

8 SOLUTIONS MANUAL

Now we can use: CFA = OCF – Net capital spending – Change in NWC $33,950 = $110,225 – 73,800 – Change in NWC Change in NWC = $2,475 This means that the company increased its NWC by $2,475. 14.

The solution to this question works the income statement backwards. Starting at the bottom: Net income = Dividends + Addition to retained earnings = $2,370 + 6,800 = $9,170 Now, looking at the income statement: EBT – EBT × Tax rate = Net income Recognize that EBT × Tax rate is the calculation for taxes. Solving this for EBT yields: EBT = NI/(1 – Tax rate) = $9,170/(1 – .22) = $11,756 Now you can calculate: EBIT = EBT + Interest = $11,756 + 5,300 = $17,056 The last step is to use: EBIT = Sales – Costs – Depreciation $17,056 = $76,800 – 36,900 – Depreciation Depreciation = $22,844

15.

The balance sheet for the company looks like this:

Cash Accounts receivable Inventory Current assets Tangible net fixed assets Intangible net fixed assets Total assets

Balance Sheet $ 165,000 Accounts payable 149,000 Notes payable 372,000 Current liabilities $ 686,000 Long-term debt Total liabilities $2,093,000 858,000 Common stock Accumulated ret. earnings $3,637,000 Total liab. & owners‘ equity

Total liabilities and owners‘ equity is: TL & OE = CL + LTD + Common stock + Retained earnings Solving this equation for common stock gives us: Common stock = $3,637,000 – 1,778,000 – 1,553,500

$ 273,000 201,500 $ 474,500 1,079,000 $1,553,500 ?? 1,778,000 $3,637,000

CHAPTER 2 - 9 Common stock = $305,500 16.

The market value of shareholders‘ equity cannot be negative. A negative market value in this case would imply that the company would pay you to own the stock. The market value of shareholders‘ equity can be stated as: Shareholders‘ equity = Max[(TA – TL), 0]. So, if TA are $11,600, equity is equal to $1,300, and if TA are $9,400, equity is equal to $0. We should note here that the book value of shareholders‘ equity can be negative.

10 SOLUTIONS MANUAL 17.

Income Statement Sales $865,000 COGS 535,000 A&S expenses 125,000 Depreciation 170,000 EBIT $35,000 Interest 90,000 Taxable income –$55,000 Taxes (25%) 0 Net income –$55,000

b. OCF = EBIT + Depreciation – Taxes OCF = $35,000 + 170,000 – 0 OCF = $205,000 c. Net income was negative because of the tax deductibility of depreciation and interest expense. However, the actual cash flow from operations was positive because depreciation is a non-cash expense and interest is a financing expense, not an operating expense. 18.

A firm can still pay out dividends if net income is negative; it just has to be sure there is sufficient cash flow to make the dividend payments. Change in NWC = Net capital spending = Net new equity = 0. (Given) Cash flow from assets = OCF – Change in NWC – Net capital spending Cash flow from assets = $205,000 – 0 – 0 = $205,000 Cash flow to stockholders = Dividends – Net new equity = $128,000 – 0 = $128,000 Cash flow to creditors = Cash flow from assets – Cash flow to stockholders Cash flow to creditors = $205,000 – 128,000 = $77,000 Cash flow to creditors = Interest – Net new LTD Net new LTD = Interest – Cash flow to creditors = $90,000 – 77,000 = $13,000

19.

a. Income Statement Sales Cost of goods sold Depreciation EBIT Interest Taxable income Taxes (22%) Net income

$38,072 27,168 6,759 $ 4,145 3,050 $ 1,095 241 $ 854

b. OCF = EBIT + Depreciation – Taxes = $4,145 + 6,759 – 241 = $10,663 c. Change in NWC = NWCend – NWCbeg = (CAend – CLend) – (CAbeg – CLbeg) = ($9,904 – 5,261) – ($8,025 – 4,511) = $1,129

CHAPTER 2 - 11

Net capital spending = NFAend – NFAbeg + Depreciation = $28,053 – 22,790 + 6,759 = $12,022 CFA

= OCF – Change in NWC – Net capital spending = $10,663 – 1,129 – 12,022 = –$2,488

The cash flow from assets can be positive or negative, since it represents whether the firm raised funds or distributed funds on a net basis. In this problem, even though net income and OCF are positive, the firm invested heavily in both fixed assets and net working capital; it had to raise a net $2,488 in funds from its stockholders and creditors to make these investments. = Interest – Net new LTD = $3,050 – 0 = $3,050

d. Cash flow to creditors Cash flow to stockholders

= Cash flow from assets – Cash flow to creditors = –$2,488 – 3,050 = –$5,538

We can also calculate the cash flow to stockholders as: Cash flow to stockholders

= Dividends – Net new equity

Solving for net new equity, we get: Net new equity

= $2,170 – (–5,538) = $7,708

The firm had positive earnings in an accounting sense (NI > 0) and had positive cash flow from operations. The firm invested $1,129 in new net working capital and $12,022 in new fixed assets. The firm had to raise $2,488 from its stakeholders to support this new investment. It accomplished this by raising $7,708 in the form of new equity. After paying out $2,170 of this in the form of dividends to shareholders and $3,050 in the form of interest to creditors, $2,488 was left to meet the firm‘s cash flow needs for investment. 20.

a. Total assets2020 Total liabilities2020 Owners‘ equity2020

= $1,327 + 5,470 = $6,797 = $530 + 2,891 = $3,421 = $6,797 – 3,421 = $3,376

Total assets2021 Total liabilities2021 Owners‘ equity2021

= $1,438 + 6,587 = $8,025 = $595 + 3,075 = $3,670 = $8,025 – 3,670 = $4,355

b. NWC2020 = CA2020 – CL2020 = $1,327 – 530 = $797 NWC2021 = CA2021 – CL2021 = $1,438 – 595 = $843 Change in NWC = NWC2021 – NWC2020 = $843 – 797 = $46 c. We can calculate net capital spending as: Net capital spending = Net fixed assets2021 – Net fixed assets2020 + Depreciation Net capital spending = $6,587 – 5,470 + 1,499 = $2,616

12 SOLUTIONS MANUAL So, the company had a net capital spending cash flow of $2,616. We also know that net capital spending is: Net capital spending = Fixed assets bought – Fixed assets sold $2,616 = $2,740 – Fixed assets sold Fixed assets sold = $2,740 – 2,616 = $124 To calculate the cash flow from assets, we must first calculate the operating cash flow. The income statement is: Income Statement Sales Costs Depreciation expense EBIT Interest expense EBT Taxes (21%) Net income

$16,831 7,849 1,499 $ 7,483 427 $ 7,056 1,482 $ 5,574

So, the operating cash flow is: OCF = EBIT + Depreciation – Taxes = $7,483 + 1,499 – 1,482 = $7,500 And the cash flow from assets is: Cash flow from assets = OCF – Change in NWC – Net capital spending = $7,500 – 46 – 2,616 = $4,838 d. Net new borrowing = LTD2021 – LTD2020 = $3,075 – 2,891 = $184 Cash flow to creditors = Interest – Net new LTD = $427 – 184 = $243 Net new borrowing Debt retired

= $184 = Debt issued – Debt retired = $554 – 184 = $370

21. To construct the cash flow identity, we will begin with cash flow from assets. Cash flow from assets is: Cash flow from assets = OCF – Change in NWC – Net capital spending So, the operating cash flow is: OCF = EBIT + Depreciation – Taxes OCF = $81,741 + 72,489 – 14,028 OCF = $140,202 Next, we will calculate the change in net working capital, which is: Change in NWC = NWCend – NWCbeg

CHAPTER 2 - 13 Change in NWC = (CAend – CLend) – (CAbeg – CLbeg) Change in NWC = ($77,250 – 35,834) – ($61,240 – 31,870) Change in NWC = $12,046 Now, we can calculate the capital spending. The capital spending is: Net capital spending = NFAend – NFAbeg + Depreciation Net capital spending = $539,679 – 457,454 + 72,489 Net capital spending = $154,714 Now, we have the cash flow from assets, which is: Cash flow from assets = OCF – Change in NWC – Net capital spending Cash flow from assets = $140,202 – 12,046 – 154,714 Cash flow from assets = –$26,558 The company‘s assets generated an outflow of $26,558. The cash flow from operations was $140,202, and the company spent $12,046 on net working capital and $154,714 on fixed assets. The cash flow to creditors is: Cash flow to creditors = Interest paid – New long-term debt Cash flow to creditors = Interest paid – (Long-term debtend – Long-term debtbeg) Cash flow to creditors = $25,630 – ($201,900 – 181,000) Cash flow to creditors = $4,730 The cash flow to stockholders is a little trickier in this problem. First, we need to calculate the new equity sold. The equity balance increased during the year. The only way to increase the equity balance is through retained earnings or selling equity. To calculate the new equity sold, we can use the following equation: New equity = Ending equity – Beginning equity – Addition to retained earnings New equity = $379,195 – 305,824 – 27,883 New equity = $45,488 What happened was the equity account increased by $73,371. Of this increase, $27,883 came from addition to retained earnings, so the remainder must have been the sale of new equity. Now we can calculate the cash flow to stockholders as: Cash flow to stockholders = Dividends paid – Net new equity Cash flow to stockholders = $14,200 – 45,488 Cash flow to stockholders = –$31,288 The company paid $4,730 to creditors and raised $31,288 from stockholders. Finally, the cash flow identity is: Cash flow from assets = Cash flow to creditors + Cash flow to stockholders –$26,558 = $4,730 + –$31,288 The cash flow identity balances, which is what we expect.

14 SOLUTIONS MANUAL

CHAPTER 2 - 15 Challenge 22.

Net capital spending = NFAend – NFAbeg + Depreciation = (NFAend – NFAbeg) + (Depreciation + ADbeg) – ADbeg = (NFAend – NFAbeg)+ ADend – ADbeg = (NFAend + ADend) – (NFAbeg + ADbeg) = FAend – FAbeg

23. Cash Accounts receivable

24.

Balance sheet as of Dec. 31, 2020 $11,279 Accounts payable 14,934 Notes payable

Inventory

26,551

Current assets

$52,764

Current liabilities

$10,326 $37,778 $99,261 $147,365

Net fixed assets

$94,601

Long-term debt Owners' equity

Total assets

$147,365

Total liab. & equity

Cash Accounts receivable

Balance sheet as of Dec. 31, 2021 $12,021 Accounts payable 17,529 Notes payable

Inventory

28,421

Current assets

$57,971

$8,150 2,176

$8,632 2,133

Current liabilities

$10,765 $45,798 $102,301 $158,864

Net fixed assets

$100,893

Long-term debt Owners' equity

Total assets

$158,864

Total liab. & equity

2020 Income Statement Sales $21,514.00 COGS 7,397.00 Other expenses 1,759.00 Depreciation 3,089.00 EBIT $9,269.00 Interest 1,443.00 EBT $7,826.00 Taxes (21%) 1,643.46 Net income $6,182.54

2021 Income Statement Sales $24,047.00 COGS 8,750.00 Other expenses 1,531.00 Depreciation 3,229.00 EBIT $10,537.00 Interest 1,723.00 EBT $8,814.00 Taxes (21%) 1,850.94 Net income $6,963.06

Dividends Additions to RE

$2,573.00 3,609.54

OCF = EBIT + Depreciation – Taxes = $10,537 + 3,229 – 1,850.94 = $11,915.06 Change in NWC = NWCend – NWCbeg = (CA – CL)end – (CA – CL)beg = ($57,971 – 10,765) – ($52,764 – 10,326) = $4,768

$3,008.00 3,955.06

16 SOLUTIONS MANUAL

Net capital spending = NFAend – NFAbeg + Depreciation = $100,893 – 94,601 + 3,229 = $9,521 Cash flow from assets = OCF – Change in NWC – Net capital spending = $11,915.06 – 4,768 – 9,521 = –$2,373.94 Cash flow to creditors = Interest – Net new LTD Net new LTD = LTDend – LTDbeg Cash flow to creditors = $1,723 – ($45,798 – 37,778) = –$6,297 Net new equity = Common stockend – Common stockbeg Common stock + Retained earnings = Total owners‘ equity Net new equity = (OE – RE)end – (OE – RE)beg = OEend – OEbeg + REbeg – REend REend = REbeg + Additions to RE2021  Net new equity = OEend – OEbeg + REbeg – (REbeg + Additions to RE2021) = OEend – OEbeg – Additions to RE2021 Net new equity = $102,301 – 99,261 – 3,955.06 = –$915.06 CFS CFS

= Dividends – Net new equity = $3,008 – (–915.06) = $3,923.06

As a check, cash flow from assets is –$2,373.94. CFA CFA

= Cash flow to creditors + Cash flow to stockholders = –$6,297 + 3,923.06 = –$2,373.94

CHAPTER 3 WORKING WITH FINANCIAL STATEMENTS Answers to Concepts Review and Critical Thinking Questions 1.

a. If inventory is purchased with cash, then there is no change in the current ratio. If inventory is purchased on credit, then there is a decrease in the current ratio if it was initially greater than 1.0. b. Reducing accounts payable with cash increases the current ratio if it was initially greater than 1.0. c. Reducing short-term debt with cash increases the current ratio if it was initially greater than 1.0. d. As long-term debt approaches maturity, the principal repayment and the remaining interest expense become current liabilities. Thus, if debt is paid off with cash, the current ratio increases if it was initially greater than 1.0. If the debt has not yet become a current liability, then paying it off will reduce the current ratio since current liabilities are not affected. e. Reduction of accounts receivables and an increase in cash leaves the current ratio unchanged. f. Inventory sold at cost reduces inventory and raises cash, so the current ratio is unchanged. g. Inventory sold for a profit raises cash in excess of the inventory recorded at cost, so the current ratio increases.

The firm has increased inventory relative to other current assets; therefore, assuming current liability levels remain unchanged, liquidity has potentially decreased.

A current ratio of .50 means that the firm has twice as much in current liabilities as it does in current assets; the firm potentially has poor liquidity. If pressed by its short-term creditors and suppliers for immediate payment, the firm might have a difficult time meeting its obligations. A current ratio of 1.50 means the firm has 50 percent more current assets than it does current liabilities. This probably represents an improvement in liquidity; short-term obligations can generally be met completely with a safety factor built in. A current ratio of 15.0, however, might be excessive. Any excess funds sitting in current assets generally earn little or no return. These excess funds might be put to better use by investing in productive long-term assets or distributing the funds to shareholders.

a. Quick ratio provides a measure of the short-term liquidity of the firm, after removing the effects of inventory, generally the least liquid of the firm‘s current assets. b. Cash ratio represents the ability of the firm to completely pay off its current liabilities with its most liquid asset (cash). c. Total asset turnover measures how much in sales is generated by each dollar of firm assets. d. Equity multiplier represents the degree of leverage for an equity investor of the firm; it measures the dollar worth of firm assets each equity dollar has a claim to. e. Long-term debt ratio measures the percentage of total firm capitalization funded by long-term debt.

18 SOLUTIONS MANUAL Times interest earned ratio provides a relative measure of how well the firm‘s operating earnings can cover current interest obligations. g. Profit margin is the accounting measure of bottom-line profit per dollar of sales. h. Return on assets is a measure of bottom-line profit per dollar of total assets. i. Return on equity is a measure of bottom-line profit per dollar of equity. j. Price-earnings ratio reflects how much value per share the market places on a dollar of accounting earnings for a firm. f.

Common-size financial statements express all balance sheet accounts as a percentage of total assets and all income statement accounts as a percentage of total sales. Using these percentage values rather than nominal dollar values facilitates comparisons between firms of different size or business type. Common-base year financial statements express each account as a ratio between their current year nominal dollar value and some reference year nominal dollar value. Using these ratios allows the total growth trend in the accounts to be measured.

Peer group analysis involves comparing the financial ratios and operating performance of a particular firm to a set of peer group firms in the same industry or line of business. Comparing a firm to its peers allows the financial manager to evaluate whether some aspects of the firm‘s operations, finances, or investment activities are out of line with the norm, thereby providing some guidance on appropriate actions to take to adjust these ratios if appropriate. An aspirant group would be a set of firms whose performance the company in question would like to emulate. The financial manager often uses the financial ratios of aspirant groups as the target ratios for his or her firm; some managers are evaluated by how well they match the performance of an identified aspirant group.

Return on equity is probably the most important accounting ratio that measures the bottom-line performance of the firm with respect to the equity shareholders. The DuPont identity emphasizes the role of a firm‘s profitability, asset utilization efficiency, and financial leverage in achieving an ROE figure. For example, a firm with ROE of 20 percent would seem to be doing well, but this figure may be misleading if it were marginally profitable (low profit margin) and highly levered (high equity multiplier). If the firm‘s margins were to erode slightly, the ROE would be heavily impacted.

The book-to-bill ratio is intended to measure whether demand is growing or falling. It is closely followed because it is a barometer for the entire high-tech industry, where levels of revenues and earnings have been relatively volatile.

If a company is growing by opening new stores, then presumably total revenues would be rising. Comparing total sales at two different points in time might be misleading. Same-store sales control for this by only looking at revenues of stores open within a specific period.

10.

a. For an electric utility such as Con Ed, expressing costs on a per-kilowatt-hour basis would be a way to compare costs with other utilities of different sizes. b. For a retailer such as Target, expressing sales on a per-square-foot basis would be useful in comparing revenue production against other retailers. c. For an airline such as Southwest, expressing costs on a per-passenger-mile basis allows for comparisons with other airlines by examining how much it costs to fly one passenger one mile.

CHAPTER 3 - 19 d. For an online service provider such as Comcast, using a cost user would allow for comparisons with smaller services. A per subscriber basis would also make sense. e. For a hospital such as HCA, revenues and costs expressed on a per-bed basis would be useful. f. For a college textbook publisher such as McGraw-Hill Education, the leading publisher of finance textbooks for the college market, the obvious standardization would be per book sold. 11. Reporting the sale of Treasury securities as cash flow from operations is an accounting ―trick,‖ and as such, should constitute a possible red flag about the companies accounting practices. For most companies, the gain from a sale of securities should be placed in the financing section. Including the sale of securities in the cash flow from operations would be acceptable for a financial company, such as an investment or commercial bank. 12. Increasing the payables period increases the cash flow from operations. This could be beneficial for the company as it may be a cheap form of financing, but it is basically a one-time change. The payables period cannot be increased indefinitely as it will negatively affect the company‘s credit rating if the payables period becomes too long.

Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1.

Using the formula for NWC, we get: NWC = CA – CL CA = CL + NWC CA = $5,970 + 2,630 CA = $8,600 So, the current ratio is: Current ratio = CA/CL Current ratio = $8,600/$5,970 Current ratio = 1.44 times And the quick ratio is: Quick ratio = (CA – Inventory)/CL Quick ratio = ($8,600 – 3,860)/$5,970 Quick ratio = .79 times

20 SOLUTIONS MANUAL 2.

We need to find net income first. So: Profit margin = Net income/Sales Net income = Profit margin(Sales) Net income = .05($14,200,000) Net income = $710,000 ROA = Net income/TA ROA = $710,000/$11,300,000 ROA = .0628, or 6.28% To find ROE, we need to find total equity. Since TL & OE equals TA: TA = TD + TE TE = TA – TD TE = $11,300,000 – 4,900,000 TE = $6,400,000 ROE = Net income/TE ROE = $710,000/$6,400,000 ROE = .1109, or 11.09%

Receivables turnover = Sales/Receivables Receivables turnover = $4,986,340/$513,260 Receivables turnover = 9.72 times Days‘ sales in receivables = 365 days/Receivables turnover Days‘ sales in receivables = 365/9.72 Days‘ sales in receivables = 37.57 days On average, the company‘s customers paid off their accounts in 37.57 days.

Inventory turnover = COGS/Inventory Inventory turnover = $4,738,216/$426,287 Inventory turnover = 11.12 times Days‘ sales in inventory = 365 days/Inventory turnover Days‘ sales in inventory = 365/11.12 Days‘ sales in inventory = 32.84 days On average, a unit of inventory sat on the shelf 32.84 days before it was sold.

Total debt ratio = .57 = TD/TA Substituting total debt plus total equity for total assets, we get: .57 = TD/(TD + TE) Solving this equation yields: .57(TE) = .43(TD)

CHAPTER 3 - 21 Debt-equity ratio = TD/TE = .57/.43 = 1.33 Equity multiplier = 1 + D/E = 2.33 6.

Net income

= Addition to RE + Dividends = $435,000 + 245,000 = $680,000

Earnings per share

= NI/Shares

= $680,000/175,000 = $3.89 per share

Dividends per share

= Dividends/Shares

= $245,000/175,000 = $1.40 per share

Book value per share = TE/Shares

= $5,700,000/175,000 = $32.57 per share

Market-to-book ratio

= Share price/BVPS

= $78/$32.57 = 2.39 times

PE ratio

= Share price/EPS

= $78/$3.89 = 20.07 times

Sales per share

= Sales/Shares

= $7,450,000/175,000 = $42.57

P/S ratio

= Share price/Sales per share

= $78/$42.57 = 1.83 times

ROE = (PM)(TAT)(EM) ROE = (.0605)(1.87)(1.43) ROE = .1618, or 16.18%

8. This question gives all of the necessary ratios for the DuPont identity except the equity multiplier, so, using the DuPont identity: ROE = (PM)(TAT)(EM) ROE = .1385 = (.058)(1.75)(EM) EM = .1385/(.058)(1.75) EM = 1.36 D/E = EM – 1 D/E = 1.36 – 1 D/E = .36 9.

Decrease in inventory is a source of cash. Decrease in accounts payable is a use of cash. Increase in notes payable is a source of cash. Increase in accounts receivable is a use of cash. Change in cash = Sources – Uses Change in cash = $425 – 230 + 280 – 290 Change in cash = $185 Cash increased by $185.

22 SOLUTIONS MANUAL 10. The average time to pay suppliers is the days‘ sales in payables, so: Payables turnover = COGS/Accounts payable Payables turnover = $75,318/$18,452 Payables turnover = 4.08 times Days‘ sales in payables = 365 days/Payables turnover Days‘ sales in payables = 365/4.08 Days‘ sales in payables = 89.42 days The company left its bills to suppliers outstanding for 89.42 days on average. A large value for this ratio could imply that either (1) the company is having liquidity problems, making it difficult to pay off its short-term obligations, or (2) that the company has successfully negotiated lenient credit terms from its suppliers. 11. First, we need the enterprise value, which is: Enterprise value = Market capitalization + Debt – Cash Enterprise value = $755,000 + 220,000 – 63,000 Enterprise value = $912,000 And EBITDA is: EBITDA = EBIT + Depreciation & Amortization EBITDA = $95,000 + 178,000 EBITDA = $273,000 So, the enterprise value-EBITDA multiple is: Enterprise value-EBITDA multiple = $912,000/$273,000 Enterprise value-EBITDA multiple = 3.34 times 12. The equity multiplier is: EM = 1 + D/E EM = 1 + .63 EM = 1.63 One formula to calculate return on equity is: ROE = ROA(EM) ROE = .084(1.63) ROE = .1369, or 13.69% ROE can also be calculated as: ROE = NI/TE

CHAPTER 3 - 23 So, net income is: Net income = ROE(TE) Net income = .1369($645,000) Net income = $88,313.40 13 through 15: 2020

#13

2021

#13

#14

#15

$14,588 35,258 65,567 $115,413

2.46% 5.95% 11.06% 19.47%

$17,631 41,019 71,505 $130,155

2.80% 6.53% 11.38% 20.71%

1.2086 1.1634 1.0906 1.1277

1.1399 1.0972 1.0285 1.0636

$477,413 $592,826

80.53% 100%

$498,421 $628,576

79.29% 100%

1.0440 1.0603

.9846 1.0000

Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment Total assets Liabilities and Owners‘ Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Accumulated retained earnings Total

$55,653 21,895 $77,548 $58,000

9.39% 3.69% 13.08% 9.78%

$63,073 25,324 $88,397 $62,000

10.03% 4.03% 14.06% 9.86%

1.1333 1.1566 1.1399 1.0690

1.0689 1.0908 1.0751 1.0082

$60,000 397,278 $457,278

10.12% 67.01% 77.14%

$60,000 418,179 $478,179

9.55% 66.53% 76.07%

1.0000 1.0526 1.0457

.9431 .9927 .9862

Total liabilities and owners' equity

$592,826

100%

$628,576

100%

1.0603

1.0000

The common-size balance sheet answers are found by dividing each category by total assets. For example, the cash percentage for 2020 is: $14,588/$592,826 = .0246, or 2.46% This means that cash is 2.46 percent of total assets. The common-base year answers for Question 14 are found by dividing each category value for 2021 by the same category value for 2020. For example, the cash common-base year number is found by: $17,631/$14,588 = 1.2086 This means the cash balance in 2021 is 1.2086 times as large as the cash balance in 2020.

24 SOLUTIONS MANUAL The common-size, common-base year answers for Question 15 are found by dividing the commonsize percentage for 2021 by the common-size percentage for 2020. For example, the cash calculation is found by: .0280/.0246 = 1.1399 This tells us that cash, as a percentage of assets, increased by 13.99 percent. 16.

2020

Sources/Uses

2021

Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment Total assets

$14,588 35,258 65,567 $115,413

$3,043 5,761 5,938 $14,742

U U U U

$17,631 41,019 71,505 $130,155

$477,413 $592,826

$21,008 $35,750

U U

$498,421 $628,576

S S S S

$63,073 25,324 $88,397 $62,000

Liabilities and Owners‘ Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Accumulated retained earnings Total

$55,653 21,895 $77,548 $58,000

$7,420 3,429 $10,849 $4,000

$60,000 397,278 $457,278

0 20,901 $20,901

S S

$60,000 418,179 $478,179

Total liabilities and owners' equity

$592,826

$35,750

$628,576

The firm used $35,750 in cash to acquire new assets. It raised this amount of cash by increasing liabilities and owners‘ equity by $35,750. In particular, the needed funds were raised by internal financing (on a net basis), out of the additions to retained earnings, an increase in current liabilities, and new long-term debt. 17. a.

Current ratio Current ratio 2020 Current ratio 2021

= Current assets/Current liabilities = $115,413/$77,548 = 1.49 times = $130,155/$88,397 = 1.47 times

Quick ratio Quick ratio 2020 Quick ratio 2021

= (Current assets – Inventory)/Current liabilities = ($115,413 – 65,567)/$77,548 = .64 times = ($130,155 – 71,505)/$88,397 = .66 times

CHAPTER 3 - 25 c.

Cash ratio Cash ratio 2020 Cash ratio 2021

= Cash/Current liabilities = $14,588/$77,548 = .19 times = $17,631/$88,397 = .20 times

NWC ratio NWC ratio 2020 NWC ratio 2021

= NWC/Total assets = ($115,413 – 77,548)/$592,826 = .0639, or 6.39% = ($130,155 – 88,397)/$628,576 = .0664, or 6.64%

Debt-equity ratio Debt-equity ratio 2020 Debt-equity ratio 2021

= Total debt/Total equity = ($77,548 + 58,000)/$457,278 = .30 times = ($88,397 + 62,000)/$478,179 = .31 times

Equity multiplier Equity multiplier 2020 Equity multiplier 2021

= 1 + D/E = 1 + .30 = 1.30 = 1 + .31 = 1.31

Total debt ratio Total debt ratio 2020 Total debt ratio 2021

= (Total assets – Total equity)/Total assets = ($592,826 – 457,278)/$592,826 = .23 times = ($628,576 – 478,179)/$628,576 = .24 times

Long-term debt ratio = Long-term debt/(Long-term debt + Total equity) Long-term debt ratio 2020 = $58,000/($58,000 + 457,278) = .11 times Long-term debt ratio 2021 = $62,000/($62,000 + 478,179) = .11 times Intermediate 18. This is a multistep problem involving several ratios. The ratios given are all part of the DuPont identity. The only DuPont identity ratio not given is the profit margin. If we know the profit margin, we can find the net income since sales are given. So, we begin with the DuPont identity: ROE = .11 = (PM)(TAT)(EM) = (PM)(S/TA)(1 + D/E) Solving the DuPont identity for profit margin, we get: PM = [(ROE)(TA)]/[(1 + D/E)(S)] PM = [(.11)($2,532)]/[(1 + .57)($5,987)] PM = .0296 Now that we have the profit margin, we can use this number and the given sales figure to solve for net income: PM = .0296 = NI/S NI = .0296($5,987) Net income = $177.40

26 SOLUTIONS MANUAL 19. This is a multistep problem involving several ratios. It is often easier to look backward to determine where to start. We need receivables turnover to find days‘ sales in receivables. To calculate receivables turnover, we need credit sales, and to find credit sales, we need total sales. Since we are given the profit margin and net income, we can use these to calculate total sales as: PM = .071 = NI/Sales PM = .071 = $213,700/Sales Sales = $3,009,859 Credit sales are 65 percent of total sales, so: Credit sales = .65($3,009,859) Credit sales = $1,956,408 Now we can find receivables turnover by: Receivables turnover = Credit sales/Accounts receivable Receivables turnover = $1,956,408/$126,385 Receivables turnover = 15.48 times Days‘ sales in receivables = 365 days/Receivables turnover Days‘ sales in receivables = 365/15.48 Days‘ sales in receivables = 23.58 days 20. The solution to this problem requires a number of steps. First, remember that Current assets + Net fixed assets = Total assets. So, if we find the current assets and the total assets, we can solve for net fixed assets. Using the numbers given for the current ratio and the current liabilities, we solve for current assets: Current ratio = Current assets/Current liabilities Current assets = Current ratio(Current liabilities) Current assets = 1.45($1,140) Current assets = $1,653 To find the total assets, we must first find the total debt and equity from the information given. So, we find the net income using the profit margin: Profit margin = Net income/Sales Net income = Profit margin(Sales) Net income = .083($8,370) Net income = $694.71 We now use the net income figure as an input into ROE to find the total equity: ROE = Net income/Total equity Total equity = Net income/ROE Total equity = $694.71/.165 Total equity = $4,210.36

CHAPTER 3 - 27 Next, we need to find the long-term debt. The long-term debt ratio is: Long-term debt ratio = .35 = LTD/(LTD + Total equity) Inverting both sides gives: 1/.35 = (LTD + Total equity)/LTD = 1 + (Total equity/LTD) Substituting the total equity into the equation and solving for long-term debt gives the following: 2.857 = 1 + ($4,210.36/LTD) LTD = $4,210.36/1.857 LTD = $2,267.12 Now, we can find the total debt of the company: Total debt = Current liabilities + LTD Total debt = $1,140 + 2,267.12 Total debt = $3,407.12 And, with the total debt, we can find the TD&E, which is equal to TA: Total assets = Total debt + Total equity Total assets = $3,407.12 + 4,210.36 Total assets = $7,617.48 And finally, we are ready to solve the balance sheet identity as: Net fixed assets = Total assets – Current assets Net fixed assets = $7,617.48 – 1,653 Net fixed assets = $5,964.48 21. Child: Profit margin = Net income/Sales Profit margin = $1.25/$50 Profit margin = .025, or 2.5% Store: Profit margin = Net income/Sales Profit margin = $8,500,000/$680,000,000 Profit margin = .0125, or 1.25% The advertisement is referring to the store‘s profit margin, but a more appropriate earnings measure for the firm‘s owners is the return on equity. ROE = NI/TE = NI/(TA – TD) ROE = $8,500,000/($380,000,000 – 270,000,000) ROE = .0773, or 7.73%

28 SOLUTIONS MANUAL 22. The solution requires substituting two ratios into a third ratio. Rearranging Debt/Total assets: Firm A D/TA = .60 (TA – E)/TA = .60 (TA/TA) – (E/TA) = .60 1 – (E/TA) = .60 E/TA = .40 E = .40(TA)

Firm B D/TA = .35 (TA – E)/TA = .35 (TA/TA) – (E/TA) = .35 1 – (E/TA) = .35 E/TA = .65 E = .65(TA)

Rearranging ROA = Net income/Total assets, we find: NI/TA = .045 NI = .045(TA)

NI/TA = .08 NI = .08(TA)

Since ROE = Net income/Equity, we can substitute the above equations into the ROE formula, which yields: ROE = .045(TA)/.40(TA) ROE = .045/.40 ROE = .1125, or 11.25%

ROE = .08(TA)/.65(TA) ROE = .08/.65 ROE = .1231, or 12.31%

23. This problem requires us to work backward through the income statement. First, recognize that Net income = (1 – TC)EBT. Plugging in the numbers given and solving for EBT, we get: EBT = $19,382/(1 – .21) EBT = $24,534.18 Now, we can add interest to EBT to get EBIT as follows: EBIT = EBT + Interest EBIT = $24,534.18 + 3,681 EBIT = $28,215.18 To get EBITD (earnings before interest, taxes, and depreciation), the numerator in the cash coverage ratio, add depreciation to EBIT: EBITD = EBIT + Depreciation EBITD = $28,215.18 + 4,738 EBITD = $32,953.18 Now, we can plug the numbers into the cash coverage ratio and calculate: Cash coverage ratio = EBITD/Interest Cash coverage ratio = $32,953.18/$3,681 Cash coverage ratio = 8.95 times

CHAPTER 3 - 29 24. The only ratio given that includes cost of goods sold is the inventory turnover ratio, so it is the last ratio used. Since current liabilities are given, we start with the current ratio: Current ratio = Current assets/Current liabilities 1.34 = Current assets/$415,000 Current assets = $556,100 Using the quick ratio, we solve for inventory: Quick ratio = (Current assets – Inventory)/Current liabilities Inventory = Current assets – (Quick ratio × Current liabilities) Inventory = $556,100 – (.86 × $415,000) Inventory = $199,200 Inventory turnover = COGS/Inventory 10.30 = COGS/$199,200 COGS = $2,051,760 25. Profit margin = Net income/Sales Profit margin = –£26,382/£315,650 Profit margin = –.0836, or –8.36% As long as both net income and sales are measured in the same currency, there is no problem; in fact, except for some market value ratios like EPS and BVPS, none of the financial ratios discussed in the text are measured in terms of currency. This is one reason why financial ratio analysis is widely used in international finance to compare the business operations of firms and/or divisions across national economic borders. The net income in dollars is: Net income = Profit margin × Sales Net income = –.0836($385,815) Net income = –$32,246.38 26.

Short-term solvency ratios: Current ratio = Current assets/Current liabilities Current ratio 2020 = $84,059/$71,815 = 1.17 times Current ratio 2021 = $112,563/$86,752 = 1.30 times Quick ratio Quick ratio 2020 Quick ratio 2021

= (Current assets – Inventory)/Current liabilities = ($84,059 – 34,495)/$71,815 = .69 times = ($112,563 – 44,336)/$86,752 = .79 times

Cash ratio Cash ratio 2020 Cash ratio 2021

= Cash/Current liabilities = $32,653/$71,815 = .45 times = $39,350/$86,752 = .45 times

Asset utilization ratios: Total asset turnover = Sales/Total assets Total asset turnover = $531,750/$615,435 = .86 times Inventory turnover Inventory turnover

= Cost of goods sold/Inventory = $377,294/$44,336 = 8.51 times

30 SOLUTIONS MANUAL

Receivables turnover Receivables turnover

= Sales/Accounts receivable = $531,750/$28,877 = 18.41 times

Long-term solvency ratios: Total debt ratio = (Total assets – Total equity)/Total assets Total debt ratio 2020 = ($525,158 – 343,343)/$525,158 = .35 times Total debt ratio 2021 = ($615,435 – 388,683)/$615,435 = .37 times Debt-equity ratio Debt-equity ratio 2020 Debt-equity ratio 2021

= Total debt/Total equity = ($71,815 + 110,000)/$343,343 = .53 times = ($86,752 + 140,000)/$388,683 = .58 times

Equity multiplier Equity multiplier 2020 Equity multiplier 2021

= 1 + D/E = 1 + .53 = 1.53 times = 1 + .58 = 1.58 times

Times interest earned Times interest earned

= EBIT/Interest = $107,770/$20,650 = 5.22 times

Cash coverage ratio Cash coverage ratio

= (EBIT + Depreciation)/Interest = ($107,770 + 46,686)/$20,650 = 7.48 times

Profitability ratios: Profit margin Profit margin

= Net income/Sales = $65,340/$531,750 = .1229, or 12.29%

Return on assets Return on assets

= Net income/Total assets = $65,340/$615,435 = .1062, or 10.62%

Return on equity Return on equity

= Net income/Total equity = $65,340/$388,683 = .1681, or 16.81%

27. The DuPont identity is: ROE = (PM)(TAT)(EM) ROE = (.1229)(.86)(1.58) = .1681, or 16.81%

CHAPTER 3 - 31 28.

SMOLIRA GOLF CORP. Statement of Cash Flows Cash, beginning of the year Operating activities Net income Plus: Depreciation Increase in accounts payable Increase in other current liabilities Less: Increase in accounts receivable Increase in inventory

$ 32,653

$ 65,340 $ 46,686 9,399 6,748 –11,966 –9,841

Net cash from operating activities

$ 106,366

Investment activities Fixed asset acquisition Net cash from investment activities

–$108,459 –$108,459

Financing activities Decrease in notes payable Dividends paid Increase in long-term debt Net cash from financing activities

–$ 1,210 –20,000 30,000 $ 8,790

Net increase in cash

$ 6,697

Cash, end of year

$ 39,350

29. Earnings per share Earnings per share

= Net income/Shares = $65,340/15,000 = $4.36 per share

PE ratio PE ratio

= Share price/Earnings per share = $79/$4.36 = 18.14 times

Dividends per share Dividends per share

= Dividends/Shares = $20,000/15,000 = $1.33 per share

Book value per share Book value per share

= Total equity/Shares = $388,683/15,000 shares = $25.91 per share

32 SOLUTIONS MANUAL Market-to-book ratio Market-to-book ratio

= Share price/Book value per share = $79/$25.91 = 3.05 times

PEG ratio PEG ratio

= PE ratio/Growth rate = 18.14/9 = 2.02 times

30. First, we will find the market value of the company‘s equity, which is: Market value of equity = Shares × Share price Market value of equity = 15,000($79) Market value of equity = $1,185,000 The total book value of the company‘s debt is: Total debt = Current liabilities + Long-term debt Total debt = $86,752 + 140,000 Total debt = $226,752 Now we can calculate Tobin‘s Q, which is: Tobin‘s Q = (Market value of equity + Book value of debt)/Book value of assets Tobin‘s Q = ($1,185,000 + 226,752)/$615,435 Tobin‘s Q = 2.29 Using the book value of debt implicitly assumes that the book value of debt is equal to the market value of debt. This will be discussed in more detail in later chapters, but this assumption is generally true. Using the book value of assets assumes that the assets can be replaced at the current value on the balance sheet. There are several reasons this assumption could be flawed. First, inflation during the life of the assets can cause the book value of the assets to understate the market value of the assets. Since assets are recorded at cost when purchased, inflation means that it is more expensive to replace the assets. Second, improvements in technology could mean that the assets could be replaced with more productive, and possibly cheaper, assets. If this is true, the book value can overstate the market value of the assets. Finally, the book value of assets may not accurately represent the market value of the assets because of depreciation. Depreciation is done according to some schedule, generally straight-line or MACRS. Thus, the book value and market value can often diverge.

CHAPTER 4 LONG-TERM FINANCIAL PLANNING AND GROWTH Answers to Concepts Review and Critical Thinking Questions 1. The reason is that, ultimately, sales are the driving force behind a business. A firm‘s assets, employees, and, in fact, just about every aspect of its operations and financing exist to directly or indirectly support sales. Put differently, a firm‘s future need for things like capital assets, employees, inventory, and financing are determined by its future sales level. 2. Two assumptions of the sustainable growth formula are that the company does not want to sell new equity, and that financial policy is fixed. If the company raises outside equity, or increases its debtequity ratio, it can grow at a higher rate than the sustainable growth rate. Of course, the company could also grow faster than the rate at which its profit margin increases, if it changes its dividend policy by increasing the retention ratio, or its total asset turnover increases. 3. The internal growth rate is greater than 15 percent, because at a 15 percent growth rate the negative EFN indicates that there is excess internal financing. If the internal growth rate is greater than 15 percent, then the sustainable growth rate is certainly greater than 15 percent, because there is additional debt financing used in that case (assuming the firm is not 100 percent equity-financed). As the retention ratio is increased, the firm has more internal sources of funding, so the EFN will decline. Conversely, as the retention ratio is decreased, the EFN will rise. If the firm pays out all its earnings in the form of dividends, then the firm has no internal sources of funding (ignoring the effects of accounts payable); the internal growth rate is zero in this case and the EFN will rise to the change in total assets. 4. The sustainable growth rate is greater than 20 percent, because at a 20 percent growth rate the negative EFN indicates that there is excess financing still available. If the firm is 100 percent equity financed, then the sustainable and internal growth rates are equal and the internal growth rate would be greater than 20 percent. However, when the firm has some debt, the internal growth rate is always less than the sustainable growth rate, so it is ambiguous whether the internal growth rate would be greater than or less than 20 percent. If the retention ratio is increased, the firm will have more internal funding sources available, and it will have to take on more debt to keep the debt-equity ratio constant, so the EFN will decline. Conversely, if the retention ratio is decreased, the EFN will rise. If the retention rate is zero, both the internal and sustainable growth rates are zero, and the EFN will rise to the change in total assets. 5. Presumably not, but, of course, if the product had been much less popular, then a similar fate would have awaited due to lack of sales. 6. Since customers did not pay until shipment, receivables rose. The firm‘s NWC, but not its cash, increased. At the same time, costs were rising faster than cash revenues, so operating cash flow declined. The firm‘s capital spending was also rising. Thus, all three components of cash flow from assets were negatively impacted.

34 SOLUTIONS MANUAL 7. Apparently not! In hindsight, the firm may have underestimated costs and also underestimated the extra demand from the lower price. 8. Financing possibly could have been arranged if the company had taken quick enough action. Sometimes it becomes apparent that help is needed only when it is too late, again emphasizing the need for planning. 9. All three were important, but the lack of cash or, more generally, financial resources ultimately spelled doom. An inadequate cash resource is usually cited as the most common cause of small business failure. 10. Demanding cash up front, increasing prices, subcontracting production, and improving financial resources via new owners or new sources of credit are some of the options. When orders exceed capacity, price increases may be especially beneficial.

It is important to remember that equity will not increase by the same percentage as the other assets. If every other item on the income statement and balance sheet increases by 15 percent, the pro forma income statement and balance sheet will look like this: Pro forma income statement Sales Costs Net income

$ 45,310 39,905 $ 5,405

Pro forma balance sheet Assets

$33,580

Total

$33,580

In order for the balance sheet to balance, equity must be: Equity = Total liabilities and equity – Debt Equity = $33,580 – 10,810 Equity = $22,770 Equity increased by: Equity increase = $22,770 – 19,800 Equity increase = $2,970

Debt Equity Total

$ 10,810 22,770 $ 33,580

CHAPTER 4 - 35 Net income is $5,405 but equity only increased by $2,970; therefore, a dividend of: Dividend = $5,405 – 2,970 Dividend = $2,435 must have been paid. Dividends paid is the plug variable. 2.

Here we are given the dividend amount, so dividends paid is not a plug variable. If the company pays out one-half of its net income as dividends, the pro forma income statement and balance sheet will look like this:

Pro forma income statement Sales $45,310 Costs 39,905 Net income $ 5,405

Assets Total

Pro forma balance sheet $33,580 Debt Equity $33,580 Total

$ 9,400 22,503 $31,903

Dividends $2,703 Add. to RE $2,703 Note that the balance sheet does not balance. This is due to EFN. The EFN for this company is: EFN = Total assets – Total liabilities and equity EFN = $33,580 – 31,903 EFN = $1,678 3. An increase of sales to $9,164 is an increase of: Sales increase = ($9,164 – 7,900)/$7,900 Sales increase = .16, or 16% Assuming costs and assets increase proportionally, the pro forma financial statements will look like this: Pro forma income statement Sales Costs Net income

$ 9,164.00 6,217.60 $ 2,946.40

Pro forma balance sheet Assets

$26,564.00

Total

$26,564.00

Debt Equity Total

$ 9,100.00 16,746.40 $25,846.40

If no dividends are paid, the equity account will increase by the net income, so: Equity = $13,800 + 2,946.40 Equity = $16,746.40 So the EFN is: EFN = Total assets – Total liabilities and equity EFN = $26,564 – 25,846.40 EFN = $717.60

36 SOLUTIONS MANUAL 4. An increase of sales to $23,345 is an increase of: Sales increase = ($23,345 – 20,300)/$20,300 Sales increase = .15, or 15% Assuming costs and assets increase proportionally, the pro forma financial statements will look like this: Pro forma income statement Sales $23,345.00 Costs 19,665.00 EBIT 3,680.00 Taxes (21%) 772.80 Net income $ 2,907.20

Pro forma balance sheet Assets

$ 54,050

Total

$ 54,050

Debt Equity Total

26,900.00 21,397.20 $48,297.20

The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($1,400/$2,528)($2,907.20) Dividends = $1,610 The addition to retained earnings is: Addition to retained earnings = $2,907.20 – 1,610 Addition to retained earnings = $1,297.20 And the new equity balance is: Equity = $20,100 + 1,297.20 Equity = $21,397.20 So the EFN is: EFN = Total assets – Total liabilities and equity EFN = $54,050 – 48,297.20 EFN = $5,752.80 5. Assuming costs, current liabilities, and assets increase proportionally, the pro forma financial statements will look like this: Pro forma income statement Sales $10,005.00 Costs 6,440.00 Taxable income $3,565.00 Taxes (25%) 891.25 Net income $2,673.75

CA FA TA

Pro forma balance sheet $4,830.00 CL 11,960.00 LTD Equity $16,790.00 Total D&E

$2,185.00 3,800.00 10,504.25 $16,489.25

CHAPTER 4 - 37 The payout ratio is 40 percent, so dividends will be: Dividends = .40($2,673.75) Dividends = $1,069.50 The addition to retained earnings is: Addition to retained earnings = $2,673.75 – 1,069.50 Addition to retained earnings = $1,604.25 So the EFN is: EFN = Total assets – Total liabilities and equity EFN = $16,790 – 16,489.25 EFN = $300.75 6.

To calculate the internal growth rate, we first need to calculate the ROA, which is: ROA = NI/TA ROA = $4,108/$35,500 ROA = .1157, or 11.57% The plowback ratio, b, is one minus the payout ratio, so: b = 1 – .30 b = .70 Now we can use the internal growth rate equation to get: Internal growth rate = (ROA × b)/[1 – (ROA × b)] Internal growth rate = [.1157(.70)]/[1 – .1157(.70)] Internal growth rate = .0881, or 8.81%

To calculate the sustainable growth rate, we first need to calculate the ROE, which is: ROE = NI/TE ROE = $4,108/$21,900 ROE = .1876, or 18.76% The plowback ratio, b, is one minus the payout ratio, so: b = 1 – .30 b = .70 Now we can use the sustainable growth rate equation to get: Sustainable growth rate = (ROE × b)/[1 – (ROE × b)] Sustainable growth rate = [.1876(.70)]/[1 – .1876(.70)] Sustainable growth rate = .1512, or 15.12%

38 SOLUTIONS MANUAL 8.

The maximum percentage sales increase is the sustainable growth rate. To calculate the sustainable growth rate, we first need to calculate the ROE, which is: ROE = NI/TE ROE = $4,774/$51,700 ROE = .0923, or 9.23% The plowback ratio, b, is one minus the payout ratio, so: b = 1 – .40 b = .60 Now we can use the sustainable growth rate equation to get: Sustainable growth rate = (ROE × b)/[1 – (ROE × b)] Sustainable growth rate = [.0923(.60)]/[1 – .0923(.60)] Sustainable growth rate = .0587, or 5.87% So, the maximum dollar increase in sales is: Maximum increase in sales = $38,600(.0587) Maximum increase in sales = $2,264.04

Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income statement will look like this: HEIR JORDAN CORPORATION Pro Forma Income Statement Sales Costs Taxable income Taxes (22%) Net income

$63,600 49,080 $14,520 3,194 $11,326

The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($3,500/$9,438)($11,326) Dividends = $4,200 And the addition to retained earnings will be: Addition to retained earnings = $11,326 – 4,200 Addition to retained earnings = $7,126

CHAPTER 4 - 39 10. Below is the balance sheet with the percentage of sales for each account on the balance sheet. Notes payable, total current liabilities, long-term debt, and all equity accounts do not vary directly with sales. HEIR JORDAN CORPORATION Balance Sheet ($) (%) Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment

Total assets

$ 3,140 4,200 6,500 $ 13,840

5.92 7.92 12.26 26.11

$43,200

81.51

$57,040 107.62

($)

Liabilities and Owners‘ Equity Current liabilities Accounts payable $ 2,600 Notes payable 5,700 Total $ 8,300 Long-term debt $28,000 Owners‘ equity Common stock and paid-in surplus $ 5,000 Retained earnings 15,740 Total $20,740 Total liabilities and owners‘ equity $57,040

(%)

4.91 n/a n/a n/a

n/a n/a n/a n/a

11. Assuming costs vary with sales and a 15 percent increase in sales, the pro forma income statement will look like this: HEIR JORDAN CORPORATION Pro Forma Income Statement Sales Costs Taxable income Taxes (22%) Net income

$60,950.00 47,035.00 $13,915.00 3,061.30 $10,853.70

The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($3,500/$9,438)($10,853.70) Dividends = $4,025 And the addition to retained earnings will be: Addition to retained earnings = $10,853.70 – 4,025 Addition to retained earnings = $6,828.70 The new accumulated retained earnings on the pro forma balance sheet will be: New accumulated retained earnings = $15,740 + 6,828.70 New accumulated retained earnings = $22,568.70

40 SOLUTIONS MANUAL The pro forma balance sheet will look like this: HEIR JORDAN CORPORATION Pro Forma Balance Sheet Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment

Total assets

$ 3,611.00 4,830.00 7,475.00 $ 15,916.00

$ 49,680.00

$ 65,596.00

Liabilities and Owners‘ Equity Current liabilities Accounts payable $ 2,990.00 Notes payable 5,700.00 Total $ 8,690.00 Long-term debt $ 28,000.00 Owners‘ equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners‘ equity

$ 5,000.00 22,568.70 $ 27,568.70 $ 64,258.70

So the EFN is: EFN = Total assets – Total liabilities and equity EFN = $65,596 – 64,258.70 EFN = $1,337.30 12. We need to calculate the retention ratio to calculate the internal growth rate. The retention ratio is: b = 1 – .35 b = .65 Now we can use the internal growth rate equation to get: Internal growth rate = (ROA × b)/[1 – (ROA × b)] Internal growth rate = [.083(.65)]/[1 – .083(.65)] Internal growth rate = .0570, or 5.70% 13. We need to calculate the retention ratio to calculate the sustainable growth rate. The retention ratio is: b = 1 – .25 b = .75 Now we can use the sustainable growth rate equation to get: Sustainable growth rate = (ROE × b)/[1 – (ROE × b)] Sustainable growth rate = [.141(.75)]/[1 – .141(.75)] Sustainable growth rate = .1183, or 11.83%

CHAPTER 4 - 41 14. We first must calculate the ROE to calculate the sustainable growth rate. To do this we must realize two other relationships. The total asset turnover is the inverse of the capital intensity ratio, and the equity multiplier is 1 + D/E. Using these relationships, we get: ROE = (PM)(TAT)(EM) ROE = (.073)(1/.95)(1 + 1.05) ROE = .1575, or 15.75% The plowback ratio is one minus the dividend payout ratio, so: b = 1 – ($24,000/$84,000) b = .7143 Now we can use the sustainable growth rate equation to get: Sustainable growth rate = (ROE × b)/[1 – (ROE × b)] Sustainable growth rate = [.1575(.7143)]/[1 – .1575(.7143)] Sustainable growth rate = .1268, or 12.68% 15. We must first calculate the ROE using the DuPont ratio to calculate the sustainable growth rate. The ROE is: ROE = (PM)(TAT)(EM) ROE = (.052)(3.2)(.95) ROE = .1581, or 15.81% The plowback ratio is one minus the dividend payout ratio, so: b = 1 – .35 b = .65 Now we can use the sustainable growth rate equation to get: Sustainable growth rate = (ROE × b)/[1 – (ROE × b)] Sustainable growth rate = [.1581(.65)]/[1 – .1581(.65)] Sustainable growth rate = .1145, or 11.45% Intermediate 16. To determine full capacity sales, we divide the current sales by the capacity the company is currently using, so: Full capacity sales = $830,000/.94 Full capacity sales = $882,979 The maximum sales growth is the full capacity sales divided by the current sales, so: Maximum sales growth = ($882,979/$830,000) – 1 Maximum sales growth = .0638, or 6.38%

42 SOLUTIONS MANUAL 17. To find the new level of fixed assets, we need to find the current percentage of fixed assets to full capacity sales. Doing so, we find: Fixed assets/Full capacity sales = $590,000/$882,979 Fixed assets/Full capacity sales = .6682 Next, we calculate the total dollar amount of fixed assets needed at the new sales figure. Total fixed assets = .6682($910,000) Total fixed assets = $608,055.42 The new fixed assets necessary is the total fixed assets at the new sales figure minus the current level of fixed assts. New fixed assets = $608,055.42 – 590,000 New fixed assets = $18,055.42 18. We have all the variables to calculate ROE using the DuPont identity except the profit margin. If we find ROE, we can solve the DuPont identity for profit margin. We can calculate ROE from the sustainable growth rate equation. For this equation we need the retention ratio, so: b = 1 – .25 b = .75 Using the sustainable growth rate equation and solving for ROE, we get: Sustainable growth rate = (ROE × b)/[1 – (ROE × b)] .11 = [ROE(.75)]/[1 – ROE(.75)] ROE = .1321, or 13.21% Now we can use the DuPont identity to find the profit margin as: ROE = PM(TAT)(EM) .1321 = PM(1/.65)(1 + .75) PM = (.1321)/[(1/.65)(1.75)] PM = .0491, or 4.91% 19. We are given the profit margin. Remember that: ROA = PM(TAT) We can calculate the ROA from the internal growth rate formula, and then use the ROA in this equation to find the total asset turnover. The retention ratio is: b = 1 – .25 b = .75

CHAPTER 4 - 43 Using the internal growth rate equation to find the ROA, we get: Internal growth rate = (ROA × b)/[1 – (ROA × b)] .064 = [ROA(.75)]/[1 – ROA(.75)] ROA = .0802, or 8.02% Plugging ROA and PM into the equation we began with and solving for TAT, we get: ROA = (PM)(TAT) .0802 = .057(TAT) TAT = .0802/.057 TAT = 1.41 times 20. We should begin by calculating the D/E ratio. We calculate the D/E ratio as follows: Total debt ratio = .45 = TD/TA Inverting both sides we get: 1/.45 = TA/TD Next, we need to recognize that: TA/TD = 1 + TE/TD Substituting this into the previous equation, we get: 1/.45 = 1 + TE/TD Subtracting 1 (one) from both sides and inverting again, we get: D/E = 1/[(1/.45) – 1] D/E = .82 With the D/E ratio, we can calculate the EM and solve for ROE using the DuPont identity: ROE = (PM)(TAT)(EM) ROE = (.059)(1.15)(1 + .82) ROE = .1234, or 12.34% Now we can calculate the retention ratio as: b = 1 – .40 b = .60 Finally, putting all the numbers we have calculated into the sustainable growth rate equation, we get: Sustainable growth rate = (ROE × b)/[1 – (ROE × b)] Sustainable growth rate = [.1234(.60)]/[1 – .1234(.60)] Sustainable growth rate = .0799, or 7.99%

44 SOLUTIONS MANUAL 21. To calculate the sustainable growth rate, we first must calculate the retention ratio and ROE. The retention ratio is: b = 1 – $7,500/$19,200 b = .6094 And the ROE is: ROE = $19,200/$77,000 ROE = .2494, or 24.94% So, the sustainable growth rate is: Sustainable growth rate = (ROE × b)/[1 – (ROE × b)] Sustainable growth rate = [.2494(.6094)]/[1 – .2494(.6094)] Sustainable growth rate = .1792, or 17.92% If the company grows at the sustainable growth rate, the new level of total assets is: New TA = 1.1792($67,000 + 77,000) = $169,800.92 To find the new level of debt in the company‘s balance sheet, we take the percentage of debt in the capital structure times the new level of total assets. The additional borrowing will be the new level of debt minus the current level of debt. So: New TD = [D/(D + E)](TA) New TD = [$67,000/($67,000 + 77,000)]($169,800.92) New TD = $79,004.59 And the additional borrowing will be: Additional borrowing = $79,004.59 – 67,000 Additional borrowing = $12,004.59 The growth rate that can be supported with no outside financing is the internal growth rate. To calculate the internal growth rate, we first need the ROA, which is: ROA = $19,200/($67,000 + 77,000) ROA = .1333, or 13.33% This means the internal growth rate is: Internal growth rate = (ROA × b)/[1 – (ROA × b)] Internal growth rate = [.1333(.6094)]/[1 – .1333(.6094)] Internal growth rate = .0884, or 8.84%

CHAPTER 4 - 45 22. Since the company issued no new equity, shareholders‘ equity increased by retained earnings. Retained earnings for the year were: Retained earnings = NI – Dividends Retained earnings = $29,000 – 6,400 Retained earnings = $22,600 So, the equity at the end of the year was: Ending equity = $153,000 + 22,600 Ending equity = $175,600 The ROE based on the end of period equity is: ROE = $29,000/$175,600 ROE = .1651, or 16.51% The plowback ratio is: Plowback ratio = Addition to retained earnings/NI Plowback ratio = $22,600/$29,000 Plowback ratio = .7793, or 77.93% Using the equation presented in the text for the sustainable growth rate, we get: Sustainable growth rate = (ROE × b)/[1 – (ROE × b)] Sustainable growth rate = [.1651(.7793)]/[1 – .1651(.7793)] Sustainable growth rate = .1477, or 14.77% The ROE based on the beginning of period equity is ROE = $29,000/$153,000 ROE = .1895, or 18.95% Using the shortened equation for the sustainable growth rate and the beginning of period ROE, we get: Sustainable growth rate = ROE × b Sustainable growth rate = .1895 × .7793 Sustainable growth rate = .1477, or 14.77% Using the shortened equation for the sustainable growth rate and the end of period ROE, we get: Sustainable growth rate = ROE × b Sustainable growth rate = .1651 × .7793 Sustainable growth rate = .1287, or 12.87%

46 SOLUTIONS MANUAL Using the end of period ROE in the shortened sustainable growth rate equation results in a growth rate that is too low. This will always occur whenever the equity increases. If equity increases, the ROE based on end of period equity is lower than the ROE based on the beginning of period equity. The ROE (and sustainable growth rate) in the abbreviated equation is based on equity that did not exist when the net income was earned. 23. The ROA using end of period assets is: ROA = $29,000/$215,000 ROA = .1349, or 13.49% The beginning of period assets had to have been the ending assets minus the addition to retained earnings, so: Beginning assets = Ending assets – Addition to retained earnings Beginning assets = $215,000 – 22,600 Beginning assets = $192,400 And the ROA using beginning of period assets is: ROA = $29,000/$192,400 ROA = .1507, or 15.07% Using the internal growth rate equation presented in the text, we get: Internal growth rate = (ROA × b)/[1 – (ROA × b)] Internal growth rate = [.1349(.7793)]/[1 – .1349(.7793)] Internal growth rate = .1175, or 11.75% Using the formula ROA × b, and beginning of period assets: Internal growth rate = .1507 × .7793 Internal growth rate = .1175, or 11.75% Using the formula ROA × b, and end of period assets: Internal growth rate = .1349 × .7793 Internal growth rate = .1051, or 10.51% Using the end of period ROA in the shortened internal growth rate equation results in a growth rate that is too low. This will always occur whenever the assets increase. If assets increase, the ROA based on end of period assets is lower than the ROA based on the beginning of period assets. The ROA (and internal growth rate) in the abbreviated equation is based on assets that did not exist when the net income was earned.

CHAPTER 4 - 47 24. Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income statement will look like this: Pro Forma Income Statement Sales $ 823,836 Costs 665,304 Other expenses 16,824 EBIT $ 141,708 Interest 12,090 Taxable income $ 129,618 Taxes (21%) 27,220 Net income $ 102,398 The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($27,475/$83,740)($102,398) Dividends = $33,597 And the addition to retained earnings will be: Addition to retained earnings = $102,398 – 33,597 Addition to retained earnings = $68,801 The new retained earnings on the pro forma balance sheet will be: New retained earnings = $166,705 + 68,801 New retained earnings = $235,506 The pro forma balance sheet will look like this: Pro Forma Balance Sheet Liabilities and Owners‘ Equity

Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment

Total assets

25,128 38,364 85,584 149,076

410,376

559,452

Current liabilities Accounts payable Notes payable Total Long-term debt Owners‘ equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners‘ equity

$ $ $

64,548 13,215 77,763 127,500

105,000 235,506 340,506

545,769