Corporate Finance Online -- Access Card, 2nd Edition Stanley Eakins Solution Manual

Corporate Finance Online - Access Card, 2nd Edition By Stanley Eakins

Email: Richard@qwconsultancy.com

Table of Contents Chapter 2 Financial Statement and Ratio Analysis......................................................................... 1 Chapter 3 Introduction to Time Value of Money ........................................................................... 4 Chapter 4 Annuities and Loans ....................................................................................................... 6 Chapter 5 Introduction to Risk and Return .................................................................................. 10 Chapter 6 Portfolio Theory ........................................................................................................... 13 Chapter 7 Interest Rates and Bonds .............................................................................................. 19 Chapter 8 Stock Valuation and Market Efficiency ....................................................................... 23 Chapter 9 Capital Budgeting: Introduction and Techniques......................................................... 26 Chapter 10 Capital Budgeting: Estimating Cash Flows ............................................................... 29 Chapter 11 Cost of Capital ............................................................................................................ 35 Chapter 12 Capital Structure ......................................................................................................... 38 Chapter 13 Dividends, Repurchases, and Splits ........................................................................... 43 Chapter 14 Financial Planning and Forecasting ........................................................................... 48 Chapter 15 The Management of Working Capital ........................................................................ 54 Chapter 16 International Finance .................................................................................................. 55 Chapter 17 Corporate Valuation ................................................................................................... 58 Chapter 18 Futures and Options ................................................................................................... 66

Chapter 2 Financial Statement and Ratio Analysis 3. Profitability Ratios Selected Profitability Ratios Apple Inc. Year End Sept 29, 2012 43.9% 35.3% 26.7% 35.3% 23.7%

Gross Profit Margin Operating Profit Margin Net Profit Margin ROE ROA

• • • • •

• •

The highest ROE was 39.9% in 1988, which was the Macintosh era.

The lowest ROE was –87.1% in 1997, which was the year that Jobs was hired back as CEO. The gross margins in the Macintosh era (late 1980s) were more than 50%. This is higher than at any other point in Apple’s history.

In 2011 the gross margin was 40.5%, and in 2013 it was 37.6%, so the trend is decreasing.

The main reason for declining margins is increased competition. For example, in September 2012 Apple released the iPhone 5 with a 4-inch diagonal screen, which was larger than the screen of the 4S (but smaller than the screen of the Samsung Galaxy SIII).

The extra features of the iPhone 5 boosted its cost by approximately $19 more than the 4S model. Apple retailed the i5 for US$649, which was the same price as the 4S. A static price and rising cost of goods sold will reduce the gross margin.

ROE rose dramatically after the introduction of the iPod in 2001 but was highest in the era after the introduction of the iPad (post 2010) Profitability declined in 2013 compared to 2012 and 2011, which is indicative of a declining trend. But this is the big unknown question for Apple and its investors. This is meant as an open-ended discussion question.

4. Liquidity Ratios Metro 0.99 0.34

Current Ratio Quick Ratio

•

Safeway 1.45 1.09

Safeway has larger current and quick ratios because of its larger cash reserves.

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5. Activity Ratios Ford

Daimler Benz

Total Asset Turnover Fixed Asset Turnover

0.73 5.32

0.70 5.42

Total Asset Turnover Inventory Turnover

Metro 2.25 11.82

Safeway 2.10 12.75

Metro 45% 14.64 40% 2.76

Safeway 66% 2.33 10% 3.23

6. Financing Ratios

Debt Ratio Times Interest Earned Cash Flow to Debt Asset Coverage Ratio

• • • •

Safeway has a higher debt ratio, so it has more debt relative to its total assets.

Metro has a higher times-interest-earned ratio so it has greater capacity to pay its interest out of operating income (EBIT).

Metro can repay 40% of its debt in the most recent year. If this recurs, then Metro could repay its debt 2.5 years, which is much quicker than Safeway.

Safeway has $3.23 of collateral per dollar of debt, which is larger than Metro. Metro only has $3.76 of collateral per dollar of debt.

7. Du Pont Analysis • • • • • • • • •

The sum of the left-hand side of the balance sheet is equal to total assets Debt + Equity = right hand side of the balance sheet. This is equal to total assets.

TA/E = 1 + D/E If leverage increases, then D/E increases, and given ROA, ROE will increase.

NI/Sales = net profit margin S/TA = total asset turnover If total asset turnover increases, then ROA increases and so does ROE. If net profit margin decreases, then ROA decreases and so does ROE. ROA = (net profit margin) × (total asset turnover). Net profit margin measures profitability and total asset turnover measures asset utilization.

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Selected Financial Ratios S&M Family Outlet Inc. ROE (1 + D/E) ROA TAT NPM Inventory Turnover Accounts Receivable Turnover

• • • • • • • • • • •

12.2% $1.58 7.7% $1.07 7.2% 2.61 25.88

14.1% $2.89 4.9% $0.78 6.3% 1.81 11.02

Sales increased from Year 5 to Year 6.

ROE increased from Year 5 to Year 6.

ROA declined from Year 5 to Year 6.

Inventory turnover declined from Year 5 to Year 6.

Accounts Receivable turnover declined from Year 5 to Year 6.

Both net profit margin and total asset turnover declined from Year 5 to Year 6. Both caused the decline in ROA. The debt ratio rose from 37% in Year 5 to 65% in Year 6. The (1 + D/E) ratio also rose from Year 5 to Year 6.

Leverage increased dramatically from Year 5 to Year 6, which caused an increase in ROE despite a decrease in ROA. Goodwill increased from Year 5 to Year 6.

S&M Family Outlet acquired another company in Year 6. This increased sales, total assets, liabilities, and leverage.

More investigation is necessary to understand why asset utilization and profitability are reduced in Year 6. Are these short-term due to the challenges of integrating the acquired company or are these long-term weaknesses in the new company?

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Chapter 3 Introduction to Time Value of Money 2. Future Value in One Period FV in One Period FV1 = $100 × (1.10) = 110 PV in One Period PV0 = FV1/(1 + i) = $100/(1.10) = 90.90909 PV0 = 90.91 3. Future Value over Multiple Periods FV35 = PV × (1.05)35 = 5,516.02 FV35 = PV × (1.12)35 = 52,799.62 4. Solving for the Interest Rate i1 = (FV1/PV0) – 1 = (20/10) – 1 = 1 (100%) i2 = (FV2/PV1) – 1 = (10/20) – 1 = –0.5 (–50%) (i1 + i2)/2 = (1 + (–0.5))/2 = 0.25 or 25% •

The arithmetic mean is positive, but the investor ends up with the same amount she started with. The return seems more like 0%, so the arithmetic mean is not a correct representation of the investor’s return.

FVn = PV0 × (1 + i)n FVn/PV0 = (1 + i)n [FVn/PV0]1/n = [(1 + i)n] 1/n = (1 + i) i = [FVn/PV0]1/n – 1 i = [FVn/PV0]1/n – 1 = [10/10]1/2 – 1 = 0

•

Because the investor ends up with the same amount she started with, 0% does seem like a correct representation of the investor’s return.

5. Solving for the Number of Periods The trick is to remember the following rule of logarithms: ln(yx) = × * ln(y)

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We take the logarithm of both sides of a future value problem, apply the rule to the right-hand side and simplify: ln[FVn/PV0] = ln[(1 + i)n] = n * ln(1 + i) n = ln[FVn/PV0] / ln(1+i) n = ln(2)/ln(1.02) = 0.69315/0.0198 = 35 6. Future Value with Non-Annual Compounding m = 2 and i/m = 0.10/2 = 0.05 FV = $100 × (1.05) = $105 FV1 = $100 × (1.05)2 = $110.25 FV = $1,500 × (1 + 0.08/4)20 × 4 = $7,313.16 7. Effective Interest Rate FV = $100 × (1.10) = $110 • •

Prefer Sophisto because total at tend of year is $110.25, which is larger than total from Simplisto ($110).

Simplisto needs to offer 10.25% with no compounding to match Sophisto.

EIR = (1 + 0.08/4)4 – 1 = 0.08243 EIR = (1 + 0.1999/365)365 – 1 = 0.2212

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Chapter 4 Annuities and Loans 2. Future Value of Ordinary Annuities FVannuity = PMT × FVIFA = $1,000 × (1/0.12) × [(1.12)5 – 1] FVannuity = $1,000 × 6.3528 = 6,352.80 FVannuity = PMT × FVIFA = $600 × (1/0.01) × [(1.01)360 – 1] FVannuity = $2,096,978.48 FVannuity = PMT × FVIFA = $600 × (1/0.007667) × [(1.007667)360 – 1] FVannuity = $1,048,489 •

Ideally, you want to pay a fee of 0%.

3. Present Value of Ordinary Annuities PVannuity = PMT × PVIFA = $1,000 × (1/0.12) × [1 – – (1.12)–5 ] PVannuity = $3,604.78 PVannuity = PMT × PVIFA = $90,000 × (1/0.04) × [1 – – (1.04)–25 ] PVannuity = $1,405,987.19 PVannuity = PMT × PVIFA = $100 × (1/0.10) × [1 – – (1.10)–2 ] PVannuity = $173.55 So, there will be nothing left in the account after two years. Alternatively, the balance after one year is $173.55 × (1.10) = 190.9090. Then withdraw $100, which reduces the account to $90.90.

With 10% interest, this will grow to $100 to exactly match your withdrawal at the end of the second year.

4. Equation of Value, Focal Date, and Retirement Planning •

The principle for building the equation of value is “all of the above.”

FV = $500 × (1.10)2 + $500 × (1.10) = $1,155 S = $500 is not the correct answer. It produces more savings than we need.

•

The problem with the equation of value is “all of the above.”

FV = $432.90 × (1.10)2 + $432.90 × (1.10) = $1,000

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Focal Date 2 S*(1.10)2 + S*(1.10) = $1,000 S = $432.90 Focal Date 1 S*(1.10) + S = $1,000/1.10 S*2.10 = $909.09 S = $432.90 • • • •

When solving time value of money problems, you always need a focal date.

It does not matter what date you pick.

We selected Date 1 because it is the retirement date.

When solving time value of money problems you should always draw a time line.

Focal Date = Age 60.

FV of savings = X × FVIFA5%,30 PV of withdrawals = 90,000 × PVIFA5%,25 Equate and solve for X: X = 90,000 × PVIFA5%,25/ FVIFA5%,30 = 1,268,455.01/66.43885 = $19,092.07 In months, you save for 30 × 12 = 360 months and retire for 25 × 12 = 300 months.

FV of savings = X × FVIFA0.5%,360 PV of withdrawals = (90,000/12) × PVIFA0.3333%,300 Equate and solve for X: X = 1,420,893.62/1,004.51504 = $1,414.51 per month With bequest to children the withdrawals include a lump-sum of $500,000 at month 300. This must also be discounted to the retirement date.

FV of savings = X × FVIFA0.5%,360 PV of withdrawals = (90,000/12) × PVIFA0.3333%,300 + 500,000 × PVIF0.3333%,300 Equate and solve for X: X = (1,420,893.62 + 184,245.86)/1,004.51504 = $1,597.92 per month 5. Imbedded Annuities FVannuity = PMT X FVIFA = $1,000 × (1/0.1) × [(1.1)40 – 1] FVannuity = $442,592.56 FVannuity = PMT X FVIFA = $1,000 × (1/0.1) × [(1.1)7 – 1] FVannuity = $9,487.17 FV = 9,487.17 × (1.10)40 = $429,382.30 The two girls have almost the same amount of money at retirement.

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6. Perpetuities FV = ∞ PV = 100/0.10 = 1,000 PVannuity = PMT × PVIFA = $100 × (1/0.10) × [1 – – (1.10)–30 ] PVannuity = $942.69 7. Balloon Loans Balloon = FV = Principal × (1+ i)n = $1,000 × (1.10)3 = $1,331 8. Amortized Loans PMT = $1,000 / [(1.10)–1 + (1.10)–2 + (1.10)–3] = $402.11 The Reinvestment Rate Assumption FV = PMT × FVIFA = $402.11 × (1/0.05) × [(1.05)3 – 1] = 402.11 × 3.1525 FV = 1,267.65 •

You would prefer the balloon (FV = $1,331) over the amortized loan payments with a reinvestment rate of 5% (FV = $1,267.65)

FV = PMT × FVIFA = $402.11 × (1/0.1) × [(1.1)3 – 1] = 402.11 × 3.31 FV = 1,331 • • •

You are indifferent between the balloon (FV = $1,331) and the amortized loan payments with a reinvestment rate of 10% (FV = $1,331).

True. A lender only earns x% if she can reinvest at x%.

Lenders earn interest two ways: (1) in the payments and (2) through reinvestment.

Car Loans Principal = (82,900 + 1015) × 1.13 = 94,823.95 n = 6 years m = 12 n × m = 6 × 12 = 72 i/m = 0.08/12 = 0.006667 PVIFA = 57.03452 PMT = Principal/PVIFA = 94,823.95/57.03452 = $1,662.57 EOV: Principal = Down payment + PMT × (1/i) × [1 – (1 + i)–n] PMT = (Principal – Down payment)/PVIFA = 89,823.95/57.03452 = $1,574.90

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Solve for the Total Amount of Interest Sum of PMTs = 72 × $1,662.57 = $119,705.12 Principal = $94,823.95 •

Amortized loan payments include a blend of interest and principal.

Interest = (Sum of Payments) – Principal Interest = $119,705.12 + $94,823.95 = $24,881.17 Solve for the Interest Rate i = 12% EOV: Principal = PMT × (1/i) × [1 – (1 + i)–n] + Lump-sum × (1 + i)–n i = 0.10 or 10% Loan Amortization Schedule PMT = Principal/PVIFA = 10,000/3.35216 = $2,983.16 Interest1 = Principal × i = 10,000 × 0.15 = 1,500 Principal paid in first payment = PMT – Interest1 = 2,983.16 – 1,500 = 1,483.16 Principal owing after first payment = 10,000 – 1,483.16 = $8,516.84 Interest2 = Balance Owing1 × i = 8,516.84 × 0.15 = 1,277.53 1 2 3 4 5

Payment Interest Repayment Balance $2,983.16 $1,500.00 $1,483.16 $8,516.84 $2,983.16 $1,277.53 $1,705.63 $6,811.22 $2,983.16 $1,021.68 $1,961.47 $4,849.74 $2,983.16 $727.46 $2,255.69 $2,594.05 $2,983.16 $389.11 $2,594.05 $0.00

$Balance Owing2 = $6,811.22 PV of payments = 2,983.16 × PVIFA15%,3 = 2,983.16 × 2.28323 = 6,811.22 •

You can find the principal outstanding either using an amortization table or by finding the present value of the remaining payments. Mathematicians call this the prospective method of solving for principal outstanding.

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Chapter 5 Introduction to Risk and Return 2. The Return of a Single Asset Holding Period Return D1/P0 = 0.5/17 = 0.02941 (P1 – P0)/P0 = (20 –17)/17 = 3/17= 0.17647 D1/P0 + (P1 – P0)/P0 = 0.20588 (P1 – P0 + D0)/P0 = 0.20588 Expected Return Expected payoff = 1/6 × (1 + 2 + 3 + 4 + 5 + 6) = 21/6 = 3.5 E(k) = 0.333 × 0.33 + 0.333 × 0.12 + 0.333 × –0.09 = 0.12 3. The Risk of a Single Asset • •

It is harmful to jump from an airplane without a parachute, but it is not risky. Risk requires harm and uncertainty.

Investing your live savings in lottery tickets is risky. There is the potential for harm, and the harm is uncertain.

Variance = 0.33 × (0.33 – 0.12)2 + 0.33 × (0.12 – 0.12)2 + 0.33 × (–0.09 – 0.12)2 = 0.02937 Standard Deviation = 0.1715 or 17.15% Best forecast = E(k) = 12% Forecast error = 33% – – 12% = +21%

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Surprise

Type

Big Box Electronics Inc. has grappled with two years of declining same store sales. The CEO said, “Consumer electronics is a very, very soft market. Smartphones, tablets, and TVs are becoming commoditized.”

Firm-specific

Banks posted higher profits due to increased retail lending.

Market-wide

Toll Brothers Home Construction Inc. posted higher profits this quarter due to an increase in new housing starts. Housing starts hit their highest level in the last two years.

Market-wide

Copper stocks could be set to rally this year as analysts sound the alarm on the metal’s inventory levels.

Firm-Specific

GM Inc. stock fell again today as it announced another recall affecting 300,000 vehicles due to a faulty ignition switch.

Firm-Specific

Prob(k > 40%) = Prob(k > (E(k) + 2σ) = 40%) = 2.5% 4. The Return for a Portfolio of Assets Inv0 = 6 × $10 + 2 × $20 = $100 Sale Proceeds1 = 6 × $12 + 2 × $22 = $116 kp = (116 – 100)/100 = 0.16 w1 = 60/100 = 0.6 w2 = 40/100 = 0.4 k1 = 2/10 = 0.2 k2 = 2/20 = 0.1 kp = w1 k1 + w2 k2 = 0.6 × 0.2 + 0.4 × 0.1 = 0.16

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5. Portfolio Risk and Diversification E(k) = 0.333 × 0.33 + 0.333 × 0.12 + 0.333 × –0.09 = 0.12 Variance = 0.33 × (0.33 – 0.12)2 + 0.33 × (0.12 – 0.12)2 + 0.33 × (–0.09 – 0.12)2 = 0.02937 Standard Deviation = 0.1715 or 17.15% wV = 5,000/10,000 = 0.5 and wG = 5,000/10,000 = 0.5 kp = w1 k1 + w2 k2 = 0.5 × 0.33 + 0.5 × –0.09 = 0.12 kp = w1 k1 + w2 k2 = 0.5 × –0.09 + 0.5 × 0.33 = 0.12 • • • • • •

The standard deviation of the portfolio is zero.

The standard deviation is zero because of the perfect negative correlation of the returns on the two stocks and the 50/50 portfolio weights.

Diversification reduces risk.

Diversification works best when returns are negatively correlated.

Returns should be negatively correlated across states of nature.

True. A portfolio can have less risk than its least risky asset. Look at the example with Venus and Gill.

Covariance and Correlation S

0.33

–0.09

0.33

–0.21

0.21

–0.0147

N

0.33

0.12

0.12

0

0

0

R

0.33

0.33

–0.09

0.21

–0.21

–0.0147

0.12

0.12

–0.0294

COV = –0.0294 Corr = –0.99999 COV = Corr × σ1 × σ2 = 0.12375

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Chapter 6 Portfolio Theory 2. Diversification E(kp) = 0.25 × 0.06 + 0.75 × 0.1 = 0.09 σp = [(0.252) × (0.042) + (0.752) × (0.102) + 2 × 0.25 × 0.75 × (–1) × 0.04 × 0.1]0.5 σp = 0.065 Portfolio Weights B (1 – w) A (w) 1 0 0.75 0.25 0.50 0.50 0.25 0.75 0 1

Correlation = –1 σp E(kp) 0.06 0.04 0.07 0.005 0.08 0.03 0.09 0.065 0.10 0.10

Portfolio Weights B (1 – w) A (w) 1 0 0.75 0.25 0.50 0.50 0.25 0.75 0 1

Correlation = 0 σp E(kp) 0.06 0.04 0.07 0.039 0.08 0.054 0.09 0.0757 0.10 0.10

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• • •

As you increase the correlation between stocks, the variance increases.

When the correlation between assets is +1, then the standard deviation of portfolio returns is a simple weighted average of the standard deviations of the two assets.

When the correlation between assets is +1, then you cannot form a portfolio that has less standard deviation than the asset with the lowest standard deviation.

The Variance of a Large Portfolio •

σ p2 = the average covariance

• •

To create a low risk portfolio, buy stocks with low average covariance.

The risk of a launch failure is independent of any other risks in the overall economy, so the returns on the satellite company will have a low covariance with the returns on any other stock. Thus, if added to your portfolio, this stock will lower the risk of the portfolio.

3. The Market Portfolio • •

Prefer B to A because B has same risk and higher expected return.

The efficient set is the boundary line above the vertex.

The Risk-Free Asset • • •

There is no risk of default on a U.S. Treasury Bond.

A U.S. Treasury coupon bond is not risk free. The yield is only approximately equal to the return. The final return depends on coupon reinvestment rates.

Only zero coupon bonds issued by the U.S. Treasury are risk free.

Variance = 0.2 × (0.02 – 0.02)2 + 0.6 × (0.02 – 0.02)2 + 0.2 × (0.02 – 0.02)2 = 0 Covariance = 0 because the T-Bill deviation from expected value is always zero.

Portfolio of One Risky and One Risk-Free Asset E(kp) = 0.5 × 0.12 + 0.5 × 0.05 = 0.085 σp = [(0.5)2 × (0.1715)2)]0.5 = 0.5 × 0.1715 = 0.0858 •

When you make two-asset portfolios with the risk-free asset and any other risky asset, the resulting set of risk-return combinations lies on a straight line.

The New Efficient Set • •

The straight line through M lies everywhere (except point M) above the Markowitz efficient set and so offers portfolios with higher returns than the efficient set.

It is not possible to construct portfolios with a better risk-return trade-off than the new efficient set.

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Value-Weighted Portfolio V1 = 6 × $10 + 2 × $20 = $100 V2 = 6 × $12 + 2 × $22 = $116 (V2/V1) – 1 = 0.16 w1 = 6 × $10/$100 = 0.6 k1 = (12/10) – 1 = 0.2 k2 = (22/20) – 1 = 0.1 w1 = (3 × $10)/(3 × $10+1 × $20) = $30/$50 = 0.6 kp = 0.6 × 0.2 + 0.4 × 0.1 = 0.16 • • •

True. The rate of return on a value-weighted portfolio is equal to the weighted average of the returns on the component assets where the weights are equal to the proportionate values of the assets.

True. Use values in the base period to calculate weights True. Any portfolio that has the same weights as a value portfolio will have the same return as the value weighted portfolio.

Stock Market Indices V2/V1 = 116/100 = 1.16 Index = 1.16 × 100 = 116 • • •

True.

True.

Dividends.

4. Systematic Risk • There is no diversifiable risk in the market portfolio.

• Market portfolio holders don’t care about diversifiable risk.

• Standard deviation measures total risk, which includes diversifiable risk, so it isn’t the best measure of risk for a market portfolio holder.

Marginal Risk 𝜕𝜎 = 𝐶𝑂𝑉(𝑘 , 𝑘 ) 𝜕𝑤 Systematic Risk Principle P0 = $1/(0.20–0.05) = 1/0.15 = $6.67 P0 = $1/(0.10–0.05) = 1/0.05 = $20 • • •

You won’t buy any shares. They are too expensive.

Your risk preferences won’t be reflected in the market price.

True.

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Intuition for Beta Relative amplitude of cyclicals = 2 Relative amplitude of defensivess = 0.5 Estimatin ng Beta

Slope = 2.67 2 •

The T slope is the t change in n the return on o the stockk when the m market returnn changes byy 1.

Beta = ∆k ki/∆kM, so ∆k ∆ i = B × ∆kM = 2 × 1% = 2%. The rreturn on thee stock shoulld be 3% + 22% = 5%.

•

The T R2 statisttic for the lin ne is 100% because b the ddata points liie on the linee.

Propertiees of Beta • •

The T beta of th he market po ortfolio is 1.

The T beta of th he risk free asset a is 0.

5. Portfo olios with th he Risk-Freee Asset E(kp) = 8.5% 8 βp = (1 – w) × βF + w × βMF = 0.5 5 × 0 + 0.5 × 1.25 = 0.6225

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• • • •

When W you bu uy a T-Bill, you y are long.

When W you bu uy a T-Bill, you y are lendiing money too the governnment.

When W the gov vernment sellls a T-bill, it i is borrowinng.

When W the gov vernment sellls a T-bill, it i is short.

P0 = FV/(1 + kF) = (1 + kF)/(1 + kF) = $1 A Portfollio with Borrrowing Equity = $1 wEC = $2 2/$1 = 2 wF = –$1 1/$1 = –1 E(kp) = wEC × 12% + wF × 5% = 2 × 12 – 1 × 5% = 19% % βp = wECC × 1.25 + wF × 0 = 2 × 1.25 1 = 2.5 Treynor Index I T = (E(kEC 0 = 0.07/1.25 = 0.056 or 5.66% E ) – kF)/BEC C = (0.12 – 0.05)/1.25 Slope = Rise/Run R = (0.12 ( – 0.05))/(1.25 – 0) = 0.056 •

True.

T The Treeynor index is equal to th he slope of tthe portfolioo possibility lline.

Performaance Evaluattion with thee Treynor Ind dex TA = (0.1 12 – 0.05)/1.25 = 0.07/1..25 = 0.056 TB = (0.1 15 – 0.05)/2.25 = 0.10/2..25 = 0.044 • •

Asset A A has more m excess return per unit u of system matic risk. (T That is what the Treynorr in ndex measurres.)

The T line for Asset A A is steeeper.

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6. Risk and Return in Equilibrium Trading due to Disequilibrium •

The price of Asset A will rise due to excess demand.

E(kA) = (10 – 8.99)/8.99 = 0.1123 TA = (0.1123 – 0.05)/1.25 = 0.05 •

The price of Asset B will fall due to excess supply.

E(kB) = (20 – 17.20)/17.20 = 0.1628 TB = (0.1628 – 0.05)/2.25 = 0.05 Capital Market Equilibrium • •

After trading, both assets will lie on the same portfolio possibility line.

The market’s Treynor index is: “All of the Above”

Market Risk Premium: E(km)–kf = 0.12 – 0.04 = 0.08 or 8% E(k) = kF + B × [E(km) – kf] = 0.04 + 1.5 × [0.12 – 0.04] = 0.16 • • • • • •

No. The CAPM calculates the expected rate of return, which is the long-run average.

Individual yearly returns will typically be different from the average.

The y-intercept is the risk free rate.

The slope of the SML is the market risk premium: E(km)–kf E(k) = kF + B × [E(km) – kf] = 0.04 + 0.8 × [0.11 – 0.04] = 0.096 Because the promised return, 9%, is less than the equilibrium return, you should not invest.

If B < 0, then E(k) < kF since E(k) = kF – B × [E(km) – kf] and kF > [kF – B × [E(km)– kf]].

Why? What makes a negative beta so attractive that it is rewarded with a return smaller than the risk free rate?

If B = 2, then E(k) = kF + 2 × [E(km) – kf] or E(k) = 2 × E(km) – kf

TA = (0.083 – 0.05)/0.47 = 0.07 TB = (0.125 – 0.05)/1.5 = 0.05 Bp = wBM + (1 – w)BF = 1.5. Solve for w. w = 1.5 because BM =1 and BF = 0. kp = wkM + (1 – w)kF = 1.5 × 0.12 – 0.5 × 0.05 = 0.155 kp – kZ = 0.155 – 0.125 = 0.03 or 3%

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Chapter 7 Interest Rates and Bonds 2. Zero Coupon Bond Features and Markets • • • • • • •

Maturity = July 1, 1866 Civil War The state of Arkansas was part of the Confederacy.

The Confederacy lost.

General Lee surrendered at Appomattox, Virginia, on April 9, 1865.

The state of Arkansas was unable to honour its promises after the surrender.

In other words, the state of Arkansas defaulted on its bond obligations.

3. Zero Coupon Bond Yields and Pricing k2 = [FV/Price]1/n – 1 = [1,100/960.78]1/2 – 1 = 0.07 

 $100 𝑘 =   − 1 = 0.01 𝑜𝑟 1% $99.009

4. Determinants of the Shape of the Yield Curve Inflation kn = (1.10)(1.05) – 1 = 1.155 – 1 = 0.155 kn = (1.10)(1.06) – 1 = 1.166 – 1 = 0.166 Expectations Theory k2 = [(1 + k1) × (1 + E(k1))]1/2 –1 = [1.06 × 1.08]1/2 –1 = 0.07 • •

If the yield on a one-year bond is 6% and the yield on a two-year bond is 7%, then the yield curve is upward sloping.

If the yield curve is upward sloping, the future rates are expected to be greater than current rates.

Maturity Preference k2 = [(1 + k1) × (1 + E(k1))]1/2 –1 = [1.06 × 1.06]1/2 –1 = 0.06 •

If the yield on a one-year bond is 6% and the yield on a two-year bond is 6%, then the yield curve is flat according to the expectations theory.

19

• •

If the yield on a one-year bond is 6% and the expected one-year yield (next year) is also 6%, then the two year yield will be greater than 6%, according to the maturity preference theory.

If the yield on a one-year bond is 6% and the expected one-year yield (next year) is also 6%, then the yield curve will be (slightly) upward sloping, according to the maturity preference theory.

Default Risk •

The default risk premium was greatest during the financial crises of 2008.

Summary • •

The best expression for the yield on a T-Bill is YTM = kr + INF since the MRP is zero, the LRP is zero and the DRP is zero.

Because government T-bills are short maturity, they have no maturity premium. They are actively traded on the money market and so have no liquidity premium. They are issued by the government and so have no default risk premium.

5. Coupon Bond Yields and Pricing The Relationship between Zeroes and Coupon Bonds $Price =

$FV $10 = = $9.901 1 (1 + k1 ) (1.01)1

$Price =

$FV $110 = = $105.729 2 (1 + k 2 ) (1.02) 2

•

Same. The cash flows from the two zeroes are identical to the cash flows from the twoyear coupon bond.

P1 + P2 = $9.901 + $105.729 = $115.63 Pbond = $100 × (1.06)–1 + $1,100 × (1.07)–2 = $1,055.12 Yield to Maturity ytm = 6.95% FV = $100 × (1.08) + $1,100 = $1,208 



𝐹𝑉  1,208  𝑘=  −1=  − 1 = 0.07 𝑃𝑟𝑖𝑐𝑒 1,055.12 FV = $100 × (1.0695) + $1,100 = $1,206.95

20





𝐹𝑉  1,206.95  𝑘=  −1=  − 1 = 0.0695 𝑃𝑟𝑖𝑐𝑒 1,055.12 •

True. If you can reinvest at the yield to maturity rate, then your overall return will equal the yield to maturity.

Coupon Bond Prices Pbond = $80 × PVIFA12%,15 + $1,000 × (1.12)–15 = $727.57 Pbond = $40 × PVIFA6%,30 + $1,000 × (1.06)–30 = $724.70 6. Coupon Bond Price Properties • • • •

The Ranger oil bond trades at a discount.

YTM > coupon rate.

Bonds trade at a discount when YTM > coupon rate.

Bonds trade at a premium when YTM < coupon rate.

Bond Price Changes over Time Pbond = $1,100 × (1.0695)–1 = $1,028.518 %∆P = ($1,028.518 – $1,055.12)/ $1,055.12 = –26.602/1,055.12 = –0.02521 Coupon Yield = $C/P0 = $100/$1,055.12 = 0.094776 Total Return = ($C + P1 – P0)/P0 = ($100 + $1,028.518 – $1,055.12)/$1,055.12 = 0.0695 Coupon Yield + %∆P = 0.094776 + (–0.02521) = 0.0695 • • •

True. The sum of the coupon yield and the capital gain yield is equal to the yield to maturity.

Premium bonds fall in price.

Discount bonds rise in price.

Bond Prices and Interest Rates Move Inversely P0 = $100 × (1.10)–10 = $38.55 P0 = $100 × (1.05)–10 = $61.39

21

Longer Maturity Bonds Have More Interest Rate Risk P0 = $100 × (1.10)–1 = $90.909 P0 = $100 × (1.05)–1 = $95.238 •

The line for the 10-year bond is steeper.

%∆P10 = (61.39/38.55) – 1 = 60% %∆P1 = (95.238/90.909) – 1 = 5% •

Buy long maturity bonds.

22

Chapter 8 Stock Valuation and Market Efficiency 2. Intrinsic and Market Value • •

If market value < intrinsic value, then buy.

If market value > intrinsic value, then sell.

3. Preferred Shares PPreferred = 1.50/0.125 = $12 k = D/P = (0.07 × $100)/41.67 = 0.168 4. Common Share Valuation with Dividend Discount Model Valuation with One-Year Holding Period P0 = (60.16)/1.12 = $53.71 •

True. Based on the one-year holding period model, this statement appears to be true.

Generalized Dividend Discount Model •

True. Now the intuition from the one-year holding period model is shown to be incorrect.

Constant Growth D2 = D0 × (1 + g)2 = $1 × (1.08)2 = $1.1664 • • •

One year until next dividend You do NOT receive D0.

The stock price is infinity if g > k.

P0 = $3/(0.15 – 0.08) = $42.86 Solve for Stockholders’ Required Return k = D1/P0 + g k = 2 × (1.10)/44 + 0.1 = 0.15 Price Changes Under Constant Growth P1 = D2/(k – g) [P1/P0] – 1 = g 23

Non-Constant Dividend Growth Model PV2 = D3/(k – g) = $30/(0.09 – 0.03) = $500 P0 = $500/(1.09)2 = $420.84 D3 = Po × (k – g) × (1 + k)2 = $37.069 Super-Normal Growth Model D1 = $2.24. D2 = $2.51. D3 = $2.81. D4 = $3.09.

PV3 = 3.09/(0.15 – 0.1) = 61.80 PV0 = PV3 × (1 + k)–3 = 61.80 × 0.6575 = 40.63 PV0 = 2.24/(1.15) + 2.51/(1.15)2 + 2.81/(1.15)3 = 5.60 P0 = 40.63 + 5.60 = 46.33 5. Stock Repurchases and the Total Payout Model • • •

Repurchases are a larger share of payouts in the United States.

Repurchases are a growing trend.

Recession, decrease, expansion, increase

Share Repurchase Mechanics PB = EB/100 = $100/100 = $1 NA = NB – NR = 100 – 10 = 90 Share = 9/90 = 0.1 or 10% PA = EA/90 = $90/90 = $1 ∆W = WA – WB = (1 × $1 + 9 × $1) – (10 × $1) = $0 •

True. When a company buys back shares at a price equal to fair value (PR = PB), then the price remains unchanged after the repurchase, and no wealth is transferred.

Constant Growth Total Payout Model E0 = (412.9 + 904.7) × (1.04)/(0.08 – 0.04) = 34,257.6 P0 = E0/N = 34,257.6/487 = $70.34

24

6. Relative Valuation Models P/E P0 = (P/E) × EPS = 18.8 × 3 = $56.40 •

Because Nike’s fair price (Intrinsic value) is less than its market value, you should expect the market price to fall and so you should short sell the stock.

P/EPS = 65/3 = 21.67 •

If the P/E ratio is larger than the constant, then the shares are overvalued, and you should sell.

25

Chapter 9 Capital Budgeting: Introduction and Techniques 1. Payback Period Fraction of Year = 0.67 Payback = 1.67 years Payback = 3.33 years 2. Net Present Value NPV = –1000 + 600/(1.1) + 600/(1.1)2 = $41.32 NPV = –1000 + 100/(1.1) + 200/(1.1)2 + 500/(1.1)3 + 600/(1.1)4 = $41.66 3. Profitability Index and Capital Rationing If NPV > 0, then PV(Cash Inflows) > PV(Cash Outflows), so PI > 1.

Project A B C • • •

Investment (Outflow) $9M $10M $10M

Profitability Index 1.194 1.2 1.18

NPV $1.75M $2M $1.8M

PI Rank 2 1 3

A + B are the two highest ranked by PI and the total investment is $19M, which is within the #20M budget.

B + C have the highest total NPV at $3.8 million.

When capital is rationed, select projects to maximize summed NPV.

4. Internal Rate of Return IRRL = 11.5% 0 = –100 + 110/(1 + k) k = IRR = 10% NPV = –100 + 110/(1.05) = $4.76

26

5. NPV Profiles Cost of Capital (k) 5% 6.72%

Model S $180 $143

Model L $202 $143

10%

$79

$42

NPV Profiles $500 $400 $300

Model S Model L

NPV ($)

$200 $100 $0 -$100 -$200 -$300 -$400

Interest Rate

• • • • • • •

The lines intersect.

The lines intersect at 6.72%.

Below 6.72%, the NPV of Model L is higher.

Above 6.72%, the NPV of Model S is higher.

Depends on the cost of capital. If k < 6.72%, then Model L is better; otherwise Model S is better.

The x-axis intercept is the interest rate that makes the NPV = 0 or, in other words, the IRR. PA + B are the two highest ranked by PI and the total investment is $19M, which is within the #20M budget.

27

• • • • •

B + C have the highest total NPV at $3.8 million.

When capital is rationed, select projects to maximize summed NPV. You would pick the project with the higher IRR = Model S. No. Different cash flow timing causes the IRR decision rule to mis-rank projects.

6. Mini-Case: The Lockheed L-1011 Tristar

Year 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977

• • • • •

t= 0 1 2 3 4 5 6 7 8 9 10

Q

35 35 35 35 35 35

PreCosts –$100 –200 –200 –200 –200

Costs

–490 –490 –490 –490 –490 –490

Revs

560 560 560 560 560 560

CF –100 –200 –200 –200 –690 70 70 70 70 70 560 –480

Cmltv –100 –300 –500 –700 –1390 –1320 –1250 –1180 –1110 –1040 –480

PVIF 1.0000 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855

PV –100 –182 –165 –150 –471 43 40 36 33 30 216 –672

The undiscounted sum of cash flows is –$480M, so the project does not payback.

The NPV of the project is –$672 million.

The undiscounted break-even is 450 aircraft (75 per year). At this level, profits from sales equal the pre-production costs.

The NPV payback is 2,467 aircraft (411 per year). This would have constituted more than 100% of the market for wide-bodied aircraft over this period.

The L-1011 project had no chance of breaking even at the forecasted production level of 200 aircraft. It does not appear that Daniel Haughton was honest with the Congressional Committee. The loss of shareholder value between January 1, 1967, and June 30, 1971, was –$627 million. This is almost exactly equal to the NPV of the project, which reinforces our intuition of NPV as equalling the change in shareholder value associated with the adoption of a project.

28

Chapter 10 Capital Budgeting: Estimating Cash Flows 2. Depreciation and Taxes Depreciation Tax Shield KOT Industries Income Statement Bolo

Bozo

Revenues COGS and SG&A Depreciation

$100 50 20

$100 50 n.a.

EBIT

30

50

Interest

0

0

Earnings Before Tax

30

50

Taxes (@40%)

12

20

Net Income

18

30

Difference in Taxes = $8 Depreciation Tax Shield = $20 × 0.4 = $8 Operating Cash Flows OCF = Sales – Costs – T × (Sales – Costs – Depr) OCF = (Sales – Costs – Depr.) × (1 – T) + Depr.

OCF = (Sales – Costs) × (1 – T) + Depr × T OCF = EBIT × (1 – T) + Depr.

OCF = NOPAT + Depr.

•

So B, C, & D are correct.

MACRS Depreciation Depr1 = $300,000 × 0.1429 = $42,870

29

Year 1 Original Cost

Year 2

Year 3

Year 4

300,000 300,000 300,000 300,000

MACRS Rate (7-year Property) 0.1429

0.2449

0.1749

0.1249

Depreciation Expense

42,870

73,470

52,470

37,470

Cumulative Depreciation

42,870

116,340 168,810 206,280

Book Value

257,130 183,660 131,190 93,720

Tax Impact of Salvage Tax on sale = 0.35 * ($40,000 – $50,000) = –$3,500 Tax on sale = 0.35 * ($60,000 – $50,000) = $3,500 3. Expansion Projects – – – =

Initial purchase price of new asset Installation/shipping cost of new asset Increase in net working capital Initial cash flow

–$300,000 $0 –$10,000 –$310,000

1

2

3

4

Revenues

400,000

400,000

400,000

400,000

Operating Costs

300,000

300,000

300,000

300,000

Depreciation

42,870

73,470

52,470

37,470

EBIT

57,130

26,530

47,530

62,530

Taxes

22,852

10,612

19,012

25,012

NOPAT

34,278

15,918

28,518

37,518

+ Depreciation

42,870

73,470

52,470

37,470

OCF

77,148

89,388

80,988

74,988

Net Salvage = $110,742 – [0.4 × ($110,742 – $93,720)] = $103,933 Terminal Cash Flows = $74,988 + $103,933 + $10,000 = $188,921

30

Year

Cash Flow Type

0 1 2 3 4

Initial Operating Operating Operating Terminal

$ Cash Flow –310,000 77,148 89,388 80,988 188,921

NPV = $23,892 4. Replacement Projects Replacement Project Initial Cash Flows Initial = –$12,000 + ($2,000 – 0.35 × ($2,000 – $1,000)) – $0 = –$10,350

Replacement Project Operating Cash Flows Year 1 Panel A: Old Machine Cost (Basis) dr Depr ADepr.

Book Panel B: New Machine Cost (Basis) dr Depr Adepr.

Book Δdepr.

$13,000 0.1429 1,858 1,858 11,142

Year 2

Year 3

Year 4

$13,000 0.1749 2,274 7,315 5,685

$13,000 0.1249 1,624 8,939 4,061

$12,000 0.1429 1,715 1,715 10,285 –559

$12,000 0.2449 2,939 4,654 7,346 1,315

$13,000 0.2449 3,184 5,041 7,959

Δdepr1 = –559 Δdepr2 = 1,315 Replacement Project Terminal Cash Flows Net SalvageNEW = $8,000 – [0.35 × ($8,000 – $7,346)] = $7,771.24 Net SalvageOLD = $2,000 – [0.35 × ($2,000 – $4,061)] = $2,721.42

31

Replacement Project Example –

Initial purchase price of new asset

–$12,000

+

Net salvage value of old asset

+$7,120

–

Increase in net working capital

–$1,000

=

Initial cash flow

–$5,880

Panel A: Old Machine Cost (Basis) dr Depr ADepr.

Book Panel B: New Machine Cost (Basis) dr Depr ADepr.

Book ΔDepr.

Year 1

Year 2

Year 3

$11,000 0.20 2,200 2,200 8,800

$11,000 0.32 3,520 5,720 5,280

$11,000 0.192 2,112 7,832 3,168

$12,000 0.20 2,400 2,400 9,600 –1,120

$12,000 0.32 3,840 6,240 5,760 1,728

32

Year 0

OPERATING CASH FLOWS

Revenues Costs EBITDA Depreciation EBIT Taxes NOPAT Depreciation OCF

Year 1

Year 2

2,000 –2,000 4,000 –1,120 5,120 2,048 3,072 –1,120 1,952

2,000 –2,000 4,000 1,728 2,272 909 1,363 1,728 3,091

Net salvagenew = $4,000 – [0.4 × ($4,000 – $5,760)] = $4,704 Net salvageold = $2,000 – [0.4 × ($2,000 – $3,168)]) = $2,467 Net salvageold 1 yr = $6,000 – [0.4 × ($6,000 – $8,800)] = $7,120

+ + – + =

OCF Net SalvageNEW Net SalvageOLD Decrease in net working capital Terminal year cash flow Year 0 1 2

Cash Flow Type Initial Operating Terminal

$3,091 $4,704 –$2,467 $1,000 $6,328

$ Cash Flow –5,880 1,952 6,328

PVIF 1.0000 0.9091 0.8264

NPVRUMPEL = $1,124.30 5. Capital Budgeting Refinements Bob is incorrect. $100,000 is a sunk cost. Ignore it. NPV = $23,892 Annual Operating Cash Flow due to Reduced Sales = –$6,000 PVLost Sales = –$6,000 × PVIFA10%,4 = –$19,019 NPV = $23,892 – $19,109 = $4,873

33

PV of Cash –5,880 1,775 5,230

Annual Operating Cash Flow due to Lease = $7,920; $1,100 × 12 × (1 – 0.4) PVOCF Due to Lease = –$7,920 × PVIFA10%,4 = $25,105 This is an opportunity cost, so subtract from initial NPV estimate: NPV = $23,892 – $25,105 = –$1,213. Don’t make Grapeful Soda; lease to Lesh.

6. Comparing Projects with Unequal Lives NPVS = –$40,000 + $18,000 × PVIFA9%,3 = $5,563.30 NPVL/5 = $6,344.77/5 = $1,269 NPVS/3 = $5,563.30/3 = $1,854 EAAL =$6,344.77/3.8897 = $1,631 EAAS = $5,563.30/2.5313 = $2,198 Which Light Bulb?

Annual $Cost (DuraMax) = kw per hour × #hours × $electricity price per kwh Annual $Cost (DuraMax) = 0.06 × 1,460 × 0.11 = $9.636 Annual $Cost for 1.7566 LEDs = 1.766× 1.28 = $2.2689 NPV = –Bulb Price – $annual cost × PVIFA5%,Bulb Life NPVDuraMax = –$1.62 – $9.636 × PVIFA5%,1 = –$10.79 NPVLED = –$31.787 – $2.2689 × PVIFA5%,17 = –$57.37 NPVDuraMax = –$10.79 NPVLED = –$57.37 EAADuraMax = NPV/PVIFA = –$10.79/0.9524 = –$11.33 EAALED = NPV/PVIFA = –$57.37/11.2741 = –$5.09 Replacement Chain NPVA = $13,397.31 NPVB = $11,472.58

34

Chapter 11 Cost of Capital 2. Cost of Capital kp = wDkD + wEkE = 0.25 × 0.08 + 0.75 × 0.25 = 0.2075 kWACC = wDkD(1 – T) + wEkE + wPkP = 0.114 3. Cost of Debt C/FV = yield = 6% (Because price = face value) kD = YTM = 7.69% (through trial and error) kD × (1–T) = 5% × (1–0.4) = 3% kD = $50/$1,000 = 5% KOT Industries Method #1 Operating Cash Flows EBIT

$217

– Interest

50

Earnings Before Tax

$167

– Taxes (@40%)

$69

Net Income

$100

OCF = Net Income + Interest

$150

WACC = 0.5 × 0.05 + 0.5 × 0.1 = 7.5% VKOT = $150/0.075 = $2,000

35

KOT Industries Method #2 Operating Cash Flows EBIT

$217

Interest

n.a.

Earnings Before Tax

$217

Taxes (@40%)

$87

Net Income

$130

OCF = Net Income

$130

WACC = 0.5 × 0.05 × (1–T) + 0.5 × 0.1 = 6.5% VKOT = $130/0.065 = $2,000 4. Cost of Equity E(k) = kF + βi × [E(kM) – kF] = 0.05 + 1.3 × [0.12 – 0.05] = 0.141 k =

D +g P

kE = ($1/$10) + 0.04 = 0.14 • •

Stockholders are residual claimants and so exposed to more risk.

Because their claim is more risky, stockholders should earn a higher return than bondholders on average.

5. Capital Structure Weights V = D + E = 80 + 120 = 200 wE = E/V = 120/200 = 0.6 wD = D/V = 80/200 = 0.4 E = $12 × 1 million = $12M D = $5 million × 0.985 = $4.925M V = E + D = 16.925 wE = E/V = 0.70901 wD = D/V = 0.29099

36

6. Comprehensive Exercise Debt Price = $4.925 = $0.5 × PVIFA10,k + $5 × PVIF10,k kD = 10.247% (by trial and error.) kD = 15.4% E(k) = kF + βi × [E(kM) – kF] = 0.07 + 1.2 × [0.14 – 0.07] = 0.154 kW = 0.29099 × 0.10247 × (1–0.4) + 0.70901 × 0.154 = 12.71% Wayne Enterprises kE = kF + βi × [E(kM) – kF] = 0.03 + 0.8 × [0.09 – 0.03] = 0.078 kD = 0.05 kP = 0.06 D = $0.35M × PVIFA10,5% + $10M × PVIF10,5% = $8.84 P = 1M × (0.08 × $5/0.06) = $6.67 E = 5M × $25 = $125M V = D + P + E = $140.51 wE = E/V = 0.8896 wD = D/V = 0.0629 wP = P/V = 0.0474 kWACC = wDkD(1–T) + wEkE + wPkP = 0.0743

37

Chapter 12 Capital Structure 2. Leverage • •

American Railcars has a higher ratio of PP&E-to-Total Assets than Microsoft.

American Railcars has a higher ratio of Debt-to-Equity than Microsoft.

American Railcar

Microsoft

37% 271% 1395%

6% 23% 28%

%Change in Sales %Change in EBIT %Change in EPS

DOL DFL DTL

American Railcar 7.3 5.1 38.0

Microsoft 4.1 1.2 5.0

3. The Effect of Financial Leverage on EPS

$EBIT $Interest Pre-Tax Income Taxes (@0%) Net Income #Shares Out EPS

Under All equity Plan BAD NORMAL $600,000 $1,200,000 $0 $0 $600,000 $1,200,000 $0 $0 $600,000 $1,200,000 400,000 400,000 $1.50 $3.00

GOOD $1,800,000 $0 $1,800,000 $0 $1,800,000 400,000 $4.50

$EBIT Less: $Interest Pre-Tax Income Less: Taxes Net Income #Shares Out EPS

Under 50% Debt/50% Equity Plan BAD NORMAL $600,000 $1,200,000 400,000 400,000 200,000 800,000 $0 $0 200,000 800,000 200,000 200,000 $1 $4

GOOD $1,800,000 400,000 1,400,000 $0 1,400,000 200,000 $7

38

• • • •

In n a normal economy, thee 50/50 plan generates a higher EPS..

In n a bad econ nomy, the alll equity plan produces a larger EPS. In n a good eco onomy, the 50/50 5 generaates a higher EPS. The T 50/50 plaan has a morre volatile EP PS across staates of naturre. The rangee is $6 underr the 50/50 plan bu ut only $3 un nder the all equity e plan.

EBIT $600,000 0 $1,200,000 $1,800,000

• • • •

EBIT v EPS 100% Equity $1.50 $3 $4.5

50%- 50% $1 $4 $7

The T line for th he 50/50 plaan is steeper..

EBIT-EPS E indifference point is at EB BIT = $800,0000.

Iff EBIT is abo ove $800,00 00, then shareholders preefer the 50/50 plan.

Iff EBIT is bellow $800,00 00, then sharreholders preefer the all equity plan.

4. M&M M Mechanicss FCF = EB BIT Huck Glo ove DCF Vaalue V0 = $10 0M/0.08 = $1 125M

39

Rumpel Felt Unlevered Value VU = $10/0.11 = $90.91 EU = VU = $90.91 •

True. Since the yield equals the coupon rate, the market value of the bonds equals the face value. So, market value is also D.

Fritz Electric: • •

$coupons = $1,000 × 0.05 = $50 True. Net Income = $EBIT – D * kD

Dividends = Net Income = $500 – $50 = $450 EL = $450/0.10 = $4,500 V = D + EL = $1,000 + $4,500 = $5,500 wE = E/V = $4,500/$5,500 = 0.8182 wD = D/V = $1,000/$5,500 = 0.182 kW = 0.182 × 0.05 + 0.8182 × 0.1 = 0.0909 or 9.09% V = EBIT/kW = 500/0.0909 = $5,500 5. M&M Prop I VU = EU = $100 VL = EL + D = $40 + $50 = $90 Cash flow to buy 10% of EL = –0.1 × EL = –$4 Cash flow to buy 10% of D = –0.1 × D = –$5 Cash flow from short selling 10% of EU (VU) = 0.1 × VU = $10 Net Cash Flow = –$4 – $5 + $10 = $1

Position Long EL Long D Short EU NET • •

Cash Flows to Investor at End of Year Weak Economy 0.1 × [EBIT – D × (1 + kD)] 2.5 0.1 × D × (1 + kD) 5.5 –0.1 × EBIT –8 0

Strong Economy 14.5 5.5 –20 0

In both states of nature, the investments generate no income or liability.

These trades, if executed simultaneously, would involve no risk and no investment and so would constitute arbitrage.

40

Broken Glass Toy Co. VU = $150/0.05 = $3,000 VL = VU = $3,000 EL = VL – D = $3,000 – $200 = $2,800 •

According to M&M Proposition I (no taxes) a company cannot change its value by changing its capital structure.

6. M&M Prop II 𝑘 = 𝑘 + [𝑘 − 𝑘 ] • •

𝐷 𝐸

kE increases when D/E increases. kW is constant as D/E changes. Because value doesn’t change with leverage, WACC does not either.

Broken Glass Toy Co. VL = D + EL = $200 + ($2 × 400) = $1,000 kU = kW = EBIT/V = $150/$1,000 = 0.15 kE = 0.15 + [0.15 – 0.10] × (200/800) = 0.1625 kW = kU = 0.15 by Prop II After Recap, V = $1,000 by M&M Proposition I. D = $200 + $100, so EL = 700 kE = 0.15 + [0.15 – 0.10] × (300/700) = 0.1714 (by Proposition II) kW = 15% by Proposition I (and II) Number shares = 400 – 50 = 350 Price = EL/350 = 700/350 = $2 7. M&M Prop I (with Tax) Reefer Trucking VU = EBIT × (1 – T)/kU = 3 × (1 – 0.35)/0.16 = 12.1875M VL = VU + TD = 12.1875M + 0.35 × 4 = 13.5875M EL = VL – D = 13.5875M – 4 = 9.5875 PB =VU/NB = 12.1875/1 = $12.19 Shares Purchased = NR = $4M/$12.1875 = 328,205 SharesAFTER = NA = NB – NR = 1,000,000 – 328,205 = 671,795 PriceAFT = EL/NA = 9.5875/0.328205 = $14.27 •

The price after the repurchase is higher than the price offered for repurchased shares, so rational shareholders would not have tendered shares to the company.

41

BONUS PA = (VL – D)/(NB – NR) Sub in Prop I PA = (VU + TD – D)/(NB – NR) Sub in fact that NR = D/PR PA = (VU + TD – D)/(NB – D/PR) Let PR = PA and solve for PA PA = (VU + TD – D)/(NB – D/PA) PA = VL/NB = $13.5875/1 = PREPO = $13.5875 8. M&M Prop II (with Tax) kU = kW = 15% (Unlevered firm.)

D/E = D/V / (1 – D/V) = 0.15/(1 – 0.25) = 0.3333 kE = 0.15 + [0.15 – 0.08] × (1 – 0.35) × 0.3333 = 0.1652 kE = 0.15 + [0.15 – 0.08] × (1 – 0.35) × 1 = 0.1955 • • •

The market value of the firm increases with leverage.

Because market value increases with leverage, kW (WACC) decreases with leverage.

To maximize firm value, choose the highest leverage possible: D/V = 1.

42

Chapter 13 Dividends, Repurchases, and Splits 2. Distributions • • • • •

There is an increasing trend toward repurchasing.

Dividends steadily increase. Repurchases vary with the business cycle (i.e., the decline in recessions).

False. About 65% of companies paid no dividends in 2011.

True. Between 1985 and 2010, the proportion of nonpayers has increased.

Dividends are quite concentrated with the top 10% of firms accounting for one third of all dividends.

3. Dividends Dividend Timing • • • •

The settlement delay is three days.

True.

Ex day = May 13 Cum day = December 22

The Impact of Dividends on the Share Price • •

True.

True.

Karkas Cold Cuts Pre-dividend value: V = E = $60 Pre-dividend stock price: PB = E/N = $60/100 = $0.6 VA = VB – ($0.1 × 100) = $50 PA = VA/N = $50/100 = $0.5 • •

True.

True.

Wealth Before = 10 × PB = $6 Wealth After = 10 × PA + 10 × $0.10 = $6 • • • • •

On first glance, yes it does look like a short strategy could be profitable.

True.

The person who took the long-side of the trade when you shorted Yes. In their mind, they still own the stock.

You (the short-seller) will have to pay.

43

•

$0

Pan-Am Pre-dividend value: VB = $4 + $10/0.2 = $54 Cost of dividend: 0.6M × 6.67 = $4M Value of firm after dividend: VA = VB – $4M = $50M Price after dividend: PA = VA/N = $50/0.6 = $83.3 Taxes and Clienteles • • •

Investors with income in groups A & B have a lower marginal tax rate on dividends and so would prefer dividends.

Investors with income in groups E & F have a lower marginal tax rate on capital gains and so would prefer capital gains.

Investors with income in groups C & D have the same tax rate on dividends as on capital gains and so are indifferent.

If TD = 0.15 and TG = 0.25 After-tax wealth after dividend: WA = 100 × PA + 100 × $2 – (100 × $2 × TD + 100 × [PA – PB] × TG) WA = $1,000 + $200 – ($30 + 0) = $1,170 After-tax wealth from no dividend: WA = 100 × PA – (100 × (PA – PB) × TG) WA = $1,200 – ($50) = $1,150 •

Want to receive dividend.

If TD = 0.25 and TG = 0.15 After-tax wealth after dividend: WA = 100 × PA + 100 × $2 – (100 × $2 × TD + 100 × [PA – PB] × TG) WA = $1,000 + $200 – ($50 + 0) = $1,150 After-tax wealth from no dividend: WA = 100 × PA – (100 × [PA – PB] × TG) WA = $1,200 – ($30) = $1,170 •

Want no dividend.

44

Dividend Policy Pitney Bowes: Dt+1 = Dt + ΔEPS × Target Payout × λ Dt+1 = 0.365 + 0.05 × 0.6 × 0.005 = 0.36515 Crumple Auto Body: ωE × $Investmentst = 0.6 × $800,000 = $480,000 Dt = ($600,000 – $480,000)/600,000 = $0.20 4. Stock Repurchases Premium Repurchase Pre-repurchase value: VB = $4 + $10/0.2 = $54 Cost of repurchase: PR × NR = $100 × 40,000 = $4M Value of firm after repurchase: VB = VB – $4M = $50 Shares outstanding after: NA = NB – NR = 600,000 – 40,000 = 560,000 f = 40,000/600,000 = 6.67% Price after repurchase: PA = $90 × (1/(1 – 0.06667)) – $100 × (0.06667/(1 – 0.06667)) = $89.29 Shareholder sells 6.67% of holdings: WB = $9,000 WA = $9,000 ∆W = $0 Shareholder keeps shares (does not participate in repurchase): WB = $9,000 WA = $8,929 ∆W = –$71 Fair Price Repurchase: Cost of repurchase: PR × NR = $90 × 44,444 = $4M Value of firm after repurchase: VA = VB – $4M = $50 f = NR/NB = 7.41% Price after repurchase: PA = $90 × (1/(1–0.0741)) – $90 × (0.0741/(1–0.0741)) = $90 Shareholder sells 7.4% of holdings: WB = $9,000 WA = $9,000 ∆W = $0 45

Shareholder keeps shares (does not participate in repurchase): WB = $9,000 WA = $9,000 ∆W = $0 Discount Repurchase: Cost of repurchase: PR × NR =$80 × 50,000 = $4M Value of firm after repurchase: VA = $50 f = 50,000/600,000 = 8.33% Price after repurchase: PA = $90 × (1/(1–0.0833)) – $80 × (0.0833/(1–0.0833)) = $90.91 Shareholder sells 8.3% of holdings: WB = $9,000 WA = $9,000 ∆W = $0 Shareholder keeps shares (does not participate in repurchase): WB = $9,000 WA = $9,091 ∆W = +$91 • • • •

True.

True.

True.

True.

5. Information Signaling and Agency • • •

Dividend increases are more common.

Price falls after dividend cuts.

Price rises after dividend increases.

V = E = $4B + $1B/0.1 = $14B; P = E/N = $14B/1B = $14 per share V = E = $4B + $0.75B/0.1 = $11.5B; P = $11.5 per share Vex = Eex = $2B + $1B/0.1 = $12B; Pex = $12 per share Kirk Kirkorian’s Wealth: Cost of buying 100M @ $11.5 = $1.15B Receives dividend of $2 × 100M = $200M Shares after dividend worth 100M × $12 = $1.2B Total wealth after dividend = $1.4B Change in wealth = 1.4 – 1.15 = 0.25B or 21.74% 46

6. Stock Splits and Stock Dividends SPLITS S = 200/100 = 2 Shares OutAfter = 600. A 3-for-1 split.

Shares OutAfter = 3/2 × 300 = 450 S = 450/300 = 1.5 Shares OutAfter = 1/5 × 1,000 = 200 S = 200/1000 = 0.2 PA = PB/S = $90/2 = $45

47

Chapter 14 Financial Planning and Forecasting 2. Sales Forecasting Village Farms Sales Revenuest+1 = Qt+1 × Pt+1 Sales Revenuest+1 = Qt × (Pt × 1.32) Sales Revenuest+1 = (220 acres × 522,700lbs/acre) × ($1.1647 × 1.32) Sales Revenuest+1 = 115,000,000 × 1.5374 = $176,801,460 Sales Revenuest+1 = Qt+1 × (Pt × 1.32) Sales Revenuest+1 = (220 acres × 880,000lbs/acre) × ($1.1647 × 1.32) Sales Revenuest+1 = 193,600,000 × 1.5374 = $297,641,414 Samsung Salest+1 = $250 × 0.32 × (850M × 1.05) = $71.4 billion Lululemon Existing stores: Salest+1 = 211 × 2,834 × ($1,823 × 1.05) = $1,144.612 New Stores Salest+1 = 30 × 2,834 × ($1,823 × 1.05)/2 = $81.371 Salest+1 = 1,144.612 + 81.371 = $1,225.982 3. Cash Budget Cash Inflows March Collections from Sales Last Month = 0.5 × SalesF = 0.5 × $15,800 = 7,900 March Total Collections = $7,900 April Collections from Last Month = 0.5 × SalesM = 0.5 × $15,800 = 7,900 April Collections from Two Months Ago = 0.5 × SalesF = 0.5 × $15,800 = 7,900 April Total Collections = $15,800

48

Sales Revenues Collections from Sales Last Month Collections from Sales 2 Months Ago Total Collections •

January $0 $0 $0 $0

February $15,800 $0 $0 $0

March $15,800 $7,900 $0 $7,900

April $15,800 $7,900 $7,900 $15,800

Accounts Receivable at end of April = $23,700. $7,900 of March sales are uncollected and all of April sales.

Outflows January $0 $10,000 $0

Sales Revenues Purchases Payments • •

February $15,800 $10,000 $10,000

March $15,800 $10,000 $10,000

April $15,800 $10,000 $10,000

During April, the company buys the raw materials for production in May, so there is a full month of purchases in inventory at the end of April.

Because the company pays suppliers one month after purchases, at the end of April payables are equal to purchases during April.

Budget Total Collections OUTFLOWS: Payments SG&A Expenses Interest Expense Net Cash Flow Starting Cash Ending Cash

January $0

February $0

March $7,900

April $15,800

$0 $3,750 $0 –3,750

$10,000 3,750 0 –13,750

$10,000 $3,750 75 –5,925

$10,000 $3,750 134 1,916

$10,000 $6,250

$6,250 –$7,500

–7,500 –13,425

–13,425 –11,509

49

February Net Cash Flows = $0 – $10,000 – $3,750 = –$13,750 February Ending Cash Balance = Starting Cash Balance + Net Cash Flow February Ending Cash Balance = 6,250 + (–13,750) = –7,500 March Interest Expense = (i/m) × Ending CashMARCH = 0.01 × 7,500 = $75 Worst Cash Balance = –$13,425 (in March) Cash Budget for Boston Whaler March

May 10

June 20

July 10

August 10

Sept

0.9

1.8 1.8

3 3.6 0.3 6.9

6 6 0.6 12.6

3 12 1 16

3 6 2 11

1.5 6 1 8.5

3

5 3 1.2 2 0

10 5 2.4 2 0 9.4 –2.5

5 10 1.2 2 5 18.2 –5.6

5 5 1.2 2 0 8.2 7.8

2.5 5 0.6 2 0

10 7.5

7.5 1.9

1.9 9.7

3

Sales Collections Same Month Last Month Two Months Ago Total Collections Purchases Payments Wages Expenses, Rent & Other Refurb Total Outlays Net Cash

April 6

0.72 2 0

Start Cash End Cash

Cash balance at end of July = 9.7

50

5

2.5 2 0

4. Financial Statements Forecasting Percent-of-Sales Ratios Ratio

Year 1 0.47 0.21 0.33 0.80

*Costs/Sales Tax Rate (Tax/EBT) Dividend Payout Rate (Divs/Net Income) Current Assets/Sales *Costs = cost of goods sold + SG&A Interest $Interest = PV × i = $900 × 0.05 = $45 Interest Rate = (PV × i)/PV = $40/$800 = 0.05 or 5% $Interest1 = $40 Interest Rate = (PV × i)/PV = $40/$374.88 = 0.1067 or 10.67% Amount Owing1 = Long-term Debt = $450 $Interest2 = 0.1067 × $450 = $48 Depreciation and Capital Asset Identity Depr1 = 0.25 × $11,000 = $2,750

Book Valuet–1 Depr Rate (dr) Depr Book Valuet

Depreciation Schedule Year 1 $11,000 0.25 2,750 8,250

Year 2 8,250 0.25 2,062.5 6,187.5

Net1 = $11,000 – $2,750 = $8,250

Net (Graaff)t–1 Net (Wimshurst)t–1 Depr Rate (dr) Depr Net (All)t

Depreciation Schedule Year 1 $11,000 n.a.

0.25 2,750 8,250

Net2 = $9,937.50

51

Year 2 $8,250 $5,000 0.25 3,312.50 9,937.50

Solve for the Depreciation Rate: Nett = Nett–1 + CAPEXt – Deprt Deprt = dr × (Nett–1 + CAPEXt) Nett = Nett–1 + CAPEXt – dr × (Nett–1 + CAPEXt) Nett = Nett + Deprt – dr × (Nett + Deprt) dr = Deprt/(Nett + Deprt) Forecast Depreciation and Net Fixed for St. Dilbert dr = $50/($600 + $50) = 0.076923 Depr2 = 0.076923 × ($600 + $300) = $69 Net2 = $600 + $300 – $69 = $831

Revenue COGS & SGA Depreciation EBIT Interest Pre-Tax Earnings Taxes Net Income Dividends Current Assets Fixed Assets (Net) Total Assets

Financial Statements for St. Dilbert Year 1 Ratios 500 0.2 235 0.47 50 0.076923077 215 40 0.106700811 175 36 0.21 139 46 0.330935252 Year 1 400 0.8 600 300 1,000

Current Liabilities Long-term debt Common Shares Retained Earnings Owner’s equity Liabilities and Owners’ Equity

0 450 50 500 550 1,000

52

0

Year 2 600.0 282.0 69.2 248.8 48.0 200.8 41.3 159.5 52.8 Year 2 480.0 830.8 1,310.8 0.0 654.1 50.0 606.7 656.7 1,310.8

Financial Statements for Loblaws Revenue Cost of Goods Sold SG&A Depreciation Expense EBIT Interest Expense Earnings before Taxes Income Taxes Net Earnings ASSETS Current Assets Cash Accounts Receivable Inventories Total Current Assets Net Fixed Assets Goodwill Total Assets

Year 5 $27,801

Year 5 $ 920 656 2,125 3,701 9,372 688 $ 13,761

LIABILITIES AND OWNERS’ EQUITY Current Liabilities Short Term Debt $ 627 Accounts payable 2,535 Total Current Liabilities 3,162 Long Term Debt 4,194 Other Liabilities 519 Total Liabilities $ 7,875 Common Stock 1,192 Retained Earnings 4,694 Total Owners’ Equity 5,886 Liabilities & Owners’ Equity $ 13,761

53

Year 6 $ 29,210 22,152 5,245 621 1,192 277 915 288 $ 627 Year 6 $ 1,467 649 2,269 4,385 9,637 678 $ 14,700

$

$

$

715 2,936 3,651 4,208 560 8,419 1,192 5,089 6,281 14,700

5% 0.75837 0.17956

0.31475

0.15012

Year 7 $30,817 28,904 640 29,544 1,272 283 989 311 678 Year 7 1,548 685 2,394 4,626 9,940 678 15,244

0.1005

715 3,097 3,812 3,912 560 8,285 1,192 5,767 6,959 15,244

Chapter 15 The Management of Working Capital 2. Evaluating Working Capital Management Hershey Case Balance Sheet Assets

Liabilities & Owner’s Equity

Current Assets

Current Liabilities

Fixed Assets

Long-term Liabilities

NWC99 = 567,151 NWC/TC = 0.215 or 21.5% Average Inventory Period = 93.3 Gerald Fresh Produce Case

Selected Financial Information Gerald’s Fresh Produce Year 1 60.83 Average Collection Period

Year 2 0

Selected Financial Information Gerald’s Fresh Produce Year 1 0 Average Payable Period

Year 2 30.42

Operating and Cash Cycle Cash Conversion Cycle1 = 60.83 Cash Conversion Cycle2 = –30.42

54

Owner’s Equity

Chapter 16 International Finance 2. Exchange rate basics First question: P$ = (1/S0) × PFC P$ = 1.08US$/€ × €200 = US$216 1. P$ = (1/S0) × PFC. P$ = 0.011765US$/¥ × ¥850,000 = US$10,000 2.

3.

4.

5.

PFC = S0 × P$. PFC = 0.806452 £/$ × US$160,000 = £129,032 Indirect rate Cross rate We want an exchange rate with euros per British pound: €/£.

The product of the two rates given is: 0.92£/$ × 1.24$/€ =1.1408£/€ But this is British pounds per Euro, which is the inverse of the exchange rate that is desired.

So, the solution is 1/1.1408 = 0.87658€/£

6. Appreciated 3. Exchange rate determination First question: A currency is said to appreciate if its indirect exchange rate rises (its direct exchange rate falls). The Cuban indirect exchange rate (relative to the US dollar) is US$/CUC. The increase in demand for peso by Americans causes US$/CUC to rise, and so the Cuban peso will appreciate in value relative to the dollar.

Second question: If gold is priced at $1,231 an ounce in the U.S. and 113,252 yen in Japan the exchange rate should adjust until S0 = 92¥/1US$. To compute this answer you solve for S0 in the equation: PFC = S0 × P$ 113,252¥ = S0 × $1,231 S0 = 113,252¥/$1,231= 92¥/1$

55

which is the indirect rate. To compute the direct rate you can use; 1/(92¥/$) = 0.01087$/¥.

Purchasing power parity maintains that the exchange rate would adjust to this level if not already there in order to make the price of gold equivalent to all buyers.

• • • •

• •

False; many goods that are perishable cannot be arbitraged successfully so PPP does not always mean the prices of all goods will always be the same price.

Arbitrage, or the simultaneous buying in one market and selling in another Yes Jumanji can buy gold in New York for $1,365 an ounce. If Jumanji sells in London and converts the proceeds to U.S. dollars, then they receive $1,388 = (1/S0) × PFC = 1.24$/£ × £1,120.

Profit = $1,388 – $1,365 = $23 per ounce Arbitragers will 1. buy gold in New York with dollars 2. sell gold in London and receive pounds 3. sell the pounds and receive dollars to repeat the transaction 4. increase in supply of pounds will push the dollar price of pounds lower until the price of gold is equivalent in both countries.

3. Exchange Rates and Inflation 1. A. Depreciate. According to the relative purchasing power equality, if [Inff – InfUS] > 0, then [E[St] – S0] > 0. That is, the U.S. indirect exchange rate (S0 = INR/US$) will rise. A currency is said to depreciate if its indirect exchange rate falls (its direct exchange rate rises). The Indian indirect exchange rate (relative to the U.S. dollar) is US$/INR. In this example, INR/US$ rises, so US$/INR falls. Intuitively, a currency depreciates (weakens) when it costs more to buy one unit of a foreign currency.

2. A. The U.S. indirect rate should rise by the difference in inflation rates, which is 5%.

Because the British inflation rate is higher the British pound will rise relative to the U.S. dollar. That is, S0 = £/US$ will rise. From the perspective of the Britain as the home country, its indirect exchange rate (US$/£) will fall—thus a depreciation.

4. Interest Rate Parity First question: According to the interest rate parity condition, if kfor > kUS, then F1/S0 > 1 or F1 > S0. This means that the forward (indirect) exchange rate must be larger than the spot indirect rate. Specifically, the cost (in pesos) of buying one U.S. dollar in the forward market will be larger than in the spot market. If the U.S. indirect exchange rate with the peso is 20MXN/US$, then the interest rate parity condition suggests that the forward rate will be 20.571MXN/US$. By IRP, F1 = S0 × (1 + Kfor)/(1 + K$) = 20 MXN/US$, × 1.08/1.05 = 20.571 MXN/US$.

1. A. Different risk investments can offer different returns to compensate for risk differentials.

56

2. B. Depreciate. If we think of the forward rate as the expected future spot rate, then kfor > kUS implies F1 > S0. In other words the United State’s indirect exchange rate (FC/$US) will rise over time. From the foreign country’s perspective, FC/$US is its direct exchange rate. An increase in the direct exchange rate is a depreciation of the foreign currency.

3. B. Depreciate. If the U.S. indirect exchange rate with the euro is 0.93€/US$, then the interest rate parity condition suggests that the forward rate will be 0.948€/US$. By IRP, F1 = S0 × (1 + Kfor)/(1 + K$) = 0.93 × 1.04/1.02 = 0.948€/US$. This means that the U.S. indirect rate rises, and the euro’s direct rate rises. An increase the euro’s direct rate represents a depreciation of the euro.

4. A. Interest rate arbitrage would be possible.

5. A. Fall by 2% to equate returns in both countries. If euro’s direct rate rises, then its indirect rate, US$/€, will fall. It will cost less for Americans to buy euros.

6. A. You compute the rate with the following formula; F1/S0 = (1 + Kfor)/(1 + K$) Therefore, F1/S0 = (1 + 0.04)/(1 + 0.02) F1 = 1.0196 × S0 F1 = 1.0196 × .93 = 0.9482 Note that you will earn a higher return in euros, but it will take more euros to buy a dollar after the year has passed. This change in exchange rates will equate the two returns.

5. International Finance Risk 1. A. Selling yen forward locks in the exchange rate today, and the currency will be delivered at a future date.

2. A. If all transactions occur in the domestic currency, it shifts foreign exchange risk to the other party.

3. B. Nationalization.

4. D. All of these are political risks.

5. A. Diversification benefits are higher when the economies are less correlated.

6. C. Negative correlations provide the most benefit since the economies are moving in opposite directions. Correlation coefficients range from –1.0 to +1.0.

6. Foreign Investments 1. C. Financial managers should always attempt to maximize firm value (i.e. stock price).

2. A. Factors, such as FX fluctuations, make forecasting cash flows for foreign projects even more risky than forecasting cash flows for domestic projects.

3. A. These funds are not subject to U.S. regulations even though denominated in dollars.

4. C. LIBOR or the London Interbank Offer Rate.

57

Chapter 17 Corporate Valuation 2. Advanced Financial Statements Forecasting Nett = Nett–1 + CAPEXt – Deprt Deprt = dr × (Nett–1 + CAPEXt) Nett = Nett–1 + CAPEXt – dr × (Nett–1 + CAPEXt) Nett = Nett + Deprt – dr × (Nett + Deprt) dr = Deprt/(Nett + Deprt) Simple Forecast

Revenue COGS & SGA Depreciation EBIT Interest Pre-Tax Earnings Taxes Net Income Dividends Current Assets Fixed Assets (Net) Total Assets

Financial Statements for St. Dilbert Year 1 Ratios 500 0.2 235 0.47 50 0.076923077 215 40 0.106700811 175 36 0.21 139 46 0.330935252 Year 1 400 0.8 600 300 1,000

Current Liabilities Long-term debt Common Shares Retained Earnings Owner’s equity Liabilities and Owners’ Equity

0 450 50 500 550 1,000

Historic Maintenance CAPEX mCAPEXt = Nett–1 × dr/(1 – dr)

58

0

Year 2 600.0 282.0 69.2 248.8 48.0 200.8 41.3 159.5 52.8 Year 2 480.0 830.8 1,310.8 0.0 654.1 50.0 606.7 656.7 1,310.8

dr = 621/(621 + 9,637) = 0.0605 mCAPEX6 = 9,372 × 0.0605/(1–0.0605) = 604 CAPEX6 = Nett – Nett–1 + Deprt = 9,637 – 9,372 + 621 = 886 Historic Growth CAPEX gCAPEX6 = 886 – 604 = 282 gx = 282/(29,210 – 27,801) = 0.20014 CAPEX, Net and Depreciation for Le Chateau

Total Capex2 Depr Rate, dr Maintenance Capex, mCAPEX Growth CAPEX, gCAPEX gCAPEX/∆Sales, gx

Calculation

Year 2 Value

38,202 – 34,510 + 6,687 6,687/(6,687 + 38,202) 34,510 × 0.14897/(1–0.14897)

=10,379 =0.14897 =6,041

10,379 – 6,041 4,338/(161,120 – 155,000)

F/S Forecast for Loblaw Amount Owing5 = $627 + $4,194 Interest6 = $277 Interest Rate = $277/($627 + $4,194) = 0.0575 Interest7 = 0.0575 × (715 + 4,208) = $283 mCAPEX7 = 9,637 × 0.0605/(1–0.0605) = $621 gCAPEX = 0.20014 × (30,817 – 29,210)= $322 CAPEX = $621 + 322 = $943 Depr7 = 0.0605 × (9,637 + 943) = $640 Net7 = $9,637 + $943 – $640 = $9,940 Long-term Debt7 = $3,912

59

=4,338 = 0.709

Financial Statements for Loblaws Revenue Cost of Goods Sold SG&A Depreciation Expense EBIT Interest Expense Earnings before Taxes Income Taxes Net Earnings ASSETS Current Assets Cash Accounts Receivable Inventories Total Current Assets Net Fixed Assets Goodwill Total Assets

Year 5 $27,801

Year 5 $ 920 656 2,125 3,701 9,372 688 $ 13,761

LIABILITIES AND OWNERS’ EQUITY Current Liabilities Short Term Debt $ 627 Accounts payable 2,535 Total Current Liabilities 3,162 Long Term Debt 4,194 Other Liabilities 519 Total Liabilities $ 7,875 Common Stock 1,192 Retained Earnings 4,694 Total Owners’ Equity 5,886 Liabilities & Owners’ Equity $ 13,761

60

Year 6 $ 29,210 22,152 5,245 621 1,192 277 915 288 $ 627 Year 6 $ 1,467 649 2,269 4,385 9,637 678 $ 14,700

$

$

$

715 2,936 3,651 4,208 560 8,419 1,192 5,089 6,281 14,700

5% 0.75837 0.17956

0.31475

0.15012

Year 7 $30,817 28,904 640 29,544 1,272 283 989 311 678 Year 7 1,548 685 2,394 4,626 9,940 678 15,244

0.1005

715 3,097 3,812 3,912 560 8,285 1,192 5,767 6,959 15,244

3. Free Cash Flow Operating Cash Flow OCF = Sales – Costs – T × (Sales – Costs – Depr) OCF = (Sales – Costs – Depr.) × (1 – T) + Depr.

OCF = (Sales – Costs) × (1 – T) + Depr × T OCF = EBIT × (1 – T) + Depr.

OCF = NOPAT + Depr.

• •

So, B, C & D are correct.

For income taxes, interest is deducted, so income taxes are lower by an amount equal to T × $Interest Expense.

TLOBLAW = 311/989 = 0.314754 OCFLOBLAW = $1,272 × (1 – 0.314754) + $640 = $1,318.45 Interest Tax Shield, OCF and DCF Valuation kD = 5%

EBIT Int. Expense EBT Tax @40% Net Income OCF WACC V

Method #1

Method #2

$217

$217

$50 $167 $67 $100 $150 0.5 * 5% + 0.5 * 10% = 7.5%

$0 $217 $87 $130 $130 0.5 * (1 – T) * 5% + 0.5 *10% = 6.5% $130/0.065 = $2,000

$150/0.075 = $2,000

CAPEX Loblaw: CAPEX7 = Nett – Nett–1 + Deprt = 9,939 – 9,637 + 640 = $942

61

Net Working Capital Fritz: • • • •

No Change Increased No Change Increased

Loblaw: Forecast Year 7

Year 6

Cash Accounts Receivable Inventories Total Current Assets

$

1,467 649 2,269 4,385

$

1,548 685 2,394 4,626

Short Term Debt Accounts payable Total Current Liabilities NWC

$

715 2,936 3,651 –$18

$

715 3,097 3,812 –$19

∆NWC7 = –$19 – (–$18) = –$1 Free Cash Flow for Loblaw + – – =

Operating Cash Flow CAPEX Increase in NWC Free Cash Flow

1,512 –942.63 –(–1) 570.64

Free Cash Flow for Le Chateau T = 2,262/5,654 = 0.400071 OCFLe Chateau = 6,441 × (1 – 0.40071) + 6,687 = $10,551.14 CAPEX2 = 38,202 – 34,510 + 6,687 = $10,379

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Le Chateau Inc ($000s) Cash Accounts Receivables Inventory Total Current Assets LIABILITIES AND SHAREHOLDERS’ EQUITY Accounts Payable Accruals Total Current Liabilities NWC

∆NWC2 = $13,709 – $12,125 = $1,583 FCF = 10,551.14 – 10,379 – 1,583 = –$1,411 Free Cash Flow Identity Loblaw: ∆Cash = $81 $Interest = $283 Repay (borrow) = $296 Dividends = $0 Repurchase (new issue) = $0 Tax Shield = $89 FCF = $571 Cadbury T = 103/371 = 0.27763 OCF = 543 × (1–0.27763) + 192 = $584.248 CAPEX2 = 1,869 – 1,761 + 192 = $300 ∆NWC2 = –308 – (–62) = –$246 FCF = $530

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Year 1 10,090 2,976 20,362 33,428

Year 2 9,071 4,106 22,123 35,300

10,719 494 11,213 12,125

12,027 494 12,521 13,709

4. DCF Valuation • •

To control BOD, you need 51% of the voting equity.

To receive all of the cash flows you need all of the equity and all of the debt.

Fritz: V0 = 10/(1.09) + 20/(1.09)2 + 30/[(0.09 –0.025) × (1.09)2] = $414.48 Loblaw: V0 = $571/(0.10 – 0.02) = $7,137.50 Loblaw Stock Price: E = V – D = $7,137.5 + 1,467 – $4,923 = $3,681.5 P = E/N = $3,681.5/274.1 = $13.43 Valuation of Apple Inc mCAPEX = 16.6 × 0.13/(1–0.13) = 2.48 gCAPEX = 0.1 × (177.7 – 170.9) = 0.68364 CAPEX = $2.48 + 0.68364= $3.164 Depr = 0.13 × (16.6 + 3.164) = 2.6 Interest = 0.03 × (17) = 0.5 Net Income = $40.5 Retained Earnings = $144.3 Total Liabilities & Owners’ Equity = $249.3 Cash = $76.7 OCF = 55.4 × (1– 0.26155) + 2.6 = $43.49 ∆NWC = –$11.4 – (–$10.9) = –$0.4 FCF = $43.49 – 3.164 – (–$0.4) = $40.76 PV_FCF = $40.76/(0.10 – 0.02) = $509.56 V = $509.56 + ($40.5 + $106.2) = $656.32 E = $656.32 – $17 = $639.36 Price = $639.36/0.892 = $716.77

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Revenue Cost of Goods Sold SG&A Depreciation Expense EBIT Interest Expense Other Income Earnings before Taxes Provision for Income Taxes Net Earnings ASSETS Current Assets Cash Accounts Receivable Inventories Other Total Current Assets Long-term Marketable Assets Property, Plant & Equipment, Net Goodwill Other Total Assets

Apple Inc. 2012 $156.5 87.8 10.1 3.3 55.2 0.0 0.5 55.8 14.0 $41.7

2013 $170.9 106.6 8.5 6.8 49.0 0.0 1.2 50.2 13.1 $37.0

2012 $29.1 10.9 0.8 16.8 57.7 92.1 15.5 5.4 5.5 $ 176.1

2013 $40.5 13.1 1.8 17.9 73.3 106.2 16.6 5.8 5.1 $ 207.0

LIABILITIES AND STOCKHOLDERS’ EQUITY Current Liabilities Accounts payable $21.2 Other 17.4 38.5 Total Current Liabilities Long Term Debt 0.0 19.3 Other Liabilities Total Liabilities 57.9 Shareholders’ Equity Common Stock 16.4 101.8 Retained Earnings 118.2 Total Shareholders’ Equity Liabilities & Shareholders’ Equity $ 176.1

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$22.4 21.3 43.7 17.0 22.8 83.5

$

19.8 103.8 123.5 207.0

Ratios 0.623755 0.050015

0.0300

0.2615492

Ratios 0.076660 0.010321 0.167664 0

0.130870 0.124574

2014 $177.7 110.9 8.9 2.6 55.4 0.5 0.0 54.9 14.4 $40.5

2014 $76.7 13.6 1.8 18.6 110.7 110.5 17.2 5.8 5.1 $ 249.3

$23.3 22.1 45.4 17.0 22.8 85.2 19.8 144.3 164.1 249.3

Chapter 18 Futures and Options 2. Forward Contracts • • •

False. The long position has an obligation to pay cash and receive the underlying asset.

False. Anyone can take a short position regardless of their prior position.

True.

3. Futures Contracts •

5,000.

Quote = 1536’6 Price = $15.3675 •

Most trading volume in nearest to maturity contract.

Total cost (cash value) = price × 5,000 Performance Bond/Margin Account Cash Value = $50 × 1,700 = $85,000 Daily profit2 = Cash Value2 – Cash Value1 = (1,690 – 1,700) × $25 = –$500 Temp Balance2 = Closing Balance1 + Daily Proift2 = 4,000 + (–500) = $3,500 •

Because the temporary balance is not below the maintenance margin level, there is no margin call.

Closing Balance2 = Temp Balance2 + Deposit2 = 3,500 + 0 = $3,500 Daily profit3 = Cash Value3 – Cash Value2 = (1,680 – 1,690) × $25 = –$500 Temp Balance3 = Closing Balance2 + Daily Proift3= 3,500 + (–500) = $3,000 •

Because the temporary balance is below the maintenance margin level, there is a margin call.

Deposit = Initial Margin – Temporary Balance = 4,000 – 3,000 = 1,000 Closing Balance3 = Temp Balance3 + Deposit = 3,000 + 1,000 = $4,000 Daily profit4 = Cash Value4 – Cash Value3 = (1,700 – 1,680) × $25 = $1,000 Temp Balance4 = Closing Balance3 + Daily Proift4= 4,000 + 1,000 = $5,000 Closing Balance4 = Temp Balance4 + Deposit = 5,000 + 0 = $5,000

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Cumulative Profit Sum of profits = –500 + (–500) + 1,000 = 0 CV4 – CV1 = 85,000 – 85,000 = 0 Sum of profits = 500 + 500 – 1,000 = 0 CV1 – CV4 = 85,000 – 85,000 = 0 Completing a Futures Trade Offset trade = Not sufficient information. The offset trade will involve a long position, but the question does not indicate the delivery month for the short position, so the offset trade cannot be determined. The offset must be in the exact same contract, which includes the same delivery month.

Convergence • • • • •

The CBT Soybeans futures contract requires delivery by seven business days after the 15th of the month.

The local grain elevator can supply you immediately, but you have to arrange for a truck with a semitrailer, and it will need to make five trips. Thus, it will take about one week.

The delivery times for a futures contract at settlement and a spot contract are about the same.

If two contracts are identical, then their price should be the same.

By the law of one price, the futures price at settlement should equal the spot price.

4. Hedging with Futures Contracts Farmer Gulke’s Short Hedge Offset trade = Buy 10 September soybean futures contracts.

Cumulative profits = CVM – CVS = ($2.1375 × 50,000) – ($2 × 50,000) = 6,875 Total proceeds = 100,000 + 6,875 = 106,875 With Delivery: Total proceeds = cash value in May = $2.1375 × 50,000 = $106,875 If the spot price had been $2.50 in September: Total proceeds = P × 50,000 + (2.1375 – P) × 50,000 = 106,875 Total proceeds = $2.5 × 50,000 + (2.1375 – 2.5) × 50,000 = $106,875

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Unilever’s Long Hed dge Offset traade = Sell 10 0 Septemberr soybean futtures contraccts.

Cumulatiive profits = CVS – CVM = ($2.40 × 50,000) – ($$2.1375 × 500,000) = 13,,125 Total cosst = 120,000 – 13,125 = 106,875 Total cosst = cash valu ue in May = $2.1375 × 50,000 5 = $1006,875 Total cosst = P × 50,0 000 – (P – 2.1375) × 50,0 000 = 106,8775 5. Option n Contractss • • • • • •

True.

T Put—Sell. Call—Buy. True.

T Long paays and shorrt receives prremium.

True.

T Only th he long side has h a choicee. The short sside has an oobligation.

True.

T The lon ng position pays p the prem mium at initiiation. If a caall owner exxercises, thenn she must m also pay y the strike price. p Put writer.

No. N

6. Call Option O Payo offs and Profits PayoffT = $70 Profit = Payoff P – Purrchase Price = $70 – $60 0 = $10

Y-axis in ntercept = –$ $60. This is your y maximu um loss if thhe company goes bankruupt.

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Long 1 Call C Payoff = MAX(0,ST – X) = $70 – $60 = $10 P – Purrchase Price = $10 – $3 = $7 Profit = Payoff

y-axis inttercept = –$3. This is thee lost premiu um if the opttion is not exxercised. x-axis inttercept = $63. This is thee break-even n stock pricee. The stock price must bbe at least $663 for call owneer to make a positive pro ofit.

Short 1 Call C Payoff = –1 × MAX((0,ST – X) = –1 × ($80 – $60) = –$2 0 Profit = Payoff P + Purrchase Price = –$20 + $3 3 = –$17

y-axis inttercept = $3. This is the premium if the option iss not exercissed. x-axis inttercept = $63. This is thee break-even n stock pricee. The stock price must bbe $63 or lesss for the writer to make a positive p proffit on the sho ort call.

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7. Put Option Payofffs and Proffits Long 1 Put P Payoff = MAX(0,X – ST) = $35 – $30 = $5 Profit = Payoff P – Purrchase Price = $5 – $2.25 5 = $2.75

y-axis inttercept = $32 2.75 This is th he payoff fro om selling a worthless stock for the sstrike price m minus the prremium. x-axis inttercept = $32 2.75 This is th he break-eveen stock pricee. The stock k price must $32.75 (or loower) for the put owner to make a positive p profiit.

Short 1 Put P Payoff = –1 × MAX((0,X – ST) = –1 × ($30 – $20) = –$1 0 Profit = Payoff P + Purrchase Price = –$10 + $2 2.25 = –$7.775

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y-axis inttercept = (–X X + Premium m) = –$27.75 5 This is th he cost of bu uying a worth hless stock for f the strikee price plus th the premium m. x-axis inttercept = $27.75.

This is th he break-eveen stock pricee. The stock k price must bbe $27.75 orr higher for tthe writer too make a positive p profiit on the sho ort put.

8. Option n Pricing Intrinsic value = MA AX(0,ST – X)) = 123.50 – 120 = 3.50 Intrinsic value = MA AX(0,X – ST) = 130 – 123.50 = 6.50 Time preemium = 3.50 – 3.50 = 0 Time preemium = 7.50 – 3.50 = 4.00 Time preemium = 10.375 – 3.50 = 6.875 Time preemium = 6.375 – 6.50 = –0.125 Profit = –123.50 – – 6.375 + 130 = 0.125 •

Greater G time means m there is a bigger chance c that aan option wiill move intoo the money or deeper into th he money. You Y are willin ng to pay moore for that hhigher probaability.

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The Minimum Price Bound for Option Premiums Trades: (1) buy the January call with the $120 strike for $2; (2) exercise the call; and (3) sell the share. Profit = –2 – 120 + 123.50 = $1.50 Your buying will create excess demand, which will cause the premium to rise.

Factors the Determine Option Premiums • • • •

Call premiums rise with the stock price because intrinsic value rises.

Put premiums fall as the stock price rises.

More Higher

Completing an Option Trade Payoff = MAX(0,ST –X) = 123.50 – 120 = 3.50 Profit = Payoff – Purchase Price = $3.50 – $12 = –$8.50 Proceeds from offset = $7.50 Profit = 7.50 – 12 = –$4.50 The Inherent Leverage of Options STOCK Holding Period Return HPR = ($64.67 – $63.03)/$63.03 HPR = 0.026 or 2.60% OPTION RETURN IF EXERCISE Each contract is for 100 shares, so the cost of one contract is 100 × $1.93 = $193 in May. Tony buys $63.03/$193 = 0.32658 of a contract.

The fractional purchase doesn’t affect the return calculation, so calculation simplest if done as if the fraction is 1/100 or one share.

Investment = Call Premium = $1.93 Payoff = MAX(0,S – X) = $64.67 – $62 = $2.67 Return = (Payoff – Premium)/Premium Return = ($2.67 – $1.93)/$1.93 Return = $0.74/$1.93 = 0.3834 or 38.34%

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OPTION RETURN IF REVERSE HPR = (Sell premium – Buy Premium)/Buy Premium HPR = ($2.67 – $1.93)/$1.93 HPR = 0.3834 or 38.34%

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