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FIN 5080 - Jack De Jong: Chapter 7: Stocks, Stock Valuation, and Stock Market Equilibrium

Example 1: What is the value of a preferred stock where the dividend rate is 16% on a $100 par value? The required rate of return for a stock of this risk level is 12%.

Dividend Amount = $16.00Required Rate of Return = 12.00%

Value of Preferred Stock = $133.33

Example 2: You own 250 shares of McCormick Resources preferred stock, which currently sells for$38.50 per share and pays annual dividends of $3.25 per share.a. What is your expected return?

8.44%

b. If you require an 8% return, given the current price, should you sell or buy more?

$40.63

Example 3: Gilliland Motor, Inc. paid a $3.75 dividend last year. At a constant rate of growth of 6%, what is the value of the common stock if investors require a 20% return?

Most recently paid dividend = $3.7500Required rate of return = 20.00%Growth rate = 6.00%Next expected dividend = $3.9750Value of Common Stock = $28.3929

What will be the dividend yield and capital gains yield for the next year?Dividend expected for year 2 = $4.2135Expected price at end of year 1 = $30.0964Dividend Yield = Dividend 1/Price 0 = 14.00%Capital Gains Yield = (Price 1 - Price 0)/Price 0 = 6.00%

Example 4: The common stock of KPD paid $1 in dividends last year. Dividends are expected to grow at an 8% annual rate for an indefinite number of years. a. If KPD’s current market price is $25, what is the stock’s expected rate of return? b. If your required rate of return is 11%, what is the value of the stock for you? c. Should you make the investment?

Most recently paid dividend = $1.0000Growth rate = 8.00%Next expected dividend = $1.0800Current market price = $25.00

Dividend Yield = D1/P0 = 4.32%Capital Gains Yield = g = 8.00%Expected Return on KPD = 12.32%

Example 5: Axel Co. had earnings per share of $5.00 five years ago. This year their EPS was

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N 5 PV -$5.00PMT $0.00FV $10.00Type 0 I = g 14.87%

Problem 7-18: Reizenstein Trucking (RT) has just developed a solar panel capable of generating 200%more electricity than any solar panel currently on the market. As a result, RT is expected to experience a 15% annual growth rate for the next 5 years. By the end of5 years, other firms will have developed comparable technology, and RT's growth ratewill slow to 5% per year indefinitely. Stockholders require a return of 12% on RT's stock. The most recent annual dividend, D0, which was paid yesterday, was $1.75per share. What's the value of the stock today?

Year Growth Rate Dividend Cash Flows0 $1.75001 15.00% $2.0125 $2.01252 15.00% $2.3144 $2.31443 15.00% $2.6615 $2.66154 15.00% $3.0608 $3.06085 15.00% $3.5199 $56.31806 5.00% $3.6959

Required Rate of Return on RT = 12.00%Price at End of Year 5 = D6/(rs - g) = $52.7981

Find Price Today using NPV: I 12.00%NPV $39.44

Volatility Example:

Next expected dividend = $2.00Growth Rate = 5.00%Required rate of return = 10.00%

Value of Common Stock = $40.00

Required Rate Growth Ratesof Return 4.00% 5.00% 6.00%

9.00% $40.00 $50.00 $66.6710.00% $33.33 $40.00 $50.0011.00% $28.57 $33.33 $40.00

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What is the value of a preferred stock where the dividend rate is 16% on a $100 par

You own 250 shares of McCormick Resources preferred stock, which currently sells for

b. If you require an 8% return, given the current price, should you sell or buy more?

Gilliland Motor, Inc. paid a $3.75 dividend last year. At a constant rate of growth of 6%,

The common stock of KPD paid $1 in dividends last year. Dividends are expected to

a. If KPD’s current market price is $25, what is the stock’s expected rate of return?

$10.00. They expect their growth to continue as before. What will their growth rate be?

Reizenstein Trucking (RT) has just developed a solar panel capable of generating 200%

expected to experience a 15% annual growth rate for the next 5 years. By the end of5 years, other firms will have developed comparable technology, and RT's growth rate

FIN 5080 - Jack De Jong: Chapter 7: Stocks, Stock Valuation, and Stock Market Equilibrium

MB8:Problem 7-5:

CAPM:

Year Growth Rate Dividend Cash Flows0 $2.00001 20.00% $2.4000 $2.40002 20.00% $2.8800 $61.02343 7.00% $3.0816

Risk-free rate 7.50%Market risk prem. 4.00%Beta 1.2000RRR on Stock 12.30%

P2 = D3/(rs - g) $ 58.1434 P0 hat = NPV $ 50.5250

Year Growth Rate Dividend Cash Flows

0 $ 2.0000 1 20.00% $ 2.4000 $ 2.4000 2 20.00% $ 2.8800 $ 2.8800 3 7.00% $ 3.0816 $ 65.2950 4 7.00% $ 3.2973

Risk-free rate 7.50%Market risk prem. 4.00%Beta 1.2000RRR on Stock 12.30%

P3 = D4/(rs - g) $ 62.2134 P0 = NPV $ 50.5250

Problem 7-15:

Part a:

RRR = 15.00%D0 = $ 2.00

Growth Rates P0 Hat

-5.00% $ 9.50 Part a

0.00% $ 13.33

5.00% $ 21.00

10.00% $ 44.00

15.00% #DIV/0! Part b

20.00% $ (48.00)

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Part c: NO, because g > RRR is not sustainable.

Problem 7-12:


0 $ - 1 $ - $ - 2 $ - $ - 3 $ 1.0000 $ 1.0000 4 50.00% $ 1.5000 $ 1.5000 5 50.00% $ 2.2500 $ 36.9643 6 8.00% $ 2.4300

RRR = 15.00%P5 = D6/(rs - g) $ 34.71

P0 = NPV $ 19.89 $ 26.31 Wrong answer if do not include the $0 dividends in years 1 and 2.

Problem 7-11:

RRR = 13.00%

Year Growth Rate Dividend Cash Flows0 $1.00001 50.00% $1.5000 $1.50002 25.00% $1.8750 $30.26793 6.00% $1.9875

P2 = D3/(rs - g) = $ 28.3929

P0 Hat = NPV $ 25.0316

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FIN 5080-Jack De Jong: Chapter 7: Stocks, Stock Valuation, and Stock Market EquilibriumQuiz #11: May 12, 2011

1. C Molen Inc. has an outstanding issue of perpetual preferred stock with an annual dividend of $7.50 per share. It is selling in the marketplace for $117.25 and your required rate of return on this preferred stock is 6.5%. Which of the following statements is true?

Annual dividend of preferred = $ 7.50 Required rate of return on P/S = 6.50%Current market price of P/S = $ 117.25

Intrinsic Value of P/S = $ 115.38 Expected rate of return on P/S = 6.40%

Molen's P/S is overvalued, so you would sell it if you owned it.

2. B Schnusenberg Corporation just paid a dividend of $0.75 per share, and thatdividend is expected to grow at a constant rate of 6.50% per year in the future. The company’s beta is 1.25, the required return on the market is 10.50%, and the risk–free rate is 4.50%. What is the intrinsic value of the company’s stock?

CAPM:

D0 = $ 0.7500 g = 6.50%D1 = $ 0.7988 Risk-free rate = 4.50%Market required rate = 10.50%Schnusenberg's beta = 1.25Schnusenberg's RRR = 12.00%

Schnusenberg's Intrinsic Value = P0 hat = $ 14.52

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FIN 5080-Jack De Jong: Chapter 7: Stocks, Stock Valuation, and Stock Market EquilibriumQuiz #12: May 17, 2011

1. E A stock just paid a dividend of $1.75 per share, has a constant growth rate of 3.6%, and is currently selling for $32.00 per share. What is the stock’s expected total return for the upcoming year?

D0 = $ 1.7500 g = 3.60%D1 = $ 1.8130 P0 = $ 32.0000

Dividend Yield = 5.67%

Capital Gains Yield = 3.60%

Expected rate of return = 9.27%

2. A Ackert Company’s last dividend was $1.55. The dividend growth rate isexpected to be constant at 1.5% for the next two years, after which the dividends areexpected to grow at a rate of 8% forever. The firm’s required rate of return is 12%.What is the intrinsic value of the company’s stock?


0 $ 1.5500 1 1.50% $ 1.5732 $ 1.5732 2 1.50% $ 1.5968 $ 44.7118 3 8.00% $ 1.7246

RRR on Ackert = 12.00%P2 = D3/(rs - g) = $ 43.1149

Find Price Today = NPV: I 12.00%NPV $ 37.0486

Other Calculations:P3=P2*(1+g) $ 46.5641 P1=NPV $ 39.9212

Year 1: Dividend Yield = 4.25%

Capital Gains Yield = (P1 - P0)/P0 = 7.75%

Total Expected Return in Year 1 = 12.00%

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FIN 5080 - Jack De Jong: Chapter 9: The Cost of Capital

Example 1: If we were to get our capital through a bank note where the interest rate is 11% and our marginal tax rate is 34%, what would be the cost of our loan?

Before-tax Cost of Note =- 11.00%Marginal Tax Rate = 40.00%

After-tax Cost of Debt = 6.60%

Problem 9-9: A company’s 6% coupon rate, semiannual payment, $1,000 par value bond that matures in 30 years sells at a price of $515.16. The company’s federal–plus–state tax rate is 40%. What is the firm’s component cost of debt for purposes of calculating the WACC?

Find YTM and then adjust for taxes:N 60 PV ($515.16)PMT $30.00 FV $1,000.00 Type 0 I = YTM 6.00%

6 Month YTM = 6.00%Nominal Annual YTM = 12.00%Marginal Tax Rate = 40.00%

After-tax Cost of Debt = 7.20%

What if 2% flotation costs were expected on issuing new bonds?Marginal Tax Rate = 40.00%Flotation Costs as a % = 2.00%N 60 PV ($504.86)PMT $30.00 FV $1,000.00 Type 0 I 6.12%

6 Month Before-tax Cost of Debt = 6.12%Annual Before-tax Cost of Debt = 12.23%After-tax Cost of Debt = 7.34%

What happens if the tax rate decreases to 25%?Marginal Tax Rate = 25.00%Flotation Costs as a % = 2.00%

After-tax Cost of Debt = 12.23%*(1-.25)= 9.18%

Problem 9-17(2): TII’s perpetual preferred stock has a $100 par value, pays a quarterly dividend of $2, and has a yield to investors of 11%. New perpetual preferred stock would have to provide the same yield to investors, and the company would incur a 5% flotation cost to sell it. What is the component cost of preferred stock for purposes of calculating the WACC?

T - 1r Debt ofCost tax -After d

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Quarterly Preferred Dividend = $2.00Annual Preferred Dividend = $8.00Yield on Preferred Stock = 11.00%

Market Price of Preferred Stock = $72.73

Percentage Flotation Costs = 5.00%

Comp. Cost of Preferred Stock = 11.58%

Problem 9-17(5): Betas, as reported by security analysts, range from 1.3 to 1.7; the T–bond rate is 10%; and the market risk premium is estimated by various brokerage houses to be in the range of 4.5% to 5.5%. What is the component cost of retained earnings?

Lowest Midpoint HighestRisk-free Rate 10.00% 10.00% 10.00%Market Risk Prem. 4.50% 5.00% 5.50%TII's Beta 1.30 1.50 1.70

Cost of Equity = 15.85% 17.50% 19.35%

Problem 9-17(4): The company has 4 million shares of common stock outstanding. The stock’s price = $20, but the stock has recently traded in the range of $17 to $23. The most recently paid dividend was $1.00 and the corresponding EPS was $2.00. ROE based on average equity was 24% in 2006, but management expects to increase this return on equity to 30%; however, security analysts are not aware of management’s optimism in this regard. What is the component cost of retained earnings?

where:

$1.00

$2.00

Dividend Payout Ratio = 50.00%Retention Rate = 50.00%ROE = 24.00%

Growth Rate g = 12.00%

$1.1200

$20.00

Dividend Yield = 5.60%

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Expected Growth Rate = 12.00%

Cost of Equity = 17.60%Lowest Midpoint

Brokers' Forecasts of g = 10.00% 12.50%Next expected dividend = $1.10 $1.13Dividend Yield = 5.50% 5.63%

Cost of Equity = 15.50% 18.13%

Problem 9-17(5): Assume flotation costs for issuing new common stock are 5%. What is the componentcost for new common equity?

and F = percentage flotation costs.

$1.1200

$19.00

F = percentage flotation costs = 5.00%Dividend Yield = 5.89%Expected Growth Rate = 12.00%

Cost of Equity = 17.89%Lowest Midpoint

Brokers' Forecasts of g = 10.00% 12.50%Next expected dividend = $1.10 $1.13Dividend Yield = 5.79% 5.92%


Problem 9-17(6): At a recent conference, TII’s financial VP polled some pension fund investment managers on the minimum rate of return they would have to expect on TII’s common to make them willing to buy the common rather than TII’s bonds, when the bonds yielded 12%. The responses suggested a risk premium over TII’s bonds of 4% to 6%. What is the component cost of retained earnings?

Lowest MidpointTII's Bond Yield = 12.00% 12.00%Bond Risk Premium = 4.00% 5.00%


Example 2: MEC uses only debt and equity. It can borrow at 10% if it continues to use 45% debtand 55% common equity. Its last dividend was $2, its expected growth rate is 4%, andthe stock sells at $20. MEC's marginal tax rate is 40%. What is its WACC?

Before-tax cost of debt = 10.00%Marginal tax rate = 40.00%After-tax cost of debt = 6.00%

Last dividend = $2.00Expected growth rate = 4.00%Next expected dividend = $2.08Current stock price = $20.00Dividend yield = 10.40%Capital gains yield = 4.00%Cost of retained earnings = 14.40%

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Target Weights Component Costs Wt x Comp. CostDebt 45.00% 6.00% 2.70%Common Stock 55.00% 14.40% 7.92%WACC 100.00% 10.62%

Problem 9-17: Compute TII's WACC.Travellers Inn: December 31, 2009 (Millions of Dollars)

Cash $ 10 Accts. PayableAccounts Rec. $ 20 AccrualsInventories $ 20 ST DebtCurrent Assets $ 50 Current LiabilitiesNet Fixed Assets $ 50 LT DebtTotal Assets $ 100 Preferred Stock

Common StockRetained Earn.Total Comm. Eq.Total Liab. & Eq.

LT Debt:N 40 I 6.00%PMT $40.00 FV $1,000.00 Type 0 PV -$699.07

Market Value of LT Debt = $20,972,221.88

Preferred Stock:Market Price of Preferred Stock = $72.73Number of Shares of Preferred = 50,000

Market Value of Preferred Stock = $3,636,363.64

Common Stock:Market Price of Common Stock = $20.00Number of Shares of Common = 4,000,000

Market Value of Common Stock = $80,000,000.00

Market Values Weights Component CostsLT Debt $ 20,972,221.88 20.05% 7.20%Preferred Stock $ 3,636,363.64 3.48% 11.58%Common Stock $80,000,000.00 76.48% 17.60%Total $ 104,608,585.51 100.00% WACC =

If we were to get our capital through a bank note where the interest rate is 11% and our

A company’s 6% coupon rate, semiannual payment, $1,000 par value bond that matures in 30 years sells at a price of $515.16. The company’s federal–plus–state tax rate is 40%. What is the firm’s component cost of debt for purposes of calculating the WACC?

TII’s perpetual preferred stock has a $100 par value, pays a quarterly dividend of $2, and has a yield to investors of 11%. New perpetual preferred stock would have to provide the same yield to investors, and the company would incur a 5% flotation cost to sell it. What is the component cost of preferred stock for purposes of calculating the WACC?

Betas, as reported by security analysts, range from 1.3 to 1.7; the T–bond rate is 10%; and the market risk premium is estimated by various brokerage houses to be in the range

The company has 4 million shares of common stock outstanding. The stock’s price = $20, but the stock has recently traded in the range of $17 to $23. The most recently paid dividend was $1.00 and the corresponding EPS was $2.00. ROE based on average equity was 24% in 2006, but management expects to increase this return on equity to 30%; however, security analysts are not aware of management’s optimism in this regard.

EquityCommon Total

rsStockholde Common toAvailable IncomeNet ROE

Highest15.00%

$1.155.75%

20.75%

Assume flotation costs for issuing new common stock are 5%. What is the component

and F = percentage flotation costs.

Highest15.00%

$1.156.05%

21.05%

At a recent conference, TII’s financial VP polled some pension fund investment managers on the minimum rate of return they would have to expect on TII’s common to make them willing to buy the common rather than TII’s bonds, when the bonds yielded 12%. The responses suggested a risk premium over TII’s bonds of 4% to 6%. What is the

Highest12.00%

6.00%

18.00%

MEC uses only debt and equity. It can borrow at 10% if it continues to use 45% debtand 55% common equity. Its last dividend was $2, its expected growth rate is 4%, andthe stock sells at $20. MEC's marginal tax rate is 40%. What is its WACC?

$ 10 $ 10 $ 5 $ 25 $ 30 $ 5 $ 10 $ 30 $ 40 $ 100

Wt.x Comp.Cost1.44%0.40%

13.46%15.31%

FIN 5080 - Jack De Jong: Chapter 9: The Cost of Capital

MB8:Problem 9-15:Part a: 50.00% equityPart b:

Before-tax cost of debt = kd = 8.00%Marginal tax rate = 40.00%After-tax cost of debt = 4.80%Cost of retained earnings = ks = 12.00%

Weights Component Costs Wt X Comp. Cost

Debt 50.00% 4.80% 2.40%

Retained Earnings 50.00% 12.00% 6.00%

WACC 8.40%Sumproduct 8.40%

Part c: Component cost of new C/S is higher than R/E due to FC and soWACC will increase.

MC o(2):N 30

PV $ (980.00)PMT $ 100.00 FV $ 1,000.00 Type 0 Rate = kd = 10.22%

After tax cost of debt = 6.13%

MC part l:After tax cost of debt = 7.20%

Risk-free rate 5.60%Market risk premium 6.00%Divisional beta 1.70Cost of R/E for division 15.80%

Weights Component Costs Wt X Comp. Cost

Debt 10.00% 7.20% 0.72%

Retained Earnings 90.00% 15.80% 14.22%

WACC 14.94%Sumproduct 14.94%

FIN 5080-Jack De Jong: Chapter 9: The Cost of CapitalQuiz #13: May 19, 2011

1. D A company’s perpetual preferred stock currently sells for $92.50 per share, and it pays an $8.00 annual dividend. If the company were to sell a new preferred issue, it would incur a flotation cost of 5.00% of the issue price. What is the firm’s cost of preferred stock?

Dividend on P/S = $ 8.0000 Market Price of P/S = $ 92.5000 Flotation Cost = 5.00%Net Proceeds of P/S = $ 87.8750

Cost of P/S = 9.10%

Investors Expected Return 8.65%

2. D Several years ago the Jakob Company sold a $1,000 par value, noncallable bond that now has 20 years to maturity and a 7.00% annual coupon that is paid semiannually. The bond currently sells for $925 and the company’s tax rate is 40%. If the company were to issue new bonds, they would pay flotation costs of 2% of the bond issue price. What is the component cost of debt for use in the WACC calculation?

NPER 40PV $ (906.50)PMT $ 35.00 FV $ 1,000.00 Type 0 RATE = 6 Mo.kd 3.9703%

Annual kd = 7.9406%

4.7644%

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FIN 5080-Jack De Jong: Chapter 9: The Cost of CapitalQuiz #14: May 24, 2011

1. B Weaver Chocolate Co. expects to earn $3.50 per share during the upcoming year, its dividend payout ratio is 65%, its expected constant dividend growth rate is 6.0%, and its common stock currently sells for $32.50 per share. New stock can be sold to the public at the current price, but a flotation cost of 5% will be incurred. What will be the cost of equity from new common stock?

EPS1 = $ 3.50 Dividend Payout Ratio = d 65.00%D1 = $ 2.28 P0 = $ 32.50 F = 5.00%P0 x (1 - F)= $ 30.88 Growth g = 6.00%Cost of New C/S = re = 13.37%

Cost of R/E = rs = 13.00%

2. C You were hired as a consultant to Quigley Company, whose target capital structure is 35% debt, 10% preferred, and 55% common equity. The interest rate on new debt is 6.50%, the yield on preferred is 6.00%, the cost of common from retained earnings is 11.25%, and the marginal tax rate is 40%. The firm will not be issuing any new common stock. What is Quigley’s WACC?

Target Wt. Component Cost Wt. x Comp.Cost

Debt 35.00% 3.90% 1.37%P/S 10.00% 6.00% 0.60%

R/E 55.00% 11.25% 6.19%

Total 100.00% WACC = 8.15%Sumproduct = 8.15%

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FIN 5080 - Jack De Jong: Chapter 10: Basics of Capital Budgeting: Evaluating Cash Flows

Problem 10-21: Your division is considering two investment projects, each of which requires an upfront expenditure of $25 million. You estimate the cost of capital is 10% and that the investments will produce the following after-tax cash flows (in millions of dollars):

Year Project A Project B Project C0 $ (25) $ (25) $ (25)1 $ 5 $ 20 $ 12 2 $ 10 $ 10 $ 12 3 $ 15 $ 8 $ 12 4 $ 20 $ 6 $ 12

A's CumulativePayback: Year Project A Cash Inflows Project B

0 $ (25) $ (25)1 $ 5 $ 5 $ 20 2 $ 10 $ 15 $ 10 3 $ 15 $ 30 $ 8 4 $ 20 $ 50 $ 6

Project A's Payback = 2 + ((25 - 15)/15) = 2.6667

Project B's Payback = 1 + ((25 - 20)/10) = 1.5000

Project C's Payback = Initial Cost / Annual Cash Inflow = 2.0833

Discounted Payback: Cost of capital = 10.00%PV of A's Cum. PV of

Year Project A Cash Inflows Cash Inflows0 $ (25) $ (25,000,000)1 $ 5 $ 4,545,455 $ 4,545,455 2 $ 10 $ 8,264,463 $ 12,809,917 3 $ 15 $ 11,269,722 $ 24,079,639 4 $ 20 $ 13,660,269 $ 37,739,908

Using Excel's PERCENTRANK fcn:Project A's Discounted Payback = 3 + ((25M - 24.08M)/13.66M) = 3.0674

PV of B's Cum. PV ofYear Project B Cash Inflows Cash Inflows

0 $ (25) $ (25,000,000)1 $ 20 $ 18,181,818 $ 18,181,818 2 $ 10 $ 8,264,463 $ 26,446,281 3 $ 8 $ 6,010,518 $ 32,456,799 4 $ 6 $ 4,098,081 $ 36,554,880

Using Excel's PERCENTRANK fcn:Project B's Discounted Payback = 1 + ((25M - 18.18M)/8.26M) = 1.8250

Project C's Discounted PaybackI 10.00%PV ($25.00)PMT $12.00 FV $0.00 Type 0 N = Disc. PB = 2.4511 years

Net Present Value: Cost of capital = 10.00%

Year Project A Project B Project C0 $ (25) $ (25) $ (25)1 $ 5 $ 20 $ 12 2 $ 10 $ 10 $ 12

3 $ 15 $ 8 $ 12 4 $ 20 $ 6 $ 12

NPV: $ 12.7399 $ 11.5549 $ 13.0384

$ 12.7399 Profitability Index: Cost of capital = 10.00%


NPV: $ 12.7399 $ 11.5549 $ 13.0384 PI: 1.5096 1.4622 1.5215

1.5096 1.4622 1.5215Internal Rate of Return: Cost of capital = 10.00%


NPV: $ 12.7399 $ 11.5549 $ 13.0384 PI: 1.5096 1.4622 1.5215 IRR: 27.27% 36.15% 32.36%

36.15%Modified IRR: Cost of capital = 10.00%


NPV: $ 12.7399 $ 11.5549 $ 13.0384 PI: 1.5096 1.4622 1.5215 IRR: 27.27% 36.15% 32.36%MIRR: 21.93% 20.96% 22.17%

20.96% 22.17%36.15% 32.36%

NPV Profile:Difference in

Year Project A Project B CFs: A - B0 $ (25) $ (25) $0 1 $ 5 $ 20 ($15)2 $ 10 $ 10 $0 3 $ 15 $ 8 $7 4 $ 20 $ 6 $14

Crossover Rate = IRR for Differences in CFs = 13.53%

Cost of Capital Project A Project B

0.00% $25.0000 $19.0000 5.00% $18.2438 $14.9648

10.00% $12.7399 $11.5549 13.53% $9.4564 $9.4564 15.00% $8.2071 $8.6434 20.00% $4.4367 $6.1343 25.00% $1.2720 $3.9536 30.00% ($1.4066) $2.0439 35.00% ($3.6913) $0.3597 40.00% ($5.6539) ($1.1349)

Unequal Lives Example: Suppose a firm is considering two mutually exclusive projects with acost of capital of 15%. Equipment S has an initial investment of $20,000 and cash inflows of $12,590 for 3 years. Equipment L has aninitial investment of $20,000 and cash inflows of $6,625 for 9 years.Which project should you choose, if any?

Unequal Lives Example: Cost of capital = 15.00%

Year Equipment S Equipment L0 $ (20,000) $ (20,000)1 $ 12,590 $ 6,625 2 $ 12,590 $ 6,625 3 $ 12,590 $ 6,625 4 $ 6,625 5 $ 6,625 6 $ 6,625 7 $ 6,625 8 $ 6,625 9 $ 6,625

NPV $8,745.80 $11,611.74 IRR 40.02% 30.00%


Replacement ChainYear Equipment S Equipment L

0 $ (20,000) $ (20,000)1 $ 12,590 $ 6,625 2 $ 12,590 $ 6,625 3 $ (7,410) $ 6,625 4 $ 12,590 $ 6,625

0.00

%5.

00%

10.0

0%

13.5

3%

15.0

0%

20.0

0%

25.0

0%

30.0

0%

35.0

0%

40.0

0%($10.0000)

($5.0000)

$0.0000

$5.0000

$10.0000

$15.0000

$20.0000

$25.0000

$30.0000

NPV Profile

Project A

Project B

Cost of Capital

NP

V

5 $ 12,590 $ 6,625 6 $ (7,410) $ 6,625 7 $ 12,590 $ 6,625 8 $ 12,590 $ 6,625 9 $ 12,590 $ 6,625

NPV $18,277.36 $11,611.74 IRR 40.02% 30.00%


Year Equipment S Equipment L0 $ (20,000) $ (20,000)1 $ 12,590 $ 6,625 2 $ 12,590 $ 6,625 3 $ 12,590 $ 6,625 4 $ 6,625 5 $ 6,625 6 $ 6,625 7 $ 6,625 8 $ 6,625 9 $ 6,625

NPV $8,745.80 $11,611.74 IRR 40.02% 30.00%

Equivalent Annual Annuity or EAA:Equipment S:N 3 I 15.00%PV = -NPV ($8,745.80)FV $0.00 Type 0 PMT = EAA $3,830.46

Equipment L:N 9 I 15.00%PV = -NPV ($11,611.74)FV $0.00 Type 0 PMT = EAA $2,433.52

B's CumulativeCash Inflows Alt. PB for B

$ (25) $ 20 $ (5) $ 30 $ 5 $ 38 $ 13 $ 44 $ 19

years

years 1.5000 years1.5000

years

Cum. PV of CFs $ (25,000,000) $ (20,454,545) $ (12,190,083) $ (920,361) $ 12,739,908

3.0674 yearsyears

Cum. PV of CFs $ (25,000,000) $ (6,818,182) $ 1,446,281 $ 7,456,799 $ 11,554,880

1.82500 yearsyears

Suppose a firm is considering two mutually exclusive projects with a

$20,000 and cash inflows of $12,590 for 3 years. Equipment L has aninitial investment of $20,000 and cash inflows of $6,625 for 9 years.

0.00

%5.

00%

10.0

0%

13.5

3%

15.0

0%

20.0

0%

25.0

0%

30.0

0%

35.0

0%

40.0

0%($10.0000)

($5.0000)

$0.0000

$5.0000

$10.0000

$15.0000

$20.0000

$25.0000

$30.0000

NPV Profile

Project A

Project B

Cost of Capital

NP

V

FIN 5080 - Jack De Jong: Chapter 10: Basics of Capital Budgeting: Evaluating Cash Flows

MB8:Problem 10-14:Year Plan A Plan B Plan B - Plan A

0 $ (10.00) $ (10.00) $ - 1 $ 12.00 $ 1.75 $ (10.25)2 $ - $ 1.75 $ 1.75 3 $ - $ 1.75 $ 1.75 4 $ - $ 1.75 $ 1.75 5 $ - $ 1.75 $ 1.75 6 $ - $ 1.75 $ 1.75 7 $ - $ 1.75 $ 1.75 8 $ - $ 1.75 $ 1.75 9 $ - $ 1.75 $ 1.75

10 $ - $ 1.75 $ 1.75 11 $ - $ 1.75 $ 1.75 12 $ - $ 1.75 $ 1.75 13 $ - $ 1.75 $ 1.75 14 $ - $ 1.75 $ 1.75 15 $ - $ 1.75 $ 1.75 16 $ - $ 1.75 $ 1.75 17 $ - $ 1.75 $ 1.75 18 $ - $ 1.75 $ 1.75 19 $ - $ 1.75 $ 1.75 20 $ - $ 1.75 $ 1.75

Crossover Rate = IRR of Diff. in CFs 16.07%

NPV $ 0.34 $ 0.34 Part c: Yes, WACC is opportunity cost and appropropriate discount rate.Part d: NPV Profile:WACC NPV A NPV B

0.00% $ 2.00 $ 25.00 10.00% $ 0.91 $ 4.90 16.07% $ 0.34 $ 0.34 20.00% $ - $ (1.48)30.00% $ (0.77) $ (4.20)40.00% $ (1.43) $ (5.63)

Problem 10-4:Year Project's CFs Cum. CFs Cum CFs

0 $ (52,125.00) $ (52,125.00)

1 $ 12,000.00 $ 12,000.00 $ (40,125.00)

2 $ 12,000.00 $ 24,000.00 $ (28,125.00)

3 $ 12,000.00 $ 36,000.00 $ (16,125.00)

4 $ 12,000.00 $ 48,000.00 $ (4,125.00)

5 $ 12,000.00 $ 60,000.00 $ 7,875.00

6 $ 12,000.00 $ 72,000.00 $ 19,875.00

7 $ 12,000.00 $ 84,000.00 $ 31,875.00

8 $ 12,000.00 $ 96,000.00 $ 43,875.00

WACC = 12.00% Percentrank = PB 4.3438NPV = $ 7,486.68

PI = 1.1436 1.1436PB = IO/PMT 4.3438 years

4.3438 years

Disc. PB

I = WACC 12.00%PV = IO $ (52,125.00)PMT $ 12,000.00 FV $ - Type 0 NPER = Disc. PB 6.4995 years

WACC = 12.00%Year Project's CFs PV of CFs Cum PV of CFs

0 $ (52,125.00) $ (52,125.00)

1 $ 12,000.00 $10,714.29 $ (41,410.71)

2 $ 13,000.00 $10,363.52 $ (31,047.19)

3 $ 14,000.00 $9,964.92 $ (21,082.27)

4 $ 15,000.00 $9,532.77 $ (11,549.50)

5 $ 16,000.00 $9,078.83 $ (2,470.67)

6 $ 17,000.00 $8,612.73 $ 6,142.06

7 $ 18,000.00 $8,142.29 $ 14,284.35

8 $ 19,000.00 $7,673.78 $ 21,958.13 Discounted PB = Percentrank x 8 5.2869 years

Year Recovery Fullduring Flow Cash

YearofStart at Cost dUnrecovere Recovery Full Prior to YearsofNumber Payback

Year Recovery Fullduring Flow Cash

YearofStart at Cost dUnrecovere Recovery Full Prior to YearsofNumber Payback

FIN 5080-Jack De Jong: Chapter 10: Basics of Capital Budgeting: Evaluating Cash FlowsQuiz #15: May 26, 2011

1. B Fernando Designs (FD) is considering a project that has an initial outlay of $900 at Year 0 with cash inflows of $500 annually at the ends of Year 1, Year 2, and Year 3. If FD’s WACC is 10.00%, what is the project’s discounted payback?

Year Cash Flow

0 $ (900.00)1 $ 500.00 2 $ 500.00 3 $ 500.00

I = WACC 10.00%PV = IO $ (900.00)PMT $ 500.00 FV $ - Type 0 NPER = Disc. PB 2.0822 years

Ordinary PB = IO / PMT = 1.8000 years

2. D Ehrmann Data Systems (EDS) is considering a project that has an initial outlay of $1,000 at Year 0 with cash inflows of $450 annually at the ends of Year 1, Year 2, and Year 3. If EDS’s WACC is 10%, what is the project’s MIRR?

Year Cash Flow

0 $ (1,000.00)1 $ 450.00 2 $ 450.00 3 $ 450.00

WACC = 10.00%MIRR = 14.20%IRR = 16.65%NPV = $ 119.08 PI = 1.1191

3. C A firm is considering Projects S and L which are mutually exclusive, equally risky, and not repeatable. The CEO wants to use the IRR criterion, while the CFO favors the NPV method. The firm’s WACC is 6%. Project S has an initial cash outlay at Year 0 of $1,025 with cash inflows of $380 annually at the end of Years 1, 2, 3, and 4. Project L has an initial cash outlay at Year 0 of $2,150 with cash inflows of $765 annually at the end of Years 1, 2, 3, and 4. If the wrong decision criterion is used, how much potential value would the firm lose?

Project S Project L Difference in

Year Cash Flows Cash Flows CFs: L - S

0 $ (1,025.00) $ (2,150.00) $ (1,125.00)1 $ 380.00 $ 765.00 $ 385.00 2 $ 380.00 $ 765.00 $ 385.00 3 $ 380.00 $ 765.00 $ 385.00 4 $ 380.00 $ 765.00 $ 385.00

WACC = 6.00%IRR = 17.86% 15.78% 13.86% Crossover RateNPV = $ 291.74 $ 500.81 MIRR = 12.85% 11.70%Value Lost = NPV L - NPV S = $ 209.07

FIN 5080 - Jack De Jong: Chapter 11: Cash Flow Estimation and Risk Analysis

Major Classes and Asset Lives for MACRS:

Class Type of Property3 year Certain special manufacturing tools5 year Automobiles, light duty trucks, computers, and certain special

manufacturing equipment7 year Most industrial equipment, office furniture, and fixtures10 year Certain longer-lived types of equipment27.5 year Residential rental real property like apartment buildings39 year All nonresidential real property, including commercial and

industrial buildings

Recovery Allowance Percentage for Personal Property:Ownership Class of InvestmentYear 3 Year 5 Year 7 Year 10 Year

1 33% 20% 14% 10%2 45% 32% 25% 18%3 15% 19% 17% 14%4 7% 12% 13% 12%5 11% 9% 9%6 6% 9% 7%7 9% 7%8 4% 7%9 7%

10 6%11 3%

100% 100% 100% 100%

Example #1: The Chung Chemical Corporation is considering the purchase of a chemical analysis machine. Although the machine being considered will result in an increase in EBIT of $35,000 per year, it has a purchase price of $100,000, and it will cost an additional $5,000 after tax to properly install this machine. In addition to properly operate this machine, inventory must be increased by $5,000. This machine has an expected life of 5 years, after which it will be sold for $10,000. It will be depreciated by MACRS as 5 year property. Assume a 34% marginal tax rate and a WACC of 15%.a. What is the initial outlay associated with this project?b. What are the annual operating cash flows associated with this project for years 1 through 5?c. What are the additional (nonoperating) cash flows in year 5?d. Should this machine be purchased?

Part a:

Cost of new machine $ 100,000.00 Installation and shipping $ 5,000.00 Increase to NOWC $ 5,000.00 Initial Outlay $ 110,000.00

Part b:Year MACRS % Depreciation Book Value

0 $ 105,000.00 1 20% $ 21,000.00 $ 84,000.00 2 32% $ 33,600.00 $ 50,400.00 3 19% $ 19,950.00 $ 30,450.00 4 12% $ 12,600.00 $ 17,850.00 5 11% $ 11,550.00 $ 6,300.00 6 6% $ 6,300.00 $ -

Totals 100% $ 105,000.00

Year 1 Year 2 Year 3 Year 4

Increase in EBIT $ 35,000.00 $ 35,000.00 $ 35,000.00 $ 35,000.00 Taxes at 34% $ 11,900.00 $ 11,900.00 $ 11,900.00 $ 11,900.00 NOPAT $ 23,100.00 $ 23,100.00 $ 23,100.00 $ 23,100.00 Depreciation $ 21,000.00 $ 33,600.00 $ 19,950.00 $ 12,600.00 Net Operating CF $ 44,100.00 $ 56,700.00 $ 43,050.00 $ 35,700.00

Part c:Decrease in NOWC $ 5,000.00

Cash Inflow from the Sale $ 10,000.00 Capital Gain:

Selling Price $ 10,000.00 Less: BV $ (6,300.00)Capital Gain $ 3,700.00 Tax on Cap. Gain $ 1,258.00 $ (1,258.00)Net Cash Flow from Sale $ 8,742.00

Total Nonoperating CF in Year 5 = $ 13,742.00

Part d:Year Project FCFs

0 $ (110,000.00)1 $ 44,100.00 2 $ 56,700.00 3 $ 43,050.00 4 $ 35,700.00 5 $ 48,392.00

WACC = 15.00%NPV $ 43,998.21 PI 1.4000IRR 31.2545%MIRR 23.0049%

Example 2: The R.T. Kleinman Corp. is considering selling one of its old assembly machines. The machine, purchased for $40,000 five years ago, had an expected life of 10 years and is being depreciated by MACRS as 10 year property. Assume Kleinman could sell this old

machine for $45,000. Also, assume a 34% marginal tax rate. How would this sale affect the initial outlay for a new machine to replace this one?

Year MACRS % Depreciation Book Value

0 $ 40,000.00 1 10% $ 4,000.00 $ 36,000.00 2 18% $ 7,200.00 $ 28,800.00 3 14% $ 5,600.00 $ 23,200.00 4 12% $ 4,800.00 $ 18,400.00 5 9% $ 3,600.00 $ 14,800.00

6 7% $ 2,800.00 $ 12,000.00 7 7% $ 2,800.00 $ 9,200.00 8 7% $ 2,800.00 $ 6,400.00 9 7% $ 2,800.00 $ 3,600.00

10 6% $ 2,400.00 $ 1,200.00 11 3% $ 1,200.00 $ -

Totals 100% $ 40,000.00


Selling Price $ 45,000.00 Less: BV $ (14,800.00)Capital Gain $ 30,200.00 Tax on Cap. Gain $ 10,268.00 $ (10,268.00)Net Cash Flow from Sale $ 34,732.00

Problem 11-15: The Bartram Pulley Company must decide between two mutually exclusive investment projects. Each project costs $6,750 and has an expected life of 3 years. Annual net cash flows begin 1 year after the initial investment is made and have the following probability distributions:

Project A Project BProbability Net Cash Flows Probability Net Cash Flows

20% $ 6,000.00 20% $0.0060% $ 6,750.00 60% $ 6,750.00 20% $ 7,500.00 20% $ 18,000.00

BPC has decided to evaluate the riskier project at a 12% rate and the less risky project at a 10% rate.a. What is the expected value of the annual net cash flows from each project? What is the coefficient of variation?b. What is the risk-adjusted NPV of each project?c. If it were known that Project B was negatively correlated with other cash flows of thefirm, whereas Project A was positively correlated, how would this knowledge affect the decision? If Project B's cash flows were negatively correlated with gross domesticproduct (GDP), would that influence your assessment of its risk?

Part a: Project AProbability Net Cash Flows Prob.x Net CF Prob.x((CF - Exp. CF)^2)

20% $ 6,000.00 $ 1,200.00 $ 112,500.00

60% $ 6,750.00 $ 4,050.00 $ - 20% $ 7,500.00 $ 1,500.00 $ 112,500.00

Expected Net CF $ 6,750.00 $ 225,000.00 Variance

Std. Deviation $ 474.34 CV 0.0703

Project BProbability Net Cash Flows Prob.x Net CF Prob.x((CF - Exp. CF)^2)

20% $0.00 $0.00 $ 11,704,500.00 60% $ 6,750.00 $ 4,050.00 $ 486,000.00 20% $ 18,000.00 $ 3,600.00 $ 21,424,500.00

Expected Net CF $ 7,650.00 $ 33,615,000.00 Variance

Std. Deviation $ 5,797.84 CV 0.7579

Part b:Year Project A Project B

0 $ (6,750.00) $ (6,750.00)1 $ 6,750.00 $ 7,650.00 2 $ 6,750.00 $ 7,650.00 3 $ 6,750.00 $ 7,650.00

WACC 10.00% 12.00%

Risk-Adj. NPV = $ 10,036.25 $ 11,624.01

The Chung Chemical Corporation is considering the purchase of a chemical analysis machine. Although the machine being considered will result in an increase in EBIT of

machine, inventory must be increased by $5,000. This machine has an expected life of

Year 5

$ 35,000.00 $ 11,900.00 $ 23,100.00 $ 11,550.00 $ 34,650.00

The R.T. Kleinman Corp. is considering selling one of its old assembly machines. The machine, purchased for $40,000 five years ago, had an expected life of 10 years and is being depreciated by MACRS as 10 year property. Assume Kleinman could sell this old

The Bartram Pulley Company must decide between two mutually exclusive investment

a. What is the expected value of the annual net cash flows from each project? What

c. If it were known that Project B was negatively correlated with other cash flows of thefirm, whereas Project A was positively correlated, how would this knowledge affect the

FIN 5080-Jack De Jong: Chapter 11: Cash Flow Estimation and Risk AnalysisQuiz #16: May 31, 2011

1. As a member of UA Corporation’s financial staff, you must estimate the Year 1 cash flow for a proposed project with the following annual data: sales revenue of $42,500, depreciation expense of $10,000, cash operating expenses of $17,000, interest expense of $4,000, and a marginal tax rate of 35.00%. What is UA’s Year 1 cash flow?

Sales Revenue $ 42,500.00 Cash Operating Expenses $ 17,000.00

Depreciation $ 10,000.00

EBIT $ 15,500.00 Less: Taxes at 35% $ (5,425.00)

Add: Depreciation $ 10,000.00

Net Operating Cash Flow $ 20,075.00

2. Marshall–Miller & Company is considering the purchase of a new machine for $50,000 installed. The machine will be depreciated by MACRS as 5 year property. The firm expects to operate the machine for 4 years and then to sell it for $12,500. If the marginal tax rate is 40.00%, what will the after–tax salvage value be when the machine is sold at the end of Year 4?


0 $ 50,000.00 1 20% $ 10,000.00 $ 40,000.00 2 32% $ 16,000.00 $ 24,000.00 3 19% $ 9,500.00 $ 14,500.00 4 12% $ 6,000.00 $ 8,500.00 5 11% $ 5,500.00 $ 3,000.00

6 6% $ 3,000.00 $ -

Totals 100% $ 50,000.00

Cash Inflow from the Sale $ 12,500.00 Capital Gain: Selling Price $ 12,500.00

Less: BV $ (8,500.00)

Capital Gain $ 4,000.00

Tax on Cap. Gain $ 1,600.00 $ (1,600.00)

Net Cash Flow from Sale $ 10,900.00

3. Your company, CSUS Inc., is considering a project whose data are shown below. Revenue and cash operating expenses are expected to constant over the project’s 10 year expected operating life; annual sales revenue is $42,500 and cash operating expenses are $25,000. The new equipment’s cost and depreciable basis is $70,000 and it will be depreciated by MACRS as 3 year property. The marginal tax rate is 35.00%. What is the project’s Year 4 cash flow?


0 $ 70,000.00 1 33% $ 23,100.00 $ 46,900.00 2 45% $ 31,500.00 $ 15,400.00 3 15% $ 10,500.00 $ 4,900.00

4 7% $ 4,900.00 $ -

Totals 100% $ 70,000.00

Sales Revenue $ 42,500.00 Cash Operating Expenses $ 25,000.00

Depreciation $ 4,900.00

EBIT $ 12,600.00 Less: Taxes at 35% $ (4,410.00)

Add: Depreciation $ 4,900.00

Net Operating Cash Flow $ 13,090.00

As a member of UA Corporation’s financial staff, you must estimate the Year 1 cash flow for a proposed project with the following annual data: sales revenue of $42,500, depreciation expense of $10,000, cash operating expenses of $17,000, interest expense of $4,000, and a

Marshall–Miller & Company is considering the purchase of a new machine for $50,000 installed. The machine will be depreciated by MACRS as 5 year property. The firm expects to operate the machine for 4 years and then to sell it for $12,500. If the marginal tax rate is 40.00%, what

Your company, CSUS Inc., is considering a project whose data are shown below. Revenue and cash operating expenses are expected to constant over the project’s 10 year expected operating life; annual sales revenue is $42,500 and cash operating expenses are $25,000. The new equipment’s cost and depreciable basis is $70,000 and it will be depreciated by MACRS as 3 year property. The marginal tax rate is 35.00%. What is the project’s Year 4 cash flow?

FIN 5080 - Jack De Jong: Review for Final ExamMay 31, 2011

MB8:Problem 11-7:Part a:Equipment Cost $ 70,000.00

Modification $ 15,000.00

Total Cost of Equip. $ 85,000.00

Increase NOWC $ 4,000.00

Initial Outlay $ 89,000.00 Part b:


0 $ 85,000.00 1 33% $ 28,050.00 $ 56,950.00 2 45% $ 38,250.00 $ 18,700.00 3 15% $ 12,750.00 $ 5,950.00 4 7% $ 5,950.00 $ -

Totals 100% $ 85,000.00

Year 1 Year 2 Year 3

Reduced Labor $ 25,000.00 $ 25,000.00 $ 25,000.00

Increased Deprec. $ (28,050.00) $ (38,250.00) $ (12,750.00)

EBIT $ (3,050.00) $ (13,250.00) $ 12,250.00 Less: Taxes at 40% $ 1,220.00 $ 5,300.00 $ (4,900.00)

Add: Deprec. $ 28,050.00 $ 38,250.00 $ 12,750.00

Net Oper. CFs $ 26,220.00 $ 30,300.00 $ 20,100.00

Part c:Decrease in NOWC $ 4,000.00


Selling Price $ 30,000.00 Less: BV $ (5,950.00)Capital Gain $ 24,050.00 Tax on Cap. Gain $ (9,620.00) $ (9,620.00)Net Cash Flow from Sale $ 20,380.00

Total Nonoperating CF in Year 3 = $ 24,380.00

Part d:Year Cash Flows

0 $ (89,000.00)1 $ 26,220.00 2 $ 30,300.00

3 $ 44,480.00 WACC = 10.00%NPV ($6,703.83) Reject the project

Problem 11-10:Initial Outlay $ 82,500.00


0 $ 82,500.00 1 20% $ 16,500.00 $ 66,000.00 2 32% $ 26,400.00 $ 39,600.00 3 19% $ 15,675.00 $ 23,925.00 4 12% $ 9,900.00 $ 14,025.00 5 11% $ 9,075.00 $ 4,950.00 6 6% $ 4,950.00 $ -

Totals 100% $ 82,500.00


EBD $ 27,000.00 $ 27,000.00 $ 27,000.00

Increased Deprec. $ (16,500.00) $ (26,400.00) $ (15,675.00)

EBIT $ 10,500.00 $ 600.00 $ 11,325.00 Less: Taxes at 40% $ (4,200.00) $ (240.00) $ (4,530.00)

Add: Deprec. $ 16,500.00 $ 26,400.00 $ 15,675.00

Net Oper. CFs $ 22,800.00 $ 26,760.00 $ 22,470.00


EBD $ 27,000.00 $ 27,000.00 $ 27,000.00

Increased Deprec. $ (9,075.00) $ (4,950.00) $ -

EBIT $ 17,925.00 $ 22,050.00 $ 27,000.00 Less: Taxes at 40% $ (7,170.00) $ (8,820.00) $ (10,800.00)

Add: Deprec. $ 9,075.00 $ 4,950.00 $ -

Net Oper. CFs $ 19,830.00 $ 18,180.00 $ 16,200.00

WACC = 12.00%NPV = $22,329.39 Accept Project

Problem 7-19:


0 $1.60001 20.00% $1.9200 $1.92002 20.00% $2.3040 $63.36003 6.00% $2.4422

Required Rate of Return on TTC = 10.00%Price at End of Year 2 = D3/(rs - g) = $61.0560

Find Price Today using NPV: I 10.00%NPV $54.11

Div. Yield = D1/P0 hat 3.55%CGY = rs - Div. Yield 6.45%

Part b: Price increase, div. yield decrease, CGY increasePart c: CGY = g = 6% and div. yield = 10% - 6% = 4%Part d: Investor preferences for div. or CGs

Year 4

$ 27,000.00

$ (9,900.00)

$ 17,100.00 $ (6,840.00)

$ 9,900.00

$ 20,160.00

Year 8

$ 27,000.00

$ -

$ 27,000.00 $ (10,800.00)

$ -

$ 16,200.00

Part a

Download - Final Spreadsheet

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