Solutions to Practice Problems

1. COST OF COMMON EQUITY AND WACC Patton Paints Corporation has a target capitalstructure of 40% debt and 60% common equity, with no preferred stock. Its before-tax costof debt is 12%, and its marginal tax rate is 40%. The current stock price is P0 = $22.50. Thelast dividend was D0 = $2.00, and it is expected to grow at a 7% constant rate. What is itscost of common equity and its WACC?

Debt = 35%, Common equity = 65%.P0 = $22.00, D0 = $2.25, D1 = $2.25(1.05) = $2.3625, g = 5%.

rs = D1

P0 + g = $2 . 3625$22 .00 + 5% = 15.74%.

WACC= (0.35)(0.08)(1 – 0.4) + (0.65)(15.74%)= 0.0168 + 0.1023 = 0.1191 = 11.91%.

2. WACC The Patrick Company’s year-end balance sheet is shown below. Its cost of commonequity is 16%, its before-tax cost of debt is 13%, and its marginal tax rate is 40%. Assumethat the firm’s long-term debt sells at par value. The firm’s total debt, which is the sum ofthe company’s short-term debt and long-term debt, equals $1,152. The firm has 576 sharesof common stock outstanding that sell for $4.00 per share. Calculate Patrick’s WACC usingmarket-value weights.

Assets Cash $ 130

Accounts receivable 240 Inventories 360

Plant and equipment, net 2,160 Total assets $2,890

Liabilities and EquityAccounts payable and accruals $ 10

Short-term debt 52Long-term debt 1,100Common equity 1,728

Total liabilities and equity $2,890

BV total debt = Short-term debt + Long-term debt = MV total debt = $1,167; P0 = $4.00; Shares outstanding = 576; T = 40%

MV equity = $4.00 × 576 shares = $2,304.

Capital Sources Market Value Market-Value Weight Debt $1,167 $1,167/$3,471 =33.62%Common equity 2,304 $2,304/$3,471 = 66 .38 %Total capital $3,471 100 .00 %WACC= wdrd(1 – T) + wcrs

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= 0.3362(0.10)(0.60) + 0.6638(0.14)= 0.0202 + 0.0929 = 11.31%.

3.WACC AND PERCENTAGE OF DEBT FINANCING Hook Industries’s capital structure consists solely of debt and common equity. It can issue debt at rd = 11%, and its common stockcurrently pays a $2.00 dividend per share D0 = $2.00. The stock’s price is currently $24.75,its dividend is expected to grow at a constant rate of 7% per year, its tax rate is 35%, and itsWACC is 13.95%. What percentage of the company’s capital structure consists of debt?

rs = D1/P0 + g= $2(1.07)/$24.75 + 7%= 8.65% + 7% = 15.65%.

WACC = wd(rd)(1 – T) + wc(rs); wc = 1 – wd.

13.95% = wd(11%)(1 – 0.35) + (1 – wd)(15.65%)0.1395 = 0.0715wd + 0.1565 – 0.1565wd-0.017 = -0.085wd

wd = 0.20 = 20%.

4. WACC Midwest Electric Company (MEC) uses only debt and common equity. It canborrow unlimited amounts at an interest rate of rd = 10% as long as it finances at its targetcapital structure, which calls for 45% debt and 55% common equity. Its last dividend D0

was $2, its expected constant growth rate is 4%, and its common stock sells for $20. MEC’stax rate is 40%. Two projects are available: Project A has a rate of return of 13%, and ProjectB’s return is 10%. These two projects are equally risky and about as risky as the firm’sexisting assets.a. What is its cost of common equity?b. What is the WACC?c. Which projects should Midwest accept?

a. rd = 9%, rd(1 – T) = 9%(0.6) = 5.4%.

wd = 35%; D0 = $2.20; g = 6%; P0 = $26; T = 40%.

Project A: Rate of return = 12%.Project B: Rate of return = 11%.rs = $2.20(1.06)/$26 + 6% = 14.97%.

b. WACC = 0.35(5.4%) + 0.65(14.97%) = 11.62%.c. The firm’s WACC is 11.62% and each of the projects is equally risky and as risky

as the firm’s other assets, so EEC should accept Project A because A’s rate of return is greater than the firm’s WACC. Project B should not be accepted, because B’s rate of return is less than EEC’s WACC.

5. WACC AND OPTIMAL CAPITAL BUDGET Adams Corporation is considering four average-risk projects with the following costs and rates of return:

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Project Cost Expected Rate of Return

1 $2,000 16.00%

2 3,000 15.00

3 5,000 13.75

4 2,000 12.50

The company estimates that it can issue debt at a rate of rd 10%, and its tax rate is 30%.It can issue preferred stock that pays a constant dividend of $5.00 per year at $49.00per share. Also, its common stock currently sells for $36.00 per share; the next expecteddividend, D1, is $3.50; and the dividend is expected to grow at a constant rate of 6% peryear. The target capital structure consists of 75% common stock, 15% debt, and 10%preferred stock.

a. What is the cost of each of the capital components?b. What is Adams’s WACC?c. Only projects with expected returns that exceed WACC will be accepted. Whichprojects should Adams accept?

6. a. rd(1 – T) = 0.10(1 – 0.3) = 7%.rp = $5/$50 = 10%.rs = $4.25/$38 + 5% = 16.18%.

b. WACC: After-Tax WeightedComponent Weight Cost = Cost Debt 0.15 7.00% 1.05%Preferred stock 0.10 10.00 1.00Common stock 0.75 16.18 12 .14

WACC= 14 .19 %c. Projects 1 and 2 will be accepted since their rates of return exceed the WACC.

ADJUSTING COST OF CAPITAL FOR RISK Ziege Systems is considering the followingindependent projects for the coming year:

Project Required Investment Rate of Return Risk

A $4 million 14.0% High

B 5 million 11.5 High

C 3 million 9.5 Low

D 2 million 9.0 Average

E 6 million 12.5 High

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F 5 million 12.5 Average

G 6 million 7.0 Low

H 3 million 11.5 Low

Ziege’s WACC is 10%, but it adjusts for risk by adding 2% to the WACC for high-riskprojects and subtracting 2% for low-risk projects.

a. Which projects should Ziege accept if it faces no capital constraints?

b. If Ziege can only invest a total of $13 million, which projects should it accept, and whatwould be the dollar size of its capital budget?

c. Suppose Ziege can raise additional funds beyond the $13 million, but each new increment(or partial increment) of $5 million of new capital will cause the WACC to increase by1%. Assuming that Ziege uses the same method of risk adjustment, which projectsshould it now accept, and what would be the dollar size of its capital budget?

a. If all project decisions are independent, the firm should accept all projects whose returns exceed their risk-adjusted costs of capital. The appropriate costs of capital are summarized below:

Required Rate of Cost ofProject Investment Return Capital

A $4 million 14.0% 12%B 5 million 11.5 12C 3 million 9.5 8D 2 million 9.0 10E 6 million 12.5 12F 5 million 12.5 10G 6 million 7.0 8H 3 million 11.5 8

Therefore, Ziege should accept projects A, C, E, F, and H.b. With only $13 million to invest in its capital budget, Ziege must choose the best

combination of Projects A, C, E, F, and H. Collectively, the projects would account for an investment of $21 million, so naturally not all these projects may be accepted. Looking at the excess return created by the projects (rate of return minus the cost of capital), we see that the excess returns for Projects A, C, E, F, and H are 2%, 1.5%, 0.5%, 2.5%, and 3.5%. The firm should accept the projects which provide the greatest excess returns. By that rationale, the first project to be eliminated from consideration is Project E. This brings the total investment required down to $15 million, therefore one more project must be eliminated. The next lowest excess return is Project C. Therefore, Ziege's optimal capital budget consists of Projects A, F, and H, and it amounts to $12 million.

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c. Since Projects A, F, and H are already accepted projects, we must adjust the costs of capital for the other two value producing projects (C and E).

Required Rate of Cost ofProject Investment Return Capital

C $3 million 9.5% 8% + 1% = 9%E 6 million 12.5 12% + 1% =13%

If new capital must be issued, Project E ceases to be an acceptable project. On the other hand, Project C's expected rate of return still exceeds the risk-adjusted cost of capital even after raising additional capital. Hence, Ziege's new capital budget should consist of Projects A, C, F, and H and requires $15 million of capital, so an additional $2 million must be raised above the initial $13 million constraint.

7. WACC The following table gives Foust Company’s earnings per share for the last 10 years.The common stock, 7 8 million shares outstanding, is now (1/1/16) selling for $65 00 pershare. The expected dividend at the end of the current year (12/31/16) is 55% of the 2015EPS. Because investors expect past trends to continue, g may be based on the historicalearnings growth rate. (Note that 9 years of growth are reflected in the 10 years of data.)

Year EPS Year EPS2006 $3.90 2011 $5.732007 4.21 2012 6.192008 4.55 2013 6.682009 4.91 2014 7.222010 5.31 2015 7.80

The current interest rate on new debt is 9%; Foust’s marginal tax rate is 40%; and its targetcapital structure is 40% debt and 60% equity.a. Calculate Foust’s after-tax cost of debt and common equity. Calculate the cost of equityas rs D1 / P0 + g.b. Find Foust’s WACC.

a. After-tax cost of new debt: rd(1 – T) = 0.09(1 – 0.4) = 5.4%.

Cost of common equity: Calculate g as follows:With a financial calculator, input N = 9, PV = -3.90, PMT = 0, FV = 7.80, and then solve for I/YR = g = 8.01% 8%.

rs = D1

P0 + g = (0 .55)( $7 .80 )

$65 .00 + 0.08 = $4 .29$65 . 00 + 0.08 = 0.146 = 14.6%.

b. WACC calculation:Target After-Tax Weighted

Component Weight Cost = Cost Debt 0.40 5.4% 2.16%Common equity (RE) 0.60 14.6 8 .76

WACC= 10 .92 %

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11. CAPITAL BUDGETING CRITERIA A firm with a 14% WACC is evaluating two projects forthis year’s capital budget. After-tax cash flows, including depreciation, are as follows:

a. Calculate NPV, IRR, MIRR, payback, and discounted payback for each project.b. Assuming the projects are independent, which one(s) would you recommend?c. If the projects are mutually exclusive, which would you recommend?d. Notice that the projects have the same cash flow timing pattern. Why is there a conflictbetween NPV and IRR?

a. Project M:CF0 = -30000; CF1-5 = 10000; I/YR = 14.

Solve for NPVM = $4,330.81. IRRM = 19.86%.

MIRR calculation:0 1 2 3 4 5| | | | | |

-30,000 10,000 10,000 10,000 10,000 10,00011,400.0012,996.0014,815.4416,889 .60 66,101 .04

Using a financial calculator, enter N = 5; PV = -30000; PMT = 0; FV = 66101.04; and solve for MIRRM = I/YR = 17.12%.

Payback calculation:0 1 2 3 4 5| | | | | |

-30,000 10,000 10,000 10,000 10,000 10,000Cumulative CF:-30,000-20,000-10,000 0 10,000 20,000

Regular PaybackM = 3 years.

Discounted payback calculation:0 1 2 3 4 5| | | | | |

-30,000 10,000 10,000 10,000 10,000 10,000

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1.14 (1.14)2

(1.14)3

(1.14)4

14%

14%

Discounted CF: -30,000 8,771.93 7,694.68 6,749.72 5,920.80 5,193.69Cumulative CF:-30,000-21,228.07-13,533.39-6,783.67-862.87 4,330.82

Discounted PaybackM = 4 + $862.87/$5,193.69 = 4.17 years.

Project N:CF0 = -90000; CF1-5 = 28000; I/YR = 14.

Solve for NPVN = $6,126.27. IRRN = 16.80%.

MIRR calculation:0 1 2 3 4 5| | | | | |

-90,000 28,000 28,000 28,000 28,000 28,00031,920.0036,388.8041,483.2347,290 .88

185,082 .91

Using a financial calculator, enter N = 5; PV = -90000; PMT = 0; FV = 185082.91; and solve for MIRRN = I/YR = 15.51%.

Payback calculation:0 1 2 3 4 5| | | | | |

-90,000 28,000 28,000 28,000 28,000 28,000Cumulative CF:-90,000-62,000-34,000 -6,000 22,000 50,000

Regular PaybackN = 3 + $6,000/$28,000 = 3.21 years.

Discounted payback calculation:0 1 2 3 4 5| | | | | |

-90,000 28,000 28,000 28,000 28,000 28,000Discounted CF:-90,000 24,561.40 21,545.09 18,899.20 16,578.25 14,542.32Cumulative CF:-90,000-65,438.60-43,893.51-24,994.31 -8,416.06 6,126.26

Discounted PaybackN = 4 + $8,416.06/$14,542.32 = 4.58 years.

Summary of capital budgeting rules results: Project M Project N

NPV $4,330.81 $6,126.27IRR 19.86% 16.80%MIRR 17.12% 15.51%Payback 3.0 years 3.21 yearsDiscounted payback 4.17 years 4.58 years

b. If the projects are independent, both projects would be accepted because both of their NPVs are positive.

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1.14 (1.14)2

(1.14)3

(1.14)4

14%

14%

c. If the projects are mutually exclusive then only one project can be accepted, so the project with the highest positive NPV is chosen. Accept Project N.

d. The conflict between NPV and IRR occurs due to the difference in the size of the projects. Project N is 3 times larger than Project M.

12 CAPITAL BUDGETING CRITERIA: MUTUALLY EXCLUSIVE PROJECTS Project S costs $15,000,and its expected cash flows would be $4,500 per year for 5 years. Mutually exclusive Project Lcosts $37,500, and its expected cash flows would be $11,100 per year for 5 years. If bothprojects have a WACC of 14%, which project would you recommend? Explain.

Project S: Using a financial calculator, enter the following data: CF0 = -17000; CF1-5 = 5000; I/YR = 12. NPVS = $1,023.88.Project L: Using a financial calculator, enter the following data: CF0 = -30000; CF1-5 = 8750; I/YR = 12. NPVL = $1,541.79.The decision rule for mutually exclusive projects is to accept the project with the highest positive NPV. In this situation, the firm would accept Project L because NPVL = $1,541.79 is greater than NPVS = $1,023.88.

13. IRR AND NPV A company is analyzing two mutually exclusive projects, S and L, with the following cash flows:

The company’s WACC is 10%. What is the IRR of the better project? (Hint: The better project may or may not be the one with the higher IRR.)

Input the appropriate cash flows into the cash flow register, and then calculate NPV at 8.5% and the IRR of each of the projects:Project S: CF0 = -1000; CF1 = 870; CF2 = 250; CF3-4 = 25; I/YR = 8.5. Solve for NPVS = $51.82; IRRS = 12.85%.Project L: CF0 = -1000; CF1 = 0; CF2 = 250; CF3 = 400; CF4 = 845; I/YR = 8.5. Solve for NPVL = $135.26; IRRL = 12.70%.Because Project L has the higher NPV, it is the better project, even though its IRR is less than Project S’s IRR. The IRR of the better project is IRRL = 12.70%.

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14. MIRR A firm is considering two mutually exclusive projects, X and Y, with the followingcash flows:

The projects are equally risky, and their WACC is 12%. What is the MIRR of the project thatmaximizes shareholder value?

11-13 Because both projects are the same size you can just calculate each project’s MIRR and choose the project with the higher MIRR.Project X: 0 1 2 3 4

| | | | |-1,000 110 300 430 700.00

477.30369.63

150 .44 1,000 14.14% = MIRRX 1,697 .37

$1,000 = $1,697.37/(1 + MIRRX)4.Project Y: 0 1 2 3 4

| | | | |-1,000 1,100 90 55 50.00

61.05110.89

1,504 .39 1,000 14.63% = MIRRY 1,726 .33

$1,000 = $1,726.33/(1 + MIRRY)4.Because MIRRY > MIRRX, Project Y should be chosen.Alternate step: You could calculate the NPVs, see that Project Y has the higher NPV, and just calculate MIRRY.NPVX = $118.11 and NPVY = $137.19.

15. CAPITAL BUDGETING CRITERIA A company has a 12% WACC and is considering two mutually exclusive investments (that cannot be repeated) with the following cash flows:

9

11%

1.11 (1.11)2

(1.11)3

11%

1.11 (1.11)2

(1.11)3

a. What is each project’s NPV?b. What is each project’s IRR?c. What is each project’s MIRR? (Hint: Consider Period 7 as the end of Project B’s life.)d. From your answers to parts a, b, and c, which project would be selected? If the WACCwas 18%, which project would be selected?e. Construct NPV profiles for Projects A and B.f. Calculate the crossover rate where the two projects’ NPVs are equal.g. What is each project’s MIRR at a WACC of 18%?

a. Using a financial calculator, enter each project’s cash flows into the cash flow registers and enter I/YR = 11. Then, you calculate each project’s NPV. At WACC = 11%, Project A has the greater NPV, specifically $240.64 as compared to Project B’s NPV of $161.89.

b. Using a financial calculator and entering each project’s cash flows into the cash flow registers, you would calculate each project’s IRR. IRRA = 18.1%; IRRB = 23.97%.

c. Here is the MIRR for Project A when WACC = 11%:PV costs = $300 + $387/(1.11)1 + $193/(1.11)2 + $100/(1.11)3 + $180/(1.11)7 =

$965.11.

TV inflows = $600(1.11)3 + $600(1.11)2 + $850(1.11)1 = $2,503.34.

MIRR is the discount rate that forces the TV of $2,503.34 in 7 years to equal $965.11.

Using a financial calculator enter the following inputs: N = 7, PV = -965.11, PMT = 0, and FV = 2503.34. Then, solve for I/YR = MIRRA = 14.59%.

Here is the MIRR for Project B when WACC = 11%:PV costs = $405.

TV inflows = $134(1.11)6 + $134(1.11)5 + $134(1.11)4 + $134(1.11)3 + $134(1.11)2 + $134(1.11)

= $1,176.96.

MIRR is the discount rate that forces the TV of $1,176.96 in 7 years to equal $405.

Using a financial calculator enter the following inputs: N = 7; PV = -405; PMT = 0; and FV = 1176.96. Then, solve for I/YR = MIRRB = 16.46%.

d. WACC = 11% criteria:Project A Project B

NPV $240.64 $161.89IRR 18.10% 23.97%MIRR 14.59% 16.46%

The correct decision is that Project A should be chosen because NPVA > NPVB.

At WACC = 18%, using your financial calculator enter the cash flows for each project, enter I/YR = WACC = 18, and then solve for each Project’s NPV.

NPVA = $2.66; NPVB = $63.68.

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At WACC = 18%, NPVB > NPVA so Project B would be chosen.

e.

Discount Rate NPVA NPVB0.0% $890 $399

10.0 283 17911.0 241 16218.1 0 6220.0 (49) 4124.0 (138) 030.0 (238) (51)

f. To calculate the crossover rate, create Project which represents the cash flow differences between the two projects. The IRR of Project is the crossover rate.

Year CFA CFB CF = CFA – CFB0 -300 -405 1051 -387 134 -5212 -193 134 -3273 -100 134 -2344 600 134 4665 600 134 4666 850 134 7167 -180 0 -180

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Enter the data for Project into the cash flow registers and solve for IRR = 14.53%. Note that when using your calculator, you may receive an ERROR message. In order to find the IRR, you will need to store a guess for IRR, say 10%, by STO 10 and then calculate IRR, IRR = 14.53%.

g. Here is the MIRR for Project A when WACC = 18%:PV costs = $300 + $387/(1.18)1 + $193/(1.18)2 + $100/(1.18)3 + $180/(1.18)7 = $883.95.

TV inflows = $600(1.18)3 + $600(1.18)2 + $850(1.18)1 = $2,824.26.

MIRR is the discount rate that forces the TV of $2,824.26 in 7 years to equal $883.95.

Using a financial calculator enter the following inputs: N = 7; PV = -883.95; PMT = 0; and FV = 2824.26. Then, solve for I/YR = MIRRA = 18.05%.

Here is the MIRR for Project B when WACC = 18%:PV costs = $405.

TV inflows = $134(1.18)6 + $134(1.18)5 + $134(1.18)4 + $134(1.18)3 + $134(1.18)2 + $134(1.18)

= $1,492.96.

MIRR is the discount rate that forces the TV of $1,492.96 in 7 years to equal $405.

Using a financial calculator enter the following inputs: N = 7; PV = -405; PMT = 0; and FV = 1492.96. Then, solve for I/YR = MIRRB = 20.49%.

16. MIRR Project X costs $1,000, and its cash flows are the same in Years 1 through 10. Its IRR is 12%, and its WACC is 10%. What is the project’s MIRR?

Step 1: Determine the PMT:0 1 10| | |

-1,000 PMT PMTThe IRR is the discount rate at which the NPV of a project equals zero. Since we know the project’s initial investment, its IRR, the length of time that the cash flows occur, and that each cash flow is the same, then we can determine the project’s cash flows by setting it up as a 10-year annuity. With a financial calculator, input N = 10, I/YR = 16, PV = -1000, and FV = 0 to obtain PMT = $206.90.

12

16%

Step 2:We’ve been given the WACC, so once we have the project’s cash flows we can now calculate the project’s MIRR.Calculate the project’s MIRR:

0 1 2 9 10| | | | |

-1,000 206.90 206.90 206.90 206.90223.45

.

.

.382.96

413 .59 1,000 11.60% = MIRR TV = 2,997 .27

FV of inflows: With a financial calculator, input N = 10, I/YR = 8, PV = 0, and PMT = -206.90 to obtain FV = $2,997.27.

Calculate MIRR: Then input N = 10, PV = -1000, PMT = 0, and FV = 2997.27 to obtain I/YR = MIRR = 11.60%.

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(1.08)9

(1.08)8

1.08

8%

21. OPTIMAL CAPITAL STRUCTURE Jackson Trucking Company is in the process of setting itstarget capital structure. The CFO believes that the optimal debt-to-capital ratio is somewherebetween 20% and 50%, and her staff has compiled the following projections for EPSand the stock price at various debt levels:

Assuming that the firm uses only debt and common equity, what is Jackson’s optimalcapital structure? At what debt-to-capital ratio is the company’s WACC minimized?

The optimal capital structure is that capital structure where WACC is minimized and stock price is maximized. Because Terrell’s stock price is maximized at a 30% debt-to-capital ratio, the firm’s optimal capital structure is 30% debt and 70% equity. This is also the debt level where the firm’s WACC is minimized.

22. UNLEVERED BETA Harley Motors has $10 million in assets, which were financed with $2 million of debt and $8 million in equity. Harley’s beta is currently 1 2, and its tax rate is 40%. Use the Hamada equation to find Harley’s unlevered beta, bU.

From the Hamada equation, b = bU[1 + (1 – T)(D/E)], we can calculate bU as bU = b/[1 + (1 – T)(D/E)].

bU = 1.3/[1 + (1 – 0.35)($6,000,000/$12,000,000)]bU = 1.3/[1 + 0.325]bU = 0.9811.

23. HAMADA EQUATION Cyclone Software Co. is trying to establish its optimal capitalstructure. Its current capital structure consists of 25% debt and 75% equity; however, theCEO believes that the firm should use more debt. The risk-free rate, rRF, is 5%; the marketrisk premium, RPM, is 6%; and the firm’s tax rate is 40%. Currently, Cyclone’s cost of equityis 14%, which is determined by the CAPM. What would be Cyclone’s estimated cost ofequity if it changed its capital structure to 50% debt and 50% equity?

Facts as given: Current capital structure: 25% debt, 75% equity; rRF = 4%; rM – rRF = 5%; T = 40%; rs = 12%.

Step 1:Determine the firm’s current beta.rs = rRF + (rM – rRF)b

12% = 4% + (5%)b8% = 5%b1.6 = b.

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Step 2:Determine the firm’s unlevered beta, bU.bU = bL/[1 + (1 – T)(D/E)]

= 1.6/[1 + (1 – 0.4)(0.25/0.75)]= 1.6/1.2= 1.333.

Step 3:Determine the firm’s beta under the new capital structure.bL = bU[1 + (1 – T)(D/E)]

= 1.333[1 + (1 – 0.4)(0.4/0.6)]= 1.333(1.4)= 1.866 1.87.

Step 4:Determine the firm’s new cost of equity under the changed capital structure.rs = rRF + (rM – rRF)b

= 4% + 5%(1.87)= 13.35%.

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24. RECAPITALIZATION Tapley Inc. currently has total capital equal to $5 million, has zero debt,

is in the 40% federal-plus-state tax bracket, has a net income of $1 million, and distributes40% of its earnings as dividends. Net income is expected to grow at a constant rate of5% per year, 200,000 shares of stock are outstanding, and the current WACC is 13 40%.The company is considering a recapitalization where it will issue $1 million in debt anduse the proceeds to repurchase stock. Investment bankers have estimated that if thecompany goes through with the recapitalization, its before-tax cost of debt will be 11%and its cost of equity will rise to 14 5%.a. What is the stock’s current price per share (before the recapitalization)?b. Assuming that the company maintains the same payout ratio, what will be its stockprice following the recapitalization? Assume that shares are repurchased at the pricecalculated in part a.

a. Dividends = 0.4 × $1,000,000 = $400,000. So, the current dividend per share, D0, = $400,000/200,000 = $2.00. D1 = $2.00(1.03) = $2.06. Therefore, P0 = D1/(rs – g) = $2.06/(0.123 – 0.03) = $22.15.

b. Step 1:Calculate EBIT before the recapitalization:EBIT = $1,000,000/(1 – T) = $1,000,000/0.6 = $1,666,667.Note: The firm is 100% equity financed, so there is no interest expense.

Step 2:Calculate net income after the recapitalization:[$1,666,667 – 0.10($2,000,000)]0.6 = $880,000.

Step 3:Calculate the number of shares outstanding after the recapitalization:200,000 – ($2,000,000/$22.15) = 109,707 shares.

Step 4:Calculate D1 after the recapitalization:D0 = 0.4($880,000/109,707) = $3.2085.D1 = $3.2085(1.03) = $3.3048.

Step 5:Calculate P0 after the recapitalization:P0 = D1/(rs – g) = $3.3048/(0.155 – 0.03) = $26.4384 $26.44.

25. RECAPITALIZATION Currently, Bloom Flowers Inc. has a capital structure consisting of20% debt and 80% equity. Bloom’s debt currently has an 8% yield to maturity. The risk-freerate (rRF) is 5%, and the market risk premium (rM − rRF) is 6%. Using the CAPM, Bloomestimates that its cost of equity is currently 12 5%. The company has a 40% tax rate.

a. What is Bloom’s current WACC?b. What is the current beta on Bloom’s common stock?c. What would Bloom’s beta be if the company had no debt in its capital structure? (Thatis, what is Bloom’s unlevered beta, bU?)Bloom’s financial staff is considering changing its capital structure to 40% debt and 60%equity. If the company went ahead with the proposed change, the yield to maturity onthe company’s bonds would rise to 9 5%. The proposed change will have no effect on thecompany’s tax rate.d. What would be the company’s new cost of equity if it adopted the proposed change in

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capital structure?e. What would be the company’s new WACC if it adopted the proposed change in capitalstructure?f. Based on your answer to part e, would you advise Bloom to adopt the proposedchange in capital structure? Explain.

a. Using the standard formula for the weighted average cost of capital, we find:WACC= wdrd(1 – T) + wcrs

= (0.25)(7%)(1 – 0.4) + (0.75)(14.5%)= 11.93%.

b. The firm's current levered beta at 25% debt can be found using the CAPM formula.

rs = rRF + (rM – rRF)b14.5% = 6% + (7%)b

b = 1.2143.

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c. To “unlever” the firm's beta, the Hamada equation is used.bL = bU[1 + (1 – T)(D/E)]

1.2143= bU[1 + (1 – 0.4)(0.25/0.75)]1.2143= bU(1.20)

bU = 1.0119.

d. To determine the firm’s new cost of common equity, one must find the firm’s new beta under its new capital structure. Consequently, you must “relever” the firm's beta using the Hamada equation:bL,40% = bU[1 + (1 – T)(D/E)]bL,40% = 1.0119[1 + (1 – 0.4)(0.4/0.6)]bL,40% = 1.0119(1.4)bL,40% = 1.4167.

The firm's cost of equity, as stated in the problem, is derived using the CAPM equation.rs = rRF + (rM – rRF)brs = 6% + (7%)1.4167rs = 15.92%.

e. Again, the standard formula for the weighted average cost of capital is used. Remember, the WACC is a marginal, after-tax cost of capital and hence the relevant before-tax cost of debt is now 10.5% and the cost of equity is 15.92%.WACC= wdrd(1 – T) + wcrs

= (0.4)(10.5%)(1 – 0.4) + (0.6)(15.92%)= 12.07%.

f. The firm should be advised not to proceed with the recapitalization as it causes the WACC to increase from 11.93% to 12.07%. As a result, if the firm proceeded with the recapitalization it would lead to a decrease in firm value.

26. WACC AND OPTIMAL CAPITAL STRUCTURE Elliott Athletics is trying to determine itsoptimal capital structure, which now consists of only debt and common equity. The firmdoes not currently use preferred stock in its capital structure, and it does not plan to do soin the future. Its treasury staff has consulted with investment bankers. On the basis of thosediscussions, the staff has created the following table showing the firm’s debt cost atdifferent debt levels:

Elliott uses the CAPM to estimate its cost of common equity, rs, and estimates that the riskfreerate is 5%, the market risk premium is 6%, and its tax rate is 40%. Elliott estimates that

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if it had no debt, its “unlevered” beta, bU, would be 1 2.a. What is the firm’s optimal capital structure, and what would be its WACC at theoptimal capital structure?b. If Elliott’s managers anticipate that the company’s business risk will increase in thefuture, what effect would this likely have on the firm’s target capital structure?c. If Congress were to dramatically increase the corporate tax rate, what effect would thislikely have on Elliott’s target capital structure?d. Plot a graph of the after-tax cost of debt, the cost of equity, and the WACC versus(1) the debt/capital ratio and (2) the debt/equity ratio.

Tax rate = 40%; rRF = 5.0%; bU = 1.2; rM – rRF = 6.0%

From data given in the problem and table we can develop the following table:Levered

wd wc D/E rd rd(1 – T) betaa rsb WACCc

0.00 1.00 0.0000 7.00% 4.20% 1.20 12.20% 12.20%0.20 0.80 0.2500 8.00 4.80 1.38 13.28 11.580.40 0.60 0.6667 10.00 6.00 1.68 15.08 11.450.60 0.40 1.5000 12.00 7.20 2.28 18.68 11.790.80 0.20 4.0000 15.00 9.00 4.08 29.48 13.10

Notes:a These beta estimates were calculated using the Hamada equation, bL = bU[1 + (1 – T)(D/E)].b These rs estimates were calculated using the CAPM, rs = rRF + (rM – rRF)b.c These WACC estimates were calculated with the following equation: WACC = wd(rd)(1 – T) + (wc)(rs).

a. The firm’s optimal capital structure is that capital structure which minimizes the firm’s WACC. Elliott’s WACC is minimized at a capital structure consisting of 40% debt and 60% equity. At that capital structure, the firm’s WACC is 11.45%.

b. If the firm’s business risk increased, the firm’s target capital structure would consist of less debt and more equity.

c. If Congress dramatically increases the corporate tax rate, then the tax deductibility of interest would be greater the higher the tax rate. This should lead to an increase in the firm’s use of debt in its capital structure.

d.

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Capital Costs Vs. D/(D+E)

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rd(1 - T)

The top graph is like the one in the textbook, because it uses the D/(D +E) ratio on the horizontal axis. The bottom graph is a bit like MM showed in their original article in that the cost of equity is linear and the WACC does not turn up sharply. It is not exactly like MM because it uses D/(D + E) rather than D/V, and also because MM assumed that rd is constant whereas we assume the cost of debt rises with leverage.

Note too that the minimum WACC is at the D/(D + E) and D/E levels indicated in the table, and also that the WACC curve is very flat over a broad range of debt-to-capital ratios, indicating that WACC is not sensitive to debt over a broad range. This is important, as it demonstrates that management can use a lot of discretion as to its capital structure, and that it is OK to alter the debt-to-capital ratio to take advantage of market conditions in the debt and equity markets, and to increase the debt-to-capital ratio if many good investment opportunities are available.

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Capital Costs Vs. D/E

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