DUKE UNIVERSITYFuqua School of Business

FINANCE 351 – CORPORATE FINANCEFinal Exam

Prof. Simon Gervais Fall 2011 – Term 2

Part I: Multiple Choice Questions(5 points per question for a total of 25 points)

1. Suppose that the only market imperfection comes from the presence of corporate taxes. Whichof the following statements are true?

I. As the firm issues more debt, the cost of equity (rE) increases.

II. As the firm issues more debt, the weighted average cost of capital (WACC) increases.

III. As the firm issues more debt, the return on assets (rA) increases.

A) I and II B) I and III C) II and III D) I, II and III

E) less than two statements are true.

2. In the figure below, the sloping straight line represents the opportunities for investment inthe capital market, and the solid curved line represents the opportunities for investment inplant and machinery (real assets). The company’s only asset at present is $6.3 million in cash.

$ today

$ tomorrow

7.56.33.9

4.32

9

7.5

(Note that the figure is not drawn to scale, and that all the numbers are in millions)

Let I denote the optimal amount to be invested in real assets, and N the net present valueof that investment. What is N − I?

A) −2.4 million B) −1.2 million C) 0 D) 1.2 million E) 2.4 million

3. Suppose that the only market imperfection comes from the presence of corporate taxes, andthat the corporate tax rate is 40%. Srorrim Inc. is a firm whose operations generate aperpetual stream of constant annual earnings that are paid to investors every year (i.e., thefirm is not expected to grow). Srorrim is financed with equity and debt (and its debt ispermanent). Its equity has a beta of 1.3 and is currently worth $10 million. Its debt isrisk-free. If the (unlevered) asset beta of Srorrim’s operations is equal to 1.0, how much ofthe firm’s total market value comes from tax shields?

A) $2.0 million B) $4.0 million C) $5.0 million D) $7.5 millionE) $10.0 million

4. Suppose that capital markets are perfect except for the presence of corporate and personaltaxes. Upon announcing its plan to issue $40 million worth of debt, the total market valueof Iawgom Inc. went from $100 million to $110 million. The corporate tax rate is 40%, andinvestors pay 20% of their income from debt in taxes. At what rate do investors pay taxeson equity income?

A) 0% B) 10% C) 20% D) 25% E) 33%

5. Daehsitrop Inc. and Ratsyzzam Corp. are both all-equity financed and are in the same riskclass (i.e., their operations/assets have similar risk). Next year, it is expected that Daehsitropwill pay a dividend of $3.50 per share, after which its stock price is expected to be $50.00.Ratsyzzam does not pay dividends. Its current stock price is $40.00, and it is expected tobe $47.20 in one year from now. Assume that dividends are taxed at 40%, and that capitalgains are taxed at 20%. What is Daehsitrop’s current stock price?

A) $43.78 B) $44.15 C) $44.60 D) $45.34 E) $46.76

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Part II: Essay Questions(75 total points)

1. (20 points total) The Ringoleum Corporation, a manufacturer of drum sets, is all-equityfinanced. Its 20,000 shares outstanding are currently trading at $23.40 each. The CEO andCFO of Ringoleum, Mrs. Richard and Mr. Starkey, have been approached by an investmentbank, Lizard Brothers, to arrange a management buyout of Ringoleum.

The buyout would involve buying all the shares outstanding for $35 each and taking the firmprivate. To pay for the shares, management will use $75,000 (of their own money) in cash,and has already arranged a bank loan for $600,000 at a rate of 15% (which is a fair marketrate given the risk of the new debt). The principal on the loan is to be repaid in 6 equalend-of-year installments of $100,000 and, every year, the firm will pay the interest on theoutstanding principal. The remaining $25,000 will be provided by Lizard Brothers, who willacquire a fraction of Ringoleum’s equity by doing so.

The plan behind the buyout is to take the firm public again in two years. At that point,Ringoleum will repay the outstanding principal on its loan, and lever up the firm to a long-run target debt-to-value (D/V ) ratio of 40%. It is also expected that Ringoleum will be ableto borrow at a (fair market) rate of 10% at that point.

Mr. Starkey has produced the following pro forma income statement for the next two years.The firm’s net working capital is not expected to change for a while, and the firm is notexpected to have any new capital expenditures.

End of Year1 2

Revenues 270,000 290,000Cost of goods sold 162,000 178,560Depreciation 18,000 16,440

Given the risk of the firm’s assets and operations, the appropriate discount rate for these cashflows is 20% when they are all-equity financed. The corporate tax rate is 40%.

(a) (4 points) Calculate Ringoleum’s free cash flows for the next two years.

(b) (6 points) Assuming that the deal goes through, use APV to calculate the value ofRingoleum coming from the first two years (the “LBO years”), as estimated by manage-ment and the investment bank.

(c) (4 points) Management and the investment bank think that the firm’s free cash flowswill grow at an annual rate of 10% (i.e., FCF3 = 1.10 × FCF2, and so on). Using theweighted average cost of capital (WACC, not RADR), calculate the terminal value ofRingoleum at the end of year 2. In your calculations of the weighted average cost ofcapital, do not assume that the debt beta is zero when levering/unlevering. Also, assumethat the debt is permanent (i.e., never rebalanced).

(d) (2 points) How much of this terminal value comes from debt tax shields?

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(e) (2 points) Calculate the present value of this terminal value at time 0 by discountingthe values of assets and debt tax shields at their appropriate rate.

Hint : The rate is different for the two parts.

(f) (2 points) According to management and the investment bank, what is the total valuecreated by the LBO (relative to the current market value of Ringoleum)?

2. (10 points total) Xurtlayor has $1,000 in face value of discount bonds outstanding to be paidoff next year (i.e., these bonds promise $1,000 to debtholders next year). The company has$400 in cash, that it plans to invest at the risk-free rate (which we assume to be zero) for ayear. Also, under its current real investment plan, the firm’s cash flows from operations nextyear will be $400 with probability 1

2 (the bad state) and $2,100 with probability 12 (the good

state). That is, under its current investment policy, the firm will have $800 (= $400 + $400)in the bad state and $2,500 (= $400 + $2,100) in the good state to distribute to investorsnext year. After that, the firm will cease to operate.

Now suppose that Xurtlayor has access to two different projects, both initially costing $400,to be paid at the beginning of the year using the firm’s cash.

• Project I will pay off $200 in the bad state and $500 in the good state at the end of theyear.

• Project II will pay off $450 in the bad state and $450 in the good state at the end of theyear.

In answering the following questions, assume that the risk of Xurtlayor’s operations is diver-sifiable and so the discount rate for all cash flows (including those of the new projects) is therisk-free rate, which is zero. Also, assume that there are no taxes (personal or corporate).

(a) (2 points) Calculate the net present value of each project.

(b) (5 points) If Xurtlayor undertakes one and only one project, and the CEO acts in thebest interest of the shareholders, which project will she select.

(c) (3 points) In the absence of debt, what project would have been selected? What is theexpected agency cost to the firm from having $1,000 in debt due?

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3. (30 points total) The shares of Ed Skyfoods, Inc., are currently trading at $9.00 each, andthere are 10,000 such shares outstanding. The firm borrows at a rate of 11.6%, and thecurrent value of its debt is $60,000. Ed Skyfoods is considering undertaking a new projectthat will require an initial investment (at time 0) of $14,000 ($4,000 in working capital and$10,000 in plant and equipment). The firm’s CFO has produced the following pro formaincome statement and asset requirements projections for the first few years of the project(assume that time 0 is 1980).

End of Year1980 1981 1982 1983

Revenues 0 24,000 31,000 38,000Costs of goods sold 0 26,000 29,000 33,000Depreciation 0 2,000 2,000 3,000

Net working capital∗ 4,000 6,000 3,000 0Plant and equipment∗∗ 10,000 9,000 9,000 8,000∗Current assets net of current liabilities at the end of the year.∗∗End-of-year book value of all plant and equipment (net of depreciation).

Although the financing of this new project will not significantly differ from how Ed Skyfoodscurrently finances all of its assets (i.e., same debt/equity mix and same borrowing rate),it is estimated that the risk of the new project is not typical for Ed Skyfoods. Instead it isestimated that the project is similar in risk to the operations of two publicly traded companies,Azure Aisle and Air Foods. In addition to knowing that both firms borrow at the risk-freerate, you have access to the following information about these two firms.

Azure AirAisle Foods

Debt/equity ratio 0.30 0.50Equity beta (βE) 1.15 1.50

The corporate tax rate (which all three firms are subject to) is 50%. The risk-free rate is10%, and the market risk premium is 8%. Unless appropriate, you should not assume thatthe debt beta is zero when levering/unlevering. Also, assume that all debt is permanent (i.e.,never rebalanced).

(a) (15 points) Calculate the project’s free cash flows for the period 1980-1983. Assume thatEd Skyfoods’ other operations are very profitable (so that any negative profit from theproject will be used to shield the firm’s other profits from taxes, i.e., no carry-backs orcarry-forwards are necessary).

(b) (15 points) Assuming that these free cash flows are expected to remain constant (at their1983 level) in perpetuity after 1983, use WACC to calculate the project’s net presentvalue. Use both comparable firms (with equal weights) in your estimation of the WACC.

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4. (15 points total) Ognet Aloy (OA) Inc. purchased a building for $1 million ten years ago. Thebuilding is being depreciated (to zero) over twenty years on a straight-line basis. Ognet Aloyis considering a sale and leaseback transaction with the Atlov Sram (AS) Corporation. In thetransaction, Ognet Aloy would sell the building for 600,000 to Atlov Sram, and lease it backfor ten years. The transaction would allow Atlov Sram to reset the building’s depreciationbasis to $600,000, and to depreciate it straight-line down to zero over ten years. At the endof ten years, Atlov Sram would sell the building back to Ognet Aloy for $1 (which you canignore in your calculations).

Ognet Aloy currently borrows at a rate of 12% and its marginal tax rate is 25%. Atlov Sramalso borrows at a rate of 12%, and pays corporate taxes at a rate of 50%. The ten annuallease payments from Ognet Aloy to Atlov Sram are to be made at the end of each year, andassume that they are tax-deductible for Ognet Aloy and taxable revenues for Atlov Sram.

(a) (8 points) What is the maximum lease payment that makes the sale and leasebackcontract more advantageous (relative to owning the building for ten more years) forOgnet Aloy?

(b) (7 points) What is the minimum lease payment that Atlov Sram is willing to charge?

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Solutions: Multiple Choice Questions

1. E. (I) TRUE. As the firm issues more debt, the equity becomes riskier and so requires ahigher return. (II) FALSE. As the firm issues more debt, the weighted average cost of capitaldecreases, because of the tax deductibility of interest payments on the debt. (III) FALSE.The return on assets never changes with the firm’s capital structure.

2. B. The amount invested in real assets is given by

I = 6.3 million − 3.9 million = 2.4 million.

The net present value of the investment is

N = 7.5 million − 6.3 million = 1.2 million.

Therefore, N − I = −1.2 million.

3. A. Since the debt is riskless, we have βD = 0. Thus we know that βE and βA must satisfy

βE = βA +

(

D

E

)

(1− tc)βA ⇔ 1.3 = 1.0 +

(

D

E

)

(1− 0.40)(1.0).

From this, we infer that DE

= 0.5. This implies that Srorrim’s debt is worth D = 0.5 ×

$10 million = $5 million. The total value of Srorrim’s debt tax shield is therefore

PV (debt tax shield) = tcD = 0.40× $5 million = $2 million.

4. A. The value of the firm increases by 10, which in this economy should be equal to t∗D =t∗ × 40. Thus, we must have

0.25 = t∗ = 1−(1− tc)(1− tE)

1− tD= 1−

(1− 0.40)(1 − tE)

1− 0.20.

This implies that tE = 0.

5. C. The expected after-tax rate of return on Ratsyzzam’s stock is (47.20−40.00)(1−0.20)40.00 = 14.4%.

Assume that Daehsitrop’s current stock price is P0. Given that the two firms/stocks have thesame risk, the expected after-tax rate of return on Daehsitrop’s stock must also be equal to14.4%:

0.144 =3.50(1 − 0.40) + (50.00 − P0)(1− 0.20)

P0.

Solving for P0, we get P0 = 44.60.

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Solutions: Essay Questions

1. (20 points total)

(a) (4 points) Ringoleum’s free cash flows for the next two years are calculated as follows.

End of Year1 2

Revenues 270,000 290,000− Cost of goods sold 162,000 178,560− Depreciation 18,000 16,440

EBIT 90,000 95,000− Taxes (@40%) 36,000 38,000

Unlevered net income 54,000 57,000+ Depreciation 18,000 16,440

Free cash flows 72,000 73,440

(b) (6 points) The adjusted present value (V 1-2

L ) for the first two years consists of two parts:the unlevered value of the cash flows (V 1-2

U ), and the present value of the interest taxshields. We can discount the free cash flows at rA = 20% to find

V 1-2

U =72,000

1.20+

73,440

(1.20)2= 111,000.

The debt repayment schedule is as follows (only the first two years are needed):

0 1 2 · · · 5 6

Debt outstanding 600,000 500,000 400,000 · · · 100,000 0Payments on the debt 190,000 175,000 · · · 130,000 115,000Interest paid 90,000 75,000 · · · 30,000 15,000Principal paid 100,000 100,000 · · · 100,000 100,000Interest tax shield 36,000 30,000 · · · 12,000 6,000

Therefore,

PV (interest tax shields) =36,000

1.15+

30,000

(1.15)2= 53,989,

andV 1-2

L = 111,000 + 53,989 = 164,989.

(c) (4 points) To find the terminal value at the end of year 2 (TV ), we need to discountthe free cash flows in years 3, 4, 5, and so on, at the weighted average cost of capital(WACC). To calculate this rate, we first need to calculate the cost of equity (rE) bylevering up rA (using rD = 10% on the new debt at that point):

rE = rA +

(

D

E

)

(1− tc)(rA − rD) = 0.20 +

(

0.40

0.60

)

(1− 0.40)(0.20 − 0.10) = 0.24.

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The weighted average cost of capital is therefore1

WACC =

(

D

V

)

(1− tc)rD +

(

E

V

)

rE = (0.40)(1 − 0.40)(0.10) + (0.60)(0.24) = 0.168.

The free cash flow in year 3 is 73,440(1.10) = 80,784, so that

TV =80,784

0.168 − 0.10= 1,188,000.

(d) (2 points) We need to first find the unlevered terminal value (TVU ) at the end of year 2.This is done by using rA instead of WACC to discount the growing perpetuity of thepost-LBO years:

TVU =80,784

0.20 − 0.10= 807,840.

The difference between TV and TVU represents the present value of debt tax shields,that is,

TV (debt tax shields) = 1,188,000 − 807,840 = 380,160.

(e) (2 points) To find the present value (at time 0) of the terminal value, we discount theasset part of the terminal value at rA = 20% and the debt tax shield part at rD = 15%(which is the rate on the debt for the LBO years):

PV (terminal value) =807,840

(1.20)2+

380,160

(1.15)2= 848,456.

(f) (2 points) The total value of Ringoleum, as estimated by management and the investmentbank, is

VL = V 1-2

L + PV (terminal value) = 164,989 + 848,456 = 1,013,445.

The total value created by the LBO is therefore 1,013,445− (20,000× 23.40) = 545,445.

2. (10 points total)

(a) (2 points) The net present value of each project is calculated as follows:

NPVI = −400 +

[

1

2(200) +

1

2(500)

]

= −50,

NPVII = −400 +

[

1

2(450) +

1

2(450)

]

= 50,

(b) (5 points) To answer this question, we need to calculate the value of the equity after eachof the three projects is undertaken. The CEO will undertake the project that maximizes

1Alternatively, we could have calculated the weighted average cost of capital as WACC = rA(

1− tcD

V

)

= 0.20(1−0.40 × 0.40) = 0.168.

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the value of the equity. With project I, the claims of the debtholders and equity holderswill generate the following end-of-year payoffs and will have the following values.

State

Bad Good(1/2) (1/2) Value

Debt 600 1,000 800Equity 0 1,600 800

Total 600 2,600 1,600

With project II, the claims of the debtholders and equity holders will generate thefollowing end-of-year payoffs and will have the following values.

State

Bad Good(1/2) (1/2) Value

Debt 850 1,000 925Equity 0 1,550 775

Total 850 2,550 1,700

The equity is worth more with project I, which will therefore be chosen by the CEO.

(c) (3 points) In the absence of debt, the project with the higher net present value wouldbe chosen, that is, project II. Because the firm is worth $1,700 with this project andonly $1,600 with the project chosen by the CEO (project I), the expected agency costis $100.

3. (30 points total)

(a) (15 points) The taxable profits of the project are calculated as follows.

End of Year1980 1981 1982 1983

Revenues 0 24,000 31,000 38,000− Costs of goods sold 0 26,000 29,000 33,000− Depreciation 0 2,000 2,000 3,000

EBIT 0 -4,000 0 2,000− Taxes (@50%) 0 -2,000 0 1,000

Unlevered net income 0 -2,000 0 1,000

We need to make three adjustments to find the project’s free cash flows: add deprecia-tion back (this is given), subtract changes in net working capital, and subtract capitalexpenditures. The changes in net working capital are as follows.

End of Year1980 1981 1982 1983

Net working capital 4,000 6,000 3,000 0Change in NWC 4,000 2,000 -3,000 -3,000

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Finally, the net investment in plant and equipment is calculated as

(

Net invest. in P&E)

t=

(

Book value)

t−

(

Book value)

t−1+

(

Depreciation)

t.

This is done in the following table.

End of Year1980 1981 1982 1983

Plant and equipment 10,000 9,000 9,000 8,000Depreciation 0 2,000 2,000 3,000

Net investment in P&E 10,000 1,000 2,000 2,000

We can now calculate the free cash flows for the project.

End of Year1980 1981 1982 1983

Unlevered net income 0 -2,000 0 1,000+ Depreciation 0 2,000 2,000 3,000− Change in NWC 4,000 2,000 -3,000 -3,000− Net investment in P&E 10,000 1,000 2,000 2,000

Free cash flows -14,000 -3,000 3,000 5,000

(b) (15 points) We use the comparable firms to get an estimate of βA for the project. Wecalculate each comparable firm’s (unlevered) asset by unlevering its equity beta (andusing the fact that each firm’s debt beta is zero):

βAA

A =βAA

E

1 +(

DE

)

AA

(1− tc)=

1.15

1 + (0.30)(1 − 0.50)= 1.00,

βAF

A =βAF

E

1 +(

DE

)

AF

(1− tc)=

1.50

1 + (0.50)(1 − 0.50)= 1.20.

We use βA = 1.00+1.202 = 1.10 for the project. We need to relever this beta to get the

equity beta for the project. Since Ed Skyfoods borrows at rD = 11.6%, we have:

rD = rf + βD(rm − rf ) ⇔ 0.116 = 0.10 + βD(0.08) ⇒ βD = 0.20.

We also know that, for Ed Skyfoods, E = 9.00 × 10,000 = 90,000 and D = 60,000, sothat the project’s debt-to-value ratio is 60,000

90,000+60,000 = 0.40 (since the project’s financingis the same as that of the firm). Thus the project’s equity beta is given by

βE = βA +

(

D

E

)

(1− tc)(βA − βD) = 1.10 +0.40

0.60(1− 0.50)(1.10 − 0.20) = 1.40.

Using the CAPM, we find the cost of equity for the project,

rE = rf + βE(rm − rf ) = 0.10 + 1.40(0.08) = 21.2%,

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and finally the weighted average cost of capital for the project,

WACC =

(

D

V

)

(1− tc)rD +

(

E

V

)

rE

= (0.40)(1 − 0.50)(0.116) + (0.60)(0.212) = 15.04%.

Note that the weighted average cost of capital can also be calculated as follows:

rA = rf + βA(rm − rf ) = 0.1 + (1.1)(0.08) = 18.8%

⇒ WACC =

(

1−D

Vtc

)

rA =[

1− (0.40)(0.50)]

(0.188) = 15.04%.

The net present value of the project is therefore

NPV = −14,000 −3,000

1.1504+

3,000

(1.1504)2+

5,000

0.1504

1

(1.1504)2= 10,779.34.

Note also that this value can be calculated as follows:

NPV = −14,000 −3,000

1.1504+

3,000

(1.1504)2+

5,000

(1.1504)3+

5,000

0.1504

1

(1.1504)3= 10,779.34.

4. (15 points total)

(a) (8 points) Suppose the lease payment is L, for an after-tax lease payment of L(1−0.25).If Ognet Aloy sells the building to Atlov Sram, it will receive $600,000 for an assetthat has a current book value of $500,000 (it has been depreciated for ten years at1M/20 = 50,000 a year). Thus Ognet Aloy will be taxed on $100,000, and so willreceive a net after-tax payment of $600,000 − $100,000(0.25) = $575,000. The annualdepreciation tax shield lost is (50, 000)(0.25) = 12,500. The incremental cash flows forOgnet Aloy’s “lease versus buy” decision are as follows.

0 1 to 10

Sale of building 575,000After-tax lease payments −L(1− 0.25)Depreciation tax shield lost −12,500

Net cash flows 575,000 −12,500 − L(1− 0.10)

The maximum lease payment that Ognet Aloy is willing to pay can be found by dis-counting the above net cash flows at a discount rate of 12% × (1 − 0.25) = 9%, settingthe resulting net present value equal to zero, and solving for L:

0 = 575,000 −12,500 + L(1− 0.25)

0.09

[

1−1

(1.09)10

]

⇒ L = 102,795.40.

(b) (7 points) Suppose again that the lease payment is L. Atlov Sram’s after-tax leaseincome is then L(1− 0.50). The annual depreciation tax shield is 600,000

10 (0.50) = 30,000.

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Atlov Sram’s cash flows are as follows.

0 1 to 10

Purchase price −600,000After-tax lease income L(1− 0.50)Depreciation tax shield 30,000

Net cash flows −600,000 30,000 + L(1− 0.50)

The minimum lease payment that Atlov Sram is willing to charge can be found bydiscounting the above net cash flows at a discount rate of 12%× (1−0.50) = 6%, settingthe resulting net present value equal to zero, and solving for L:

0 = −600,000 +30,000 + L(1− 0.50)

0.06

[

1−1

(1.06)10

]

⇒ L = 103,041.55.

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