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Sheet1

Spring 1998Problem 1

Bond Rating = BBB

Interest Rate = 9.00%

After-tax Cost of Debt = 5.40%

Unlevered Beta = 1.06/(1+(1-0.4)(.1111)) = 0.993756211

Beta at 25% D/E Ratio = 0.99(1+0.6(.25)) = 1.142819643

Cost of Equity = 7% + 1.14 (5.5%) = 13.27%

Cost of Capital = 5.40% (.2) + 13.27% (.8) = 11.70%

Problem 2

Change in Firm Value = (250 + 50) (.11-.10)(1.05)/(.10-.05) = 63

Change in stock price = 63/10 = $ 6.30 ($10.50 if you assume buyback at current price)

Problem 3

(100/250) (2) + (150/250) (X) = 5

Solve for X, X = 7 years


Value of Bank Loan = 4 (PVA,7%,5) + 50/(1.07)^5 = $52.05

Value of Bonds Outstanding = $50.00

PV of Operating Leases = 10 (PVA,7%,7) = $53.89

Market Value of Outstanding Debt= $155.94

Market Value of Equity = 15* 10 = $150.00

Debt Ratio = 155.94/(150+155.94) = 50.97%

Cost of Equity = 6% + 1.2 (5.5%) = 12.60%

Cost of Capital = 12.60%(.49) + 7% (1-.4)(.51) = 8.32%

Adjusted EBIT = 40 + 53.89*0.7 = $43.77

Adjusted BV of Capital = 50 + (50 + 50 + 53.89) = 203.89

Adjusted Return on Capital = 43.77 (1-.4)/203.89 = 12.88%

Problem 2

Change in Firm Value = 3 * 10 = $30.00

Firm Value (Chg in WACC) (1.05)/(WACC(after)-.05) = 250 (Chg in WACC)(1.05)/(.10 -.05)= 30

Chg in WACC = 0.57%

WACC before = 10.57%

Ke (.8) + 8%(1-.4) (.2) = 10.57%

Cost of Equity before transaction = (.1057-.0096)/.8 = 12.01%

Problem 3

Value of firm before expansion = 300 + 70*10 = 1000

Duration of assets after expansion = 7.5 (1000/1250) + 1 (250/1250) =

Weighted Duration of Assets has to be equal to 6.2years

(200/550)(1) + (100/550)(4) + (250/550) (X) = 6.2

Solve for X

X = 11.24 years

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Spring 1999 (A)Problem 1

PV of operating leases = 1,408$

Straight Debt portion of convertible debt = 1,798$Total Debt = 3,206$

EquityValue of stock = 3,000$Value of conversion option = 2500-1798= 702$Value of Equity = 3,702$

Cost of Equity = 5.5% + 1.25(6.3%) = 13.375%Cost of Debt (after-tax) = 7.5%(1-.4)= 4.50%

Cost of Capital = 13.375% (3702/6908) + 4.50% (3206/6908) = 9.26%

Problem 2

Change in Firm Value = 500

5000 (.10 - WACC after)/WACC after = 500Solve for WACC after,WACC after = 500/5500 = 9.09%Cost of Equity after = 5.5% + 1 (6.3%) = 0.11811.8(X) + 5% (1-X) = 9.09%Solve for X,

X = (9.09-5)/6.8 = 60%Debt to Capital ratio = 40%

Problem 3

Cody's should have long term debt: Negative coefficient suggests duration of 7.5 yearsBAM should have floating rate debt: Oper income tends to move with inflation


a. False. It has to be weighed off against the increase in both costs

b. True. It will reduce the marginal tax advantage of debt

c. True. The net operating loss carry forward will reduce the tax benefit of the debt. (No matter how the

the argument is structured, the firm without net operating losses will be able to borrow more money and get

a larger tax savings. The NOL will reduce the income available from which interest expenses can be deducted.

d. False. If you are more uncertain about future investment needs, you will value flexibility more and borrow less.

Problem 2

Current cost of capital = Cost of equity (because firm has no debt) = 9.20%

Change in firm value = .1375 = (Cost of capital before - Cost of capital after)/Cost of capital after0.1375 = (0.092 - Cost of capital after)/Cost of Capital after

Solving,

Cost of capital after = 0.092/(1+.1375) = 8.09%

Cost of equity after = 10.48%

Cost of debt after = 4.5%

10.48% (1-X) + 4.5% (X) = 8.09%

Solving for X,

X = 40%

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Problem 3

Duration of assets = 7

Existing Debt = 1 (duration of this debt = 4 years)

New Debt = 3

(1/(1+3)) (4) + (3/(1+3)) X = 7 ! Since the asset mix does not change, the dur

SolvingDuration of new debt = 8

Proportion on new debt that has to be 2 year debt = 25% (.25(2) + .75(10

Problem 1

10.72%

3.90%

8.47%

50%

100.00%

0.8

New Beta = 1.28

12.0400%

4.05%

8.05%

21.7391304

$6.37

$79.13

$0.59

Problem 2

2000 ! 1000/.5500

X = .25


Part a: Current cost of capital

Beta = 1.15 Math error: -0.5Cost of equity = 9.85% forgot to after-tax cost of deCost of capital = 9.23% ! Debt ratio = 10%

Part b: New cost of capitalUnlevered beta = 1.078125 ! Forgot to adjNew levered beta = 1.35535714 ! Don't forget to unlever and relever ! Math errors:New cost of equity = 10.67%

New cost of capital = 8.73%

Let X be the proportion of the debt that is 5-year debt at optimal

X (4) + (1-X) (8) = 7

The firm has to have $ 125 million in 5-year debt and $ 375 million in 10-year debt

It needs to pay off $ 275 million of 5-year debt and $ 225 million of 10 year debt.

Market value of the firm =Dollar debt at optimal of 25% = ! Don't increase the size of the

Duration of debt at optimal

c. Change in annual financing cost = cannot divide b

Change in firm value =

Change per share = ! Transfer of w

New after-tax cost of debt =

New Cost of capital=

c. Number of shares bought back = ! Since the pric

Unlevered Beta = of the existing i

if you read it as

New cost of equity = ! You lost a poi

If you did this, I

b. New debt to capital ratio =

New debt to equity ratio = ! I gave full cre

Current cost of debt = has to be that y

Current cost of capital = ! 10.72% (.67) + 3.9% (.33) However, this

Spring 2001

a. Current Cost of Equity = ! 5% + 1.04*5.5% ! If you decide t

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Part cBorrow money over next 5 years and pay dividendsIts stockholders like dividends, because it has paid large dividends in the pastIts projects earn less than its cost of capital

Problem 2Cost of capital before = 9.00%Cost of capital after 8.00%Change in firm value = 824 ! Forgot to consider the effect of growth : -1 pointIncrease in dollar debt to get to 25% = 1000Number of shares bought back = 12.5Number of shares left = 37.5 ! Did not adjust the numberIncrease in value per share = 21.9733333 ( Remember that you canno

Problem 3

a. Long term, Dollar, Fixed Rate, Straight ! Heavy infrastructure: Long! U.S. operations: Dollar

! No pricing power: Fixed! Low growth: Straightb. Long term, Mixed Currency, Floating Rate, Straight ! Brand Name: Long term

! Worldwide operations: Mix! Pricing power: You can pa

! High margins and cashfloc. Short term, Dollar, Fixed Rate, Convertible ! Speedy Obsolescence: Sh

! U.S. operations: Dollar! High Uncertainty: Floating

! High growth: Convertible

Spring 2003

Problem 1Current cost of capital = 9%Current debt ratio = 0.25Current after-tax cost of debt = 0.036Current cost of equity = 0.108

Current beta = 1.45

Unlevered beta = 1.21New levered beta = 2.30 ! Debt = 3000; Equity = 2000; Stock buyba

Cost of equity = 14.18%


Change in firm value $393.82 ! (.09 - .0819) (4000)/.0819 ! If you had th

Number of shares = 100Price at which bought back = $33.00Number bought back = 30.3030303 ! 1000/33Number remaining = 69.6969697

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Change in value per share = $4.35 ! (393.82 - (33-30) (30.30))/69.70

Price per share after transaction = $34.35

Problem 2

Duration of existing debt = 2.00

Duration of new debt = 6.50

Currency break downDollar debt = 50%

Euro debt = 50% ! $1 billion of Euro debt needed to get to $ 1 billion (1/3 o


New beta = 1.12

Cost of equity = 0.093984

Interest coverage ratio = 3.75Rating = BB+Cost of debt = 0.06After-tax cost of debt = 0.036

Cost of capital = 7.08%

Problem 2

a. Value of firm = 1050 ! 80*10+250Cost of capital = 10%

Cashflow last year = 50 1050 = 50 (1+g)/ (Cost of capital -g)Expected growth rate= 0.05 1050 = 50 (1+g)/(.10-g)

b. Increase in value from recapitalizationAnnual cost at current cost of capital = 105Annual cost at new cost of capital = 94.5Annual savings = 10.5PV at expected growth rate = 262.5

c. If investors are rational, savings will accrue to all stockholders

Increase in value per share = 3.28125New stock price = 13.28125Number of shares bought back = 18.8235294Number of shares left = 61.1764706

Problem 36 (150/500) + 8 (100/500) + X (250/500) = 10Solving for X,Duration of new bond = 13.2

Since the firm has little pricing power, you would go with fixed rate debtSince half of its revenues come from the EU region, half of its total debt of $ 500 million should be in EurosHence the firm should use 100% Fixed rate, Euro debt

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Value of unlevered firm = 1000 !100 *10 !This firm has

With $250 million in debt, used to buy back stockValue of levered firm = 1025 ! 100 *10.25Tax benefit from additional debt = 100 ! Tax rate * Dollar Debt

Value of levered firm = Value of unlevered firm + Tax benefit - (Probability of bankruptcy * Cost of bankrupt1025 = 1000 + 100 - (X* .30*1000)

Probability of bankruptcy = 25%

Problem 2

Current market value of equity = 4000Market value of debt = 1000Value of firm = 5000

Cost of capital = 10.44% = Cost of equity (.80) + 4.2% (.20)

Cost of equity = 0.12Current beta = 1.75

After debt is repaidNew beta = 1.52173913New cost of equity = 11.09% ! Equal to cost of capital

New firm value = $4,708.24 ! Change in firm value = (.1044-.1109) 500

Problem 3

a. Current asset duration = 0.75(10) + 0.25 (5) = 8.75

b. Expected asset duration if tourism business doubles = (0.75/1.25)(10) + (0.5/1.25) (5) =To solve for duration of new debt

(.5/.75)*6+(.25/.75)*X = 8 ! New debt issue = 0.25

Duration of new debt = 12

Fall 2006Problem 1

a. Cost of equity = 4.5% + 1.00*4% = 8.50%Cost of capital = 8.5% (.9) + 5% (.1) = 8.15%

b. With change in tax status and leverage

Unlevered beta = 0.9 ! 1/ (1+(1-0)(1/9))New levered beta = 1.44 ! 0.9 (1+(1-.4)(50/50))Cost of equity = 10.26%

Cost of capital = 6.93% ! 10.26% (.5)+6%(1-.4)(.5)

c. Change in firm value, assuming 3% growth rateSavings in costs each year = $12.20 ! 1000 (.0815-.0693)Increase in firm value = $310.43 ! 12.20/(.0693-.03)Firm value after transaction = $1,310.43

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Price paid on transaction

For equity = 11.5*90= $1,035.00For debt = $100.00Total price paid = $1,135.00

Value gained in transaction = $175.43

Prtoblem 2

Duration of assets after divestiture = 8.25

Duration of debt after transactiionLet the proportion of 10-year bonds after the repayment be XX(10) + (1-X) (2) = 8.25Solving for X,X = 0.78125

Dollar debt after repayment = 8 -4 = 4 ! Repaid $ 4 billion of debt10-year bonds after the repayment = 3.1252-year bonds after the repayment = 0.875

Repaid amounts10-year bonds = 2.8752-year bonds = 1.125


a. Cost of capital at existing d 8.44% ! 13%(.4)+9%(1-.4)(.6)

b.

Beta at current cost of equity 2 ! (13-5)/4

Unlevered beta = 1.0526

New Debt to Equity Ratio = 42.86% ! (600-300)/(400+300)

Levered Beta = 1.3233083

New cost of equity 10.29%New cost of capital 8.29%

Problem 2

a. Change in firm value = $11.11 ! (80+20)(.10-.09)/.09

b. Number of shares bought b 6

Share of firm value to buy b $6.00 ! 6* $1/share

Share of firm value to remai $5.11

Number of shares remaining 14 ! 20-6

Value increase per remainin $0.37

Problem 3

Duration of existing assets = 8 ! 2(5/20)+10(15/20)

Duration of existing debt = 8

Duration after transaction 6.8 ! 2(5/12.5)+10(7.5/12.5)

To estimate the duration of the new debt8(5/10) + X(5/10) = 6.8


Spring 2008

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Problem 1

Old debt to equity = 0%Current beta = 1.00 ! Cost of equity is 9%; Rf =5% and Risk premium =4%New debt to equity = 42.86% ! 600/1400; Debt used to buy back stockNew beta = 1.2571New cost of equity = 10.03%

New after-tax cost of debt = 3.60%Debt Ratio = 30.00% ! 600/ (600 +1400)

Cost of capital = 8.100%

Problem 2

Current cost of capital = 12%New cost of capital = 10.00%Market value of firm = 1000 ! 200 + 800Annual cost savings = 20

PV of savings (with g=4%) = 333.333333 ! 20/ (.1-.04): Okay if you used (1+g)

New firm value = 1333.33333

b. Value of firm = 1333.33333- Debt = 500 ! Paid off $ 300 million out of $ 800 million

Value of equity = 833.333333Number of shares = 30

Value per share = $27.78

Here is anyother way to get to the same solution

Increase in firm value = $333.33Discount on stock offered = $100.00 ! The discount on the private placementRemaining value savings = $233.33

/ Number of shares= $30.00Increase in value per share= $7.78

Added tos hare price = $27.78

Problem 3 Existing assetNew BusinessValue of business 100 50Duration of assets 7.5 3Weighted duration = 6 ! 7.5(100/150)+3 (50/150)

Existing debt New debtValue 25 50Duration 5 X

Solving for duration of new debt5 * (25/75) + X (50/75) = 6



Estimated v Weoight Cost

Debt 600 0.6 6.00% BBEquity 400 0.4 17.68% 2.28

Capital 1000 10.67%

a. Existing cost of capital

Risk measure

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30.00%

0.4285714

1.2

1.5085714

Weight CostDebt 30.00% 3.90% AEquity 70.00% 0.1305143 1.5085714

10.31%

Problem 2

10.00%

100

9.09%

Beta after = 1.4

12.400%

6.88%

0.5714286

Beta after = 1.3428571

12.06%

6.49%

Problem 3

8.4

1300

1092

108

92


a. Current cost of capitalCost of equity= 10%After-tax Cost of debt = 3.60%Debt/Capital ratio = 20.00%Cost of capital = 8.72%

10-year coupon debt to be paid off = ! Long term debt repaid

Short trm debt to be paid off = ! Short term debt repaid

X (10) + (1-X) (0) = 8.4

84% of the debt has to be 10-year zero coupon debt.

Total debt outstanding after debt retirement = ! Debt outstnading befor

!0-year zero coupon debt = ! 84% of outstanding de

12.06% (700/1100) + X (1-.4) (400/1100)= .0909

Pre-tax cost of debt =

Weighted duration of assets after cash is used = ! Weighted average of ju

Duration of the debt has to be equal to this after the debt is paid off (since cash is being us

Cost of equity after=12.4% (.6) + X(1-.4) (.4) = .0909

Pre-tax cost of debt =

I kept the firm value constant at 1000 in the example above. If you use 1100 as firm value,

D/E ratio after =

Cost of equity after =

all shares gain $1.00.

Solving for cost of capital after,

(Cost of capital before - Cost of capital after)*Existing firm value/ Cost of capital after =100

(.10-Cost of Capital after)*1000/ cost of capital after = 100Cost of capital after =

! Lever the beta, using new debt/equ

New levered beta =

Risk Measure

Current cost of equity = Current cost of capital =

If investors are rationa, all shares get an equal portion of increase in firm value

Increase in firm value = ! Since investors are rati

b. New cost of capital

New debt ratio =

New D/E ratio =

Unlevered beta =

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b. New after-tax cost of debtOperating Income 120New dollar debt = 1500New interest rate= 10%New interest expenses = 150

Adjusted tax rate = 32.00%

New after-tax cost of debt = 6.80%

c. New cost of capitalCurrent beta = 1.2Unlevered beta = 1.0435 ! Used old tax rate to unleverNew Equity value = 1000New D/E ratio = 1.5New levered beta = 2.11 ! Used new tax rate to relever but no penalty if you use 4New cost of equity = 14.54%New after-tax cost of debt = 6.80%New debt to capital ratio = 0.6


Problem 2

Current firm value = 1000Current cost of capital = 9%

Since the shares were bought back at $10.50 and investors are rationalIncrease in firm value = 50 ! Everyone has to receive $0.50 more

Increase in firm value = (Old cost of capital - New cost of capital) Firm value/(New cost of capital - growth rate)

50 = (.09-X) (1000)/(X-.03)Solving for X,


Problem 3

Duration of debt currently = 8Duration of all assets = 8

Value of all assets = 5Value of Manufacturing = 4Value of Financial Services = 1Since the duration of assets = duration of debt9 (4/5) + X (1/5) = 8

X = 4


Current D/(D+E) = 40.00% Error in computing current cost of equity/bCurrent after-tax cost of debt = 4.80% Used wrong debt to equity ratio in unleveriCost of capital = Cost of equity (.60) + 4.80% (.40) = .0972 Did not unlever beta: -1 pointCurrent cost of equity = 13% Did not compute new cost of capital correcCurrent beta (levered) = 2Unlevered beta = 1.42857143

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New cost of equity (capital) = 10.14%

Problem 2

Current value of equity = 400 Used equity value instead of firm value inCurrent value of debt = 200 Used old cost of capital to discount savingCurrent firm value = 600 Math errors: -0.5 point

Current cost of capital = 10.50% Did not compute new stock price correctly:New cost of capital = 10%Annual savings = 3 (Okay if you used (1+g) in numerator)Change in value = 37.5New price per share = 43.75Number of shares bought back 4.57142857

Problem 3

Value of acquirer = 400 Errors on weights for duration of assets: -1Value of target = 400 Errors on weights for duration of debt: -1 pDuration of combined firm's assets 5.5 Math errors: -0.5 point eachTotal debt of combined firm = 600

Duration of debt = (200/600)*4+(100/600)*6+(300/600)*X = 5.50Duration of new debt = 6.33333333

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Alternatively, you can assume that the bank debt is at market value

Market Value of Debt = 153.94

If you do this, the cost of debt will be a weighted average of 7% and

8%, the cost of debt will be around 7.5%.

29.925

6.2

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Common errors1. Reversed the cost of capital before and after in

firm value change calculation.

2. Computed change in firm value incorrectly

3. Did not use after-tax cost of debt

4. Other math errors.

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32.6086956

Common errors

1. Misread the problem to read change by instead of

change to.

tion remains 7. 2. Tried to change asset duration (why?)

3. Set up new debt incorrectly (had two unknowns withone equation)

) = 8) 4. Other errors.

78.2608696

t: -0.5

ust cost of equity : -1-0.5

the total number of shares outstanding.

alth to stockholders selling back stock = (11.50

at which you were buying back the stock was

terest rate (I did take off half a point

25%

t if you did not unlever and relever betas

gave you full credit.

it if you read the increase as 0.25%

ou do not have enough operating income to co

ill mean that the effective tax rate should be 10

o use the effective tax rate, the rationale

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! Closely held, outperformed: Not target of a takeover - No immediacy! ROC < Cost of capital : Don't invest! History of paying dividends: Pay more dividends

f shares for buyback : -1divide by 50 if you are buying back at the current price)

term 0.25 points off for each mistake

d Currencys inflation through Hence, floating rate debt

s : Straight (Some of you made the argument for convertible because of intangibility of asset, but thert term

but Competitive Industry: Fixed - So, I gave credit for both)

k reduces the value of equity

NPV of the new investment, you can add that on.

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total debt)

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no debt. This is the unlevered firm value. 1. Tried to force cost of capital approach t2. Wrong bankrupcty cost: -0.5 to -1

3. Other errors: -0.5 to -1!Note that the stock price increases on the announcement to reflect what the firm will be worth after

y)

1. Error in estimating current cost of equity2. Did not unlever beta: -0.53. Estimated new cost of equity wrong: -0.4. Used old cost of equity instead of capita5. Did not compute PV of annual savings:

6. Did not compute increase in firm value

0/.1109

Current Balance Sheet 1. Weighted bTransporation 0.75 Debt 0.5 2. Did not co

Tourism 0.25 Equity 0.5 3. Did not co4. Mixed up a

New Balance SheetTransporation 0.75 Debt 0.75 ! Issued 0.25

Tourism 0.5 Equity 0.5

! Mechanical errors: -0.5! Tax effect: -0.5

! Unlevered with tax rate: -0.5! Relevered with wrong debt to equity: -0.5! Forgot to tax effect cost of debt: -0.5

! Wrong debt ratio: -0.5

! Okay if you used (1+g) in numerator! Change in firm value incorrect: -1 to -1.5

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! Gan/Loss on Sale: -1 to -1.5

! Duration for assets computed incorrectly: -1.5 to -2

! Dolalr debt after restructuring incorrect: -1! Breakdown of debt after restructuring: -1 to -1.5

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Grading Guidelines1. Did not adjust the cost of equity at all: -1.5 points2. Error in beta estimation: -0.5 to -1 point3. Weights incorrect: -0.5 point4. Forgot to after-tax cost of debt: -0.5 point

1. Cost savings per year incorrect: -0.5 point2. PV of savings incorrect: -1 point3. Math errors: -0.5 point each

1. Divided by existing number of shares: -1 point2. Error in computing per share value: -.5 to -1 point

1. Asset duration incorrect: -0.5 to -1.5 points (depending)2. Debt duration incorrect: -0.5 to -1 point3. Math error: -0.5 point

! Wrong cost of debt : -.5! Math error: -.5

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! Wrong debt ratio: -0.5 to -1

! Forgot to unlever and relever beta: -1

! Used Debt to capital ratio to lever beta: -0.5

! Wrong cost of cebt : -.5

! Firm value computed incorrectly: -1

! Did not lever beta: -1

! Error in setting up new WACC: -.5 to -1

! Computed beta of assets including cash: -1

(Cash is used up after the transaction)

Did not comptue the new debt level right: -1

Other math errors: -.5 point

! Wrong weights: -0.5 pt! Did not after-tax debt: -.5

- Debt repaid

t

st operating

d for retirin

he answers will be differ

ty ratio

nal,

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! Used 40% as tax rate: -1 point! Used 0% as tax rate: -0.5 point! Math errors on tax rate: -0.5 point

! Did not unlever beta: -0.5 point! Left cost of equity untouched at 10%: -1 point! Weights wrong: -0.5 to -1 point! Wrong after-tax cost of debt: -0.5 (only if inconsistent

% with your answer to part b

! Did not set up firm value change : -2 to -3 point! Used wrong firm value: -0.5 point! Computed change in firm value wrong: -1 point

! No penalty for using (1+g)

!Duration of debt incorrect: -1 point! Weigths for assets incorrect: -1 point

ta: -1 pointg beta: -0.5 point

ly: -1 point

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omputation: -1 point: -1 point

-1 point

pointint

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cashflows are predictable and brand name has high marketable value)

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rough: -2 to -3

he transaction

: -0.5

in computing firm value change: -0.50.5

t all: -1

usinesses incorrectly: -0.5pute new weights after business changed: -0.5

pute new dollar debt correctly: -0.5set and debt durations: -1

f debt to fund doubling of tourism business

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