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UGBA 103 – Introduction to FinanceReview Section

Sheisha Kulkarni & Vijayant Bhatnagar

UC Berkeley – Haas School of Business

Spring 2016

UGBA 103 – Introduction to Finance 1 / 28

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Capital Structure

Payout Policy

Capital Budgeting and Valuation

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Capital Structure

Capital Structure


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Capital Structure

Question 1

Consider a project with free cash flows in one year of $145,000 or$195,000, with each outcome being equally likely. The initial

investment required for the project is $120,000 and the project’s cost ofcapital is 30%. The risk-free interest rate is 12%.

1. What is the NPV of this project?


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Capital Structure

Question 1

Consider a project with free cash flows in one year of $145,000 or$195,000, with each outcome being equally likely. The initial

investment required for the project is $120,000 and the project’s cost ofcapital is 30%. The risk-free interest rate is 12%.

1. What is the NPV of this project?

NPV = E [CF 1]

1 + r c − initial cash flow

= 0.5 × 145, 000 + 0.5× 195, 000

1.30

− 120, 000

= 170, 000

1.3 − 120, 000 = 10, 769


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Capital Structure

Question 1

Consider a project with free cash flows in one year of $145,000 or

$195,000, with each outcome being equally likely. The initialinvestment required for the project is $120,000 and the project’s cost ofcapital is 30%. The risk-free interest rate is 12%.

2. Suppose that to raise the funds for the initial investment, theproject is sold to investors as an all-equity firm. The equity holders

will receive the cash flows of the project in one year. What is theinitial market value of the unlevered equity?


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Capital Structure

Question 1


$195,000, with each outcome being equally likely. The initialinvestment required for the project is $120,000 and the project’s cost ofcapital is 30%. The risk-free interest rate is 12%.

2. Suppose that to raise the funds for the initial investment, theproject is sold to investors as an all-equity firm. The equity holders

will receive the cash flows of the project in one year. What is theinitial market value of the unlevered equity?

Equity value = E [CF 1]

1 + r c

= 0.5 × 145, 000 + 0.5 × 195, 000

1.30

= 170, 000

1.3 = 130, 769


C i l S

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Capital Structure

Question 1


$195,000, with each outcome being equally likely. The initialinvestment required for the project is $120,000 and the project’s cost of

capital is 30%. The risk-free interest rate is 12%.

3. Suppose that initial $120,000 is instead raised by borrowing at therisk-free rate. What are the cash flows of the levered equity, and

what is its initial value according to MM?


C it l St t

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Capital Structure

Question 1


$195,000, with each outcome being equally likely. The initialinvestment required for the project is $120,000 and the project’s cost of

capital is 30%. The risk-free interest rate is 12%.

3. Suppose that initial $120,000 is instead raised by borrowing at therisk-free rate. What are the cash flows of the levered equity, and

what is its initial value according to MM? equity value is total firm value minus debt value value of debt next period is debt value×r f equity cash flow is the difference between total cash flow and cash

to debt.

Value at year 0 CF Strong CF WeakDebt 120,000 134,400 134,400Equity 10,769 60,600 10,600

Total 130,769 195,000 145,000


Capital Structure

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Capital Structure

Question 2

Explain what is wrong with the following argument:“If a firm issues debt that is risk free, because there is no possibility of

default, the risk of the firm’s equity does not change. Therefore,

risk-free debt allows the firm to get the benefit of a low cost of capitalof debt without raising its cost of equity."


Capital Structure

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Capital Structure

Question 2

Explain what is wrong with the following argument:“If a firm issues debt that is risk free, because there is no possibility of

default, the risk of the firm’s equity does not change. Therefore,

risk-free debt allows the firm to get the benefit of a low cost of capitalof debt without raising its cost of equity."

The argument is wrong because any leverage raises the equity cost of

capital. Risk-free leverage raises it the most because it does not share

any of the risk.


Capital Structure

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Capital Structure

Question 3

In mid-2012, AOL Inc. had $200 million in risk-free debt, total equity

capitalization of $3.3 billion, and an equity beta of 0.92. Included inAOL’s assets was $1.6 billion in cash and risk-free securities. Assumethat the risk-free rate of interest is 2.9% and the market risk premium

is 4.1%.

1. What is AOL’s enterprise value?


Capital Structure

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Capital Structure

Question 3



is 4.1%.


Enterprise value=Total equity+Debt-CashEnterprise value=3.3+0.2-1.6=1.9 billion.


Capital Structure

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Capital Structure

Question 3



is 4.1%.



2. What is the beta of AOL’s business assets?


Capital Structure

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p

Question 3



is 4.1%.



2. What is the beta of AOL’s business assets?

β U = E

E + D β E +

D E + D

β D

= 3.3

1.9 × 0.92 = 1.6


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Question 3

In mid-2012, AOL Inc. had $200 million in debt, total equitycapitalization of $3.3 billion, and an equity beta of 0.92. Included in

AOL’s assets was $1.6 billion in cash and risk-free securities. Assumethat the risk-free rate of interest is 2.9% and the market risk premium

is 4.1%.3. What is AOL’s pre-tax WACC?


Capital Structure

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Question 3

In mid-2012, AOL Inc. had $200 million in debt, total equitycapitalization of $3.3 billion, and an equity beta of 0.92. Included in

AOL’s assets was $1.6 billion in cash and risk-free securities. Assumethat the risk-free rate of interest is 2.9% and the market risk premium

is 4.1%.3. What is AOL’s pre-tax WACC?

r WACC = r f + β U ×MRP

= 0.029 + 1.6 × 0.041 = 0.095

AOL’s pre-tax WACC is 9.5%.


Payout Policy

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Payout Policy


Payout Policy

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Question 4

EJH Company has a market capitalization of $3.1 billion and 36 million

shares outstanding. It plans to distribute $125 million through an openmarket repurchase. Assuming perfect capital markets:

1. What will the price per share of EJH be right before the

repurchase?


Payout Policy

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Question 4




repurchase?

Price per share=Equity value/sharesoutstanding=3,100/36=$86.11

2. How many shares will be repurchased?


Payout Policy

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Question 4




repurchase?



Number of shares=amount distributed/price pershare=125/86.11=1.45 million shares

3. What will the price per share of EJH be right after the repurchase?


Payout Policy

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Question 4




repurchase?



Number of shares=amount distributed/price pershare=125/86.11=1.45 million shares

3. What will the price per share of EJH be right after the repurchase?Price per share=equity value/sharesoutstanding=3,100−125

36−1.45 =$86.11


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Question 5The HNH Corporation will pay a constant dividend of $3.50 per share,per year, in perpetuity. Assume all investors pay a 22% tax on

dividends and that there is no capital gains tax. Suppose the otherinvestments with equivalent risk to HNH stock offer an after-tax returnof 9%.

1. What is the share price of HNH stock?


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Question 5The HNH Corporation will pay a constant dividend of $3.50 per share,per year, in perpetuity. Assume all investors pay a 22% tax on

dividends and that there is no capital gains tax. Suppose the otherinvestments with equivalent risk to HNH stock offer an after-tax returnof 9%.

1. What is the share price of HNH stock?

CF = Div × (1− τ d ) = 3.50× (1− 0.22) = 2.73

P = 2.73

0.09 = 30.33

2. Assume that management makes a surprise announcement that

HNH will no longer pay dividends but will use the cash torepurchase stock instead. What is the price of a share of HNHstock now?

CF = 3.50, P = 3.50

0.09 = 38.89



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Question 6Suppose Goodyear Tire and Rubber Company is considering divestingone of its manufacturing plants. The plant is expected to generate free

cash flows of $2 million per year, growing at a rate of 3% per year.Goodyear has an equity cost of capital of 9%, a debt cost of capital of7.5%, a marginal corporate tax rate of 40%, and a debt-equity ratio of

3.1. If the plant has average risk and Goodyear plans to maintain aconstant debt-equity ratio, what after-tax amount must it receive for theplant for the divestiture to be profitable?



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Question 6Suppose Goodyear Tire and Rubber Company is considering divestingone of its manufacturing plants. The plant is expected to generate free

cash flows of $2 million per year, growing at a rate of 3% per year.Goodyear has an equity cost of capital of 9%, a debt cost of capital of7.5%, a marginal corporate tax rate of 40%, and a debt-equity ratio of

3.1. If the plant has average risk and Goodyear plans to maintain aconstant debt-equity ratio, what after-tax amount must it receive for theplant for the divestiture to be profitable?

r WACC = E

E + D r E +

D

E + D r D (1 − τ C )

=

1

1 + 3.1 × 0.09 +

3.1

1 + 3.1 × 0.075× (1 − 0.4) = 0.056

V L = CF

r WACC − g =

2

0.056− 0.03 = 76.9 million

So the divestiture is profitable only if Goodyear receives more than

$76.9 million after tax. UGBA 103 – Introduction to Finance 14 / 28


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Question 7Suppose Alcatel-Lucent has an equity cost of capital of 12%, marketcapitalization of $12.06 billion, and an enterprise value of $18 billion

with a debt cost of capital of 8% and its marginal tax rate is 40%.1. What is Alcatel-Lucent’s WACC?



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r WACC = E

E + D r E +

D

E + D r D (1− τ C )

= 12.0618 × 0.12 + 18

−

12.0618 × 0.08× (1− 0.4) = 0.0962

2. If Alcatel-Lucent maintains a constant debt-equity ratio, what is thevalue of a project with average risk and the following expected free

cash flows? Year 0 1 2 3

FCF ($ million) -100 60 110 80



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r WACC = E

E + D r E +

D

E + D r D (1− τ C )

= 12.0618 × 0.12 + 18

−

12.0618 × 0.08× (1− 0.4) = 0.0962

2. If Alcatel-Lucent maintains a constant debt-equity ratio, what is thevalue of a project with average risk and the following expected free

cash flows? Year 0 1 2 3

FCF ($ million) -100 60 110 80

V L = 60

1.0962 +

110

1.09622 +

80

1.09623 = 207.01 million



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Question 8

Acort Industries has 20 million shares outstanding and a current share

price of $30 per share. It also has a long-term debt outstanding. Thisdebt is risk free, is four years away from maturity, has an annualcoupon rate of 5%, and has a $125 million face value. The first of the

remaining coupon payments will be due in exactly one year. Theriskless interest rates for all maturities are constant at 3%. Acort has

EBIT of $115 million, which is expected to remain constant each year.New capital expenditures are expected to equal depreciation andequal $22 million per year, while no changes to net working capital are

expected in the future. The corporate tax rate is 38%, and Acort is

expected to keep its debt-equity ratio constant in the future (by eitherissuing additional new debt or buying back some debt as time goeson).

1. Based on this information, estimate Acort’s WACC.



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Question 8

1. Based on this information, estimate Acort’s WACC.

Calculate equity value:

E = 20 × 30 = 600 million

Calculate debt value:

D = CPN ×1

y

1−

1

(1 + y )N

+

FV

(1 + y )N

= 6.25

0.03 ×

1−

1

(1.03)4

+

125

1.034

= 134.29 million

So the enterprise value is E+D=600+134.29=734.29 million.



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Question 8To calculate FCF, use

FCF = EBIT ×

(1−

τ C ) + Dep −

Capex −

∆NWC = 115× (1 − 0.38) = 71.3 million

Since the firm is not expected to grow, the WACC can be computedusing the following formula:

V L = FCF r WACC

⇒ r WACC = FCF V L

= 71.3734.29

= 0.0971

2. What is Ascort’s equity cost of capital?



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Question 8To calculate FCF, use

FCF = EBIT ×

(1−

τ C ) + Dep −

Capex −

∆NWC = 115× (1 − 0.38) = 71.3 million

Since the firm is not expected to grow, the WACC can be computedusing the following formula:

V L = FCF r WACC

⇒ r WACC = FCF V L

= 71.3734.29

= 0.0971

2. What is Ascort’s equity cost of capital?

r WACC = E E + D

r E + D E + D

r D (1 − τ C )

0.0971 = 600

734.29r E +

134.29

734.290.03(1 − 0.38) ⇒ r E = 0.1147

Ascort’s equity cost of capital is 11.47%.


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Question 9

The current price of Estelle Corporation stock is $40.00. Next year, thisstock price will either go up by 10% or go down by 10%. The stock

pays no dividends. The one-year risk-free interest rate is 4.0% and willremain constant. Using the Binomial Model, calculate the price of a

one-year call option on Estelle stock with a strike price of $40.00.


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Question 9

The current price of Estelle Corporation stock is $40.00. Next year, thisstock price will either go up by 10% or go down by 10%. The stock

pays no dividends. The one-year risk-free interest rate is 4.0% and willremain constant. Using the Binomial Model, calculate the price of a

one-year call option on Estelle stock with a strike price of $40.00.


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Question 9

The current price of Estelle Corporation stock is $40.00. In each of the

next two years, this stock price will either go up by 10% or go down by10%. The stock pays no dividends. The one-year risk-free interest rate

is 4.0% and will remain constant. Using the Binomial Model, calculatethe price of a one-year call option on Estelle stock with a strike price of

$40.00.

m = U − D

C U − C D =

44− 36

4− 0 = 2

C = 1

m S −

D −mC D

1 + r f

= 1

2

40−

36− 2 × 0

1 + 0.04

= 2.69


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Question 10

Suppose a stock is currently trading for $65, and in one period will

either go up by 25% or fall by 15%. If the one-period risk-free rate is4.0%, what is the price of a European put option that expires in one

period and has an exercise price of $65? Suppose the option actuallysold in the market for $8. Describe a trading strategy that yields

arbitrage profits.


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Question 10

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Question 10

Suppose a stock is currently trading for $65, and in one period will

either go up by 25% or fall by 15%. If the one-period risk-free rate is4.0%, what is the price of a European put option that expires in one

period and has an exercise price of $65? Suppose the option actuallysold in the market for $8. Describe a trading strategy that yields

arbitrage profits.


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Question 10

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Question 10Suppose a stock is currently trading for $65, and in one period willeither go up by 25% or fall by 15%. If the one-period risk-free rate is

4.0%, what is the price of a European put option that expires in oneperiod and has an exercise price of $65? Suppose the option actuallysold in the market for $8. Describe a trading strategy that yields

arbitrage profits.

m = U − D

C U −C D =

81.25− 55.25

0 − 9.75 = −2.67

P = 1

−2.67

65−

55.25 + 2.67× 9.75

1 + 0.04

= 4.92


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Question 10

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Question 10Suppose a stock is currently trading for $65, and in one period willeither go up by 25% or fall by 15%. If the one-period risk-free rate is

4.0%, what is the price of a European put option that expires in oneperiod and has an exercise price of $65? Suppose the option actuallysold in the market for $8. Describe a trading strategy that yields

arbitrage profits.

m = U − D

C U −C D =

81.25− 55.25

0 − 9.75 = −2.67

P = 1

−2.67

65−

55.25 + 2.67× 9.75

1 + 0.04

= 4.92

S −mP = D − mC D

1 + r f

P = 1

m S −

D − mC D

m (1 + r f )

P =−

0.37S + 29.27UGBA 103 – Introduction to Finance 23 / 28

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Question 10

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Question 10

Suppose a stock is currently trading for $65, and in one period willeither go up by 25% or fall by 15%. If the one-period risk-free rate is

4.0%, what is the price of a European put option that expires in oneperiod and has an exercise price of $65? Suppose the option actually

sold in the market for $8. Describe a trading strategy that yieldsarbitrage profits.

If the put is actually selling for $8, then it is overpriced. The arbitragetrading opportunity will involve selling the put, 0.37 of a stock and

invest 29.27.


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Question 11

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Question 11Suppose the current price of Narver Network systems stock $55 pershare. In each of the next two years, the stock price will either increase

by 25% or decrease by 15%. The 6% one-year risk-free rate of interestwill remain constant. Suppose the put option with a strike price of $60actually sold today for $3.87. You do not know what the option will

trade for next period. Describe a trading strategy that will yieldarbitrage profits.


Options

Question 11

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Question 11Suppose the current price of Narver Network systems stock $55 pershare. In each of the next two years, the stock price will either increase

by 25% or decrease by 15%. The 6% one-year risk-free rate of interestwill remain constant. Suppose the put option with a strike price of $60actually sold today for $3.87. You do not know what the option will

trade for next period. Describe a trading strategy that will yieldarbitrage profits.


Options

Question 11

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Question 11

Suppose the current price of Narver Network systems stock $55 per

share. In each of the next two years, the stock price will either increaseby 25% or decrease by 15%. The 6% one-year risk-free rate of interest

will remain constant. Suppose the put option with a strike price of $60actually sold today for $3.87. You do not know what the option will

trade for next period. Describe a trading strategy that will yieldarbitrage profits.Box 1:

m = 85.94− 58.44

0 − 1.56 = −17.63

P = 1

−17.63

68.75 +

58.44 + 17.63× 1.56

1 + 0.06

= 0.7


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Question 11

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Question 11


share. In each of the next two years, the stock price will either increaseby 25% or decrease by 15%. The 6% one-year risk-free rate of interest

will remain constant. Suppose the put option with a strike price of $60actually sold today for $3.87. You do not know what the option will

trade for next period. Describe a trading strategy that will yieldarbitrage profits.Box 2:

m = 58.44− 39.74

1.56− 20.26 = −1

P = 1

−1

46.75 +

39.74 + 1 × 20.26

1 + 0.06

= 9.85


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Question 11

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Question 11


share. In each of the next two years, the stock price will either increaseby 25% or decrease by 15%. The 6% one-year risk-free rate of interestwill remain constant. Suppose the put option with a strike price of $60

actually sold today for $3.87. You do not know what the option willtrade for next period. Describe a trading strategy that will yield

arbitrage profits.Box 3:

m = 68.75− 46.75

0.7 − 9.85 = −2.4

P = 1

−2.4

55−46.75 + 2.4 × 9.85

1 + 0.06

= 4.76


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Question 11

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Question 11


share. In each of the next two years, the stock price will either increaseby 25% or decrease by 15%. The 6% one-year risk-free rate of interestwill remain constant. Suppose the put option with a strike price of $60

actually sold today for $3.87. You do not know what the option willtrade for next period. Describe a trading strategy that will yield

arbitrage profits.Box 3:

m = 68.75− 46.75

0.7 − 9.85 = −2.4

P = 1

−2.4

55−46.75 + 2.4 × 9.85

1 + 0.06

= 4.76

If the put is selling for $3.87 it is underpriced. You should purchase theput and the stock, and borrow $27.67 at the risk-free rate.


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