fcf 9th edition chapter 25

8/13/2019 FCF 9th Edition Chapter 25

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Chapter 25Problems 1-30

Input boxes in tan

Output boxes in yellow

Given data in blue

Calculations in red

Answers in green

NOTE: Some functions used in these spreadsheets may require thatthe "Analysis ToolPak" or "Solver Add-in" be installed in Excel.

To install these, click on "Tools|Add-Ins" and select "Analysis ToolPakand "Solver Add-In."


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Chapter 25Question 1

Input Area:

Initial investment 1,000$

# of years 9

Rate of return 11%

Output Area:

FV 2,691.23$


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Input Area:

Amount needed 15,000$

# of years 8

Rate of return 9%

Output Area:

PV 7,301.28$


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Input Area:

Current stock price 62$Exercise price 60$Call option 4.10$Expiration (months) 3Risk-free rate 2.6%

Output Area:

Put price 1.71$


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Input Area:

Expiration (months) 6Exercise price 50$Put option 5.08$Current stock price 47$Risk-free rate 4.8%

Output Area:

Call price 3.27$


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Input Area:

Exercise price 70$Expiration (months) 3Put option 3.10$Call option 4.35$Risk-free rate 4.8%

Output Area:

Stock price 70.42$


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Input Area:

Exercise price 65$Expiration (months) 4Put option 1.05$Call option 6.27$Current stock price 69.38$

Output Area:

Rate 3.90%


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Input Area:

Expiration (months) 5Put option 8.10$Call option 6.12$Exercise price 70$Current stock price 66.81$

Output Area:

Interest rate 4.18%


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Input Area:

Current stock price 69$

Exercise price 70$

Risk-free rate 6%

Expiration (months) 3

Standard deviation 41%

Output Area:

d1 0.1055d2 (0.0995)N(d1) 0.5420N(d2) 0.4604

Call 5.65$

Put 5.61$


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Input Area:

Current stock price 86$Exercise price 90$Risk-free rate 5.50%Expiration (months) 4Standard deviation 62%

Output Area:

d1 0.1032

d2 (0.2548)

N(d1) 0.5411

N(d2) 0.3995

Call 11.24$

Put 13.60$


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Input Area:

Current stock price 89$Exercise price 85$Risk-free rate 5%Expiration (months) 9Standard deviation 39%

Output Area:

d1 0.4161

N(d1) 0.6613

For a call option the delta is0.6613 For a put option,

the delta is (0.3387)

The delta tells us the price of an optionfor a $1 change in the price of theunderlying asset.


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Input Area:

Current selling price $1,900,000Price % increase 10%Standard deviation 20%Option to buy $2,050,000Expiration (months) 12Risk-free rate 5%

Output Area:

The 'stock' price is $1,900,000and the exercise price is

$2,050,000

d1 (0.0299)

d2 (0.2299)

N(d1) 0.4881

N(d2) 0.4091

Call 129,615.91$


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Input Area:

Current selling price 1,900,000$Price % increase 10%Standard deviation 20%Option to sell 2,050,000$Expiration (months) 12Risk-free rate 5%Call 129,615.91$

Output Area:

Put 179,636.23$

You would have to pay 179,636.23$in order to guarantee the right to sellthe land for 2,050,000$


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Input Area:

Exercise price 30$Expiration (months) 4Call option 3.81$Stock price 27.05$Risk-free rate 5%

Output Area:

Put price 6.26$


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Input Area:

Expiration (months) 6Stock price 85$Standard deviation 20%Risk-free rate 4%Exercise price -$

Output Area:

d1 #DIV/0!

d2 #DIV/0!

N(d1) #DIV/0!

N(d2) #DIV/0!

B-S call price #DIV/0!

Call intrinsic value 85.00$

Call price 85.00$

An option can never sell for less thanits intrinsic value.


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Input Area:

Exercise price 70$Expiration (months) 6Stock price 74$Risk-free rate 5%Standard deviation 0%

Output Area:

Standard deviation 0%

So d1and d2go to positive infinity,

so N(d1) and N(d2) go to 1. This is the

no risk call option formula discussed in

an earlier chapter. C = S - Ee-Rt

Call price 5.73$


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Input Area:

Stock price 42$Expiration (months) 12Exercise price 50$Risk-free rate 12%Standard deviation

Output Area:

For standard deviation = infinity, d1goes

to positive infinity so N(d1) goes to 1, and

d2goes to negative infinity so N(d2) goes

to 0; C = S = 42$


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Input Area:

Face value of debt 15,000$Maturity (months) 12Market value 16,100$Standard deviation 32%Risk-free rate 6%

Output Area:

d1 0.5687

d2 0.2487

N(d1) 0.7152

N(d2) 0.5982

Equity value 3,064.54$

Debt value 13,035.46$


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Input Area:

Face value 15,000$Market value 16,100$Maturity (months) 12Standard deviation 32%Risk-free rate 6%

Project A:

NPV 1,500$Standard deviation 46%

Project B:

NPV 2,100$Standard deviation 24%

Output Area:

a. Project A:

d1 0.7079

d2 0.2479

N(d1) 0.7605

N(d2) 0.5979



Project B:

d1 1.1757

d2

0.9357

N(d1) 0.8801

N(d2) 0.8253



b. Although the NPV of project B is higher,


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the equity value with project A is higher.While NPV represents the increase inthe value of the assets of the firm, in thiscase, the increase in the value of thefirm's assets resulting from the project B

is mostly allocated to the debtholders,resulting in smaller increase in the valueof the equity. Stockholders would,therefore, prefer project A even thoughit has a lower NPV.

c. Yes. If the same group of investors haveequal stakes in the firm as bondholdersand stockholders, then total firm valuematters and project B should be chosen,since it increases the value of the firm to

18,200$ instead of17,600$

d. Stockholders may have an incentive totake on more risky, less profitable projectsif the firm is leveraged; the higher the firm'sdebt load, all else the same, the greater isthis incentive.


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Input Area:

Face value of debt 25,000$Maturity (months) 12Market value 27,300$Standard deviation 43%Risk-free rate 6%

Output Area:

d1 0.5592

d2 0.1292

N(d1) 0.7120

N(d2) 0.5514



Cost of debt 18.18%


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Input Area:

Face value 40,000$Market value 43,400$Maturity (years) 12Standard deviation 19%Risk-free rate 6%Equity(#18) 3,064.54$Equity(#20) 6,455.02$Debt(#18) 13,035.46$Debt(#20) 20,844.98$

Output Area:

a. Equity 9,519.56$

Debt 33,880.44$

b. d1 0.8402

d2 0.6502

N(d1) 0.7996

N(d2) 0.7422



c. Equity (2,776.65)$

Debt 2,776.65$

d. In a purely financial merger, when thestandard deviation of the assets declines,

the value of the equity declines as well. Theshareholders will lose exactly the amountthe bondholders gain. The bondholdersgain as a result of the coinsurance effect.That is, it is less likely that the newcompany will default on the debt.


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Input Area:

Maturity (years) 10Face value 25,000,000$Market value 16,000,000$Standard deviation 41%Risk-free rate 6%NPV 750,000$

Output Area:

a. d1 0.7668

d2 (0.5297)

N(d1) 0.7784

N(d2) 0.2982

Equity value 8,363,715.92$

b. Debt value 7,636,284.08$

c. Rd 11.86%

d. d1 0.8022

d2 (0.4944)

N(d1) 0.7888

N(d2) 0.3105

Equity value 8,951,454.33$

e. Debt value 7,798,545.67$Rd 11.65%

When the firm accepts the new project,part of the NPV accrues to bondholders.This increases the present value of thebond, thus reducing the return on the bond.

Additionally, the new project makes thefirm safer in the sense it increases the


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value of assets, thus increasing theprobability the call will end in the moneyand the bondholders will receive theirpayment.


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Input Area:

Maturity (years) 2Face value 40,000$Market value 17,000$Standard deviation 60%Risk-free rate 7%

d. # years until payment 5

Output Area:

a. PV 34,774.33$

b. d1 (0.4192)d2 (1.2677)

N(d1) 0.3376

N(d2) 0.1025

Equity value 2,175.55$Put price 19,949.88$

c. Value of bond 14,824.45$

Rd 49.63%

d. PV 28,187.52$

d1 0.2939

d2 (1.0477)N(d1) 0.6156

N(d2) 0.1474

Equity value 6,310.66$Put price 17,498.18$Value of bond 10,689.34$

Rd 26.39%

The value of the debt declines becauseof the time value of money, i.e., it will belonger until shareholders receive theirpayment. However, the required returnon the debt declines. Under the current

situation, it is not likely the company willhave the assests to pay off bondholders.Under the new plan where the companyoperates for five more years, theprobability of increasing the value ofassets to meet or exceed the face valueof debt is higher than if the company onlyoperates for two more years.


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Input Area:

Maturity (years) 5Face value 50,000$Market value 46,000$Standard deviation 44%Risk-free rate 7%

d, New standard deviation 55%

Output Area:

a. PV $35,234.40

b. d1 0.7629

d2 (0.2209)

N(d1) 0.7772

N(d2) 0.4126


c. Value of bond 24,783.26$

Rd 14.04%

d. PV 35,234.40$

d1 0.8317

d2 (0.3981)

N(d1) 0.7972

N(d2) 0.3453


Value of bond 21,493.49$

Rd 16.89%


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The value of the debt declines. Since thestandard deviation of the company's assetsincreases, the value of the put option on theface value of the bond increases, whichdecreases the bond's current value.

e. Bondholders gain/(lose) (3,289.77)$

Stockholders gain/(lose) 3,289.77$

This is an agency problem for bondholders.Management, acting to increase shareholderwealth in this manner, will reduce bondholderwealth by the exact amount that shareholderwealth is increased.


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Input Area:

Current stock price 114$Standard deviation 50%Risk-free rate 5%Strike price 105$Expiration (months) 6Dividend yield 3%

Output Area:

Going back to chapter on dividends, theprice of the stock will decline by the amountof the dividend (less any tax effects).Therefore, we would expect the price of thestock to drop when a dividend is paid,reducing the upside potential of the call by theamount of the dividend. The price of a calloption will decrease when the dividend yieldincreases.

d1 0.4377

d2 0.0841

N(d1) 0.6692

N(d2) 0.5335

Call price 20.52$


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Output Area:

N(d1) is the probability that "z" is less than or

equal to N(d1), so 1 - N(d1) is the probability

that "z" is greater than N(d1). Because

of the symmetry of the normal distribution,

this is the same thing as the probability that

"z" is less than N(-d1). So, N(d1) - 1 = N(-d1).


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Output Area:

From put-call parity, P = E*e-RT

+ C - S.

Substituting the Black-Scholes call option

formula for C and using the result in the

previous question produces the put option

formula:

P = E *e-Rt

+ C - S

= E*e-Rt

+ S*N(d1) - E*e-Rt

*N(d2) - S

= S*(N(d1) - 1) + E*e-Rt*(1 - N(d2))

= E*e-Rt

*N(-d2) - S*N(-d1)


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Input Area:

Current stock price 50$Risk-free rate 12%Standard deviation 60%Strike price 100$Expiration date -

Output Area:

Based on Black-Scholes, the call option is

worth $50. The reason is that present value

of the exercise price is zero, so the second

term disappears. Also, d1is infinite, so N(d1)

is equal to one. The problem is that the call

option is European with an infinite expiration,

so why would you pay anything for it since

you can never exercise it? The paradox canbe resolved by examining the price of the

stock. Remember that the call option formula

only applies to a non-dividend paying stock.

If the stock will never pay a dividend, it (and

a call option to buy it at any price) must be

worthless.


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Output Area:

The delta of the call option is N(d1) and the

delta of the put option is N(d1) - 1. Since you

are selling a put option, the delta of the

portfolio is N(d1) - [N(d1) - 1]. This leaves the

overall delta of your position as 1. This

position will change dollar for dollar in value

with the underlying asset. This position

replicates the dollar "action" on the

underlying asset.

fcf 9th edition chapter 25

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