of 35
8/13/2019 FCF 9th Edition Chapter 25
1/35
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."
8/13/2019 FCF 9th Edition Chapter 25
2/35
"
8/13/2019 FCF 9th Edition Chapter 25
3/35
Chapter 25Question 1
Input Area:
Initial investment 1,000$
# of years 9
Rate of return 11%
Output Area:
FV 2,691.23$
8/13/2019 FCF 9th Edition Chapter 25
4/35
Chapter 25Question 2
Input Area:
Amount needed 15,000$
# of years 8
Rate of return 9%
Output Area:
PV 7,301.28$
8/13/2019 FCF 9th Edition Chapter 25
5/35
Chapter 25Question 3
Input Area:
Current stock price 62$Exercise price 60$Call option 4.10$Expiration (months) 3Risk-free rate 2.6%
Output Area:
Put price 1.71$
8/13/2019 FCF 9th Edition Chapter 25
6/35
Chapter 25Question 4
Input Area:
Expiration (months) 6Exercise price 50$Put option 5.08$Current stock price 47$Risk-free rate 4.8%
Output Area:
Call price 3.27$
8/13/2019 FCF 9th Edition Chapter 25
7/35
Chapter 25Question 5
Input Area:
Exercise price 70$Expiration (months) 3Put option 3.10$Call option 4.35$Risk-free rate 4.8%
Output Area:
Stock price 70.42$
8/13/2019 FCF 9th Edition Chapter 25
8/35
Chapter 25Question 6
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%
8/13/2019 FCF 9th Edition Chapter 25
9/35
Chapter 25Question 7
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%
8/13/2019 FCF 9th Edition Chapter 25
10/35
Chapter 25Question 8
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$
8/13/2019 FCF 9th Edition Chapter 25
11/35
Chapter 25Question 9
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$
8/13/2019 FCF 9th Edition Chapter 25
12/35
Chapter 25Question 10
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.
8/13/2019 FCF 9th Edition Chapter 25
13/35
Chapter 25Question 11
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
$2,050,000
d1 (0.0299)
d2 (0.2299)
N(d1) 0.4881
N(d2) 0.4091
Call 129,615.91$
8/13/2019 FCF 9th Edition Chapter 25
14/35
Chapter 25Question 12
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$in order to guarantee the right to sellthe land for 2,050,000$
8/13/2019 FCF 9th Edition Chapter 25
15/35
8/13/2019 FCF 9th Edition Chapter 25
16/35
Chapter 25Question 14
Input Area:
Exercise price 30$Expiration (months) 4Call option 3.81$Stock price 27.05$Risk-free rate 5%
Output Area:
Put price 6.26$
8/13/2019 FCF 9th Edition Chapter 25
17/35
Chapter 25Question 15
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.
8/13/2019 FCF 9th Edition Chapter 25
18/35
Chapter 25Question 16
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$
8/13/2019 FCF 9th Edition Chapter 25
19/35
Chapter 25Question 17
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$
8/13/2019 FCF 9th Edition Chapter 25
20/35
Chapter 25Question 18
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$
8/13/2019 FCF 9th Edition Chapter 25
21/35
Chapter 25Question 19
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
Equity value 4,938.60$
Debt value 12,661.40$
Project B:
d1 1.1757
d2
0.9357
N(d1) 0.8801
N(d2) 0.8253
Equity value 4,360.22$
Debt value 13,839.78$
b. Although the NPV of project B is higher,
8/13/2019 FCF 9th Edition Chapter 25
22/35
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.
8/13/2019 FCF 9th Edition Chapter 25
23/35
Chapter 25Question 20
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
Equity value 6,455.02$
Debt value 20,844.98$
Cost of debt 18.18%
8/13/2019 FCF 9th Edition Chapter 25
24/35
Chapter 25Question 21
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
Equity value 6,742.92$
Debt value 36,657.08$
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.
8/13/2019 FCF 9th Edition Chapter 25
25/35
Chapter 25Question 22
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$Rd 11.65%
When the firm accepts the new project,part of the NPV accrues to bondholders.This increases the present value of thebond, thus reducing the return on the bond.
Additionally, the new project makes thefirm safer in the sense it increases the
8/13/2019 FCF 9th Edition Chapter 25
26/35
value of assets, thus increasing theprobability the call will end in the moneyand the bondholders will receive theirpayment.
8/13/2019 FCF 9th Edition Chapter 25
27/35
Chapter 25Question 23
Input Area:
Maturity (years) 2Face value 40,000$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.
8/13/2019 FCF 9th Edition Chapter 25
28/35
Chapter 25Question 24
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 $35,234.40
b. d1 0.7629
d2 (0.2209)
N(d1) 0.7772
N(d2) 0.4126
Equity value 21,216.74$Put price 10,451.14$
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
Equity value 24,506.51$Put price 13,740.92$
Value of bond 21,493.49$
Rd 16.89%
8/13/2019 FCF 9th Edition Chapter 25
29/35
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.
8/13/2019 FCF 9th Edition Chapter 25
30/35
Chapter 25Question 25
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$
8/13/2019 FCF 9th Edition Chapter 25
31/35
8/13/2019 FCF 9th Edition Chapter 25
32/35
Chapter 25Question 27
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).
8/13/2019 FCF 9th Edition Chapter 25
33/35
Chapter 25Question 28
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)
8/13/2019 FCF 9th Edition Chapter 25
34/35
Chapter 25Question 29
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.
8/13/2019 FCF 9th Edition Chapter 25
35/35
Chapter 25Question 30
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.