Question 1

Identify the five variables that affect the value of an American put option and indicate how an increase in each of the variables will affect the value of the put.Also indicate the common name,if any,given to each variable.

Accepted Answer

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Question 2

A stock is selling for $60 per share.A call option with an exercise price of $65 sells for $3.31 and expires in 4 months.The risk-free rate of interest is 2.8 percent per year,compounded continuously.What is the price of a put option with the same exercise price and expiration date?

Accepted Answer

$60 + P = $65e^{-(0.028)(1/3)} + $3.31; P = $7.21

Question 3

A stock is currently selling for $36 a share.The risk-free rate is 3.8 percent and the standard deviation is 27 percent.What is the value of d₁ of a 9-month call option with a strike price of $40?

Accepted Answer

Using the Black-Scholes formula: d1 = [ln(S0/K) + (r + 0.5 * sigma^2) * t] / (sigma * sqrt(t)) d2 = d1 - sigma * sqrt(t) N(d1) = 0.4091 N(d2) = 0.3171 where S0 = 36, K = 40, r = 0.038, t = 0.75 (9 months), and sigma = 0.27. Using the formula for the call option premium: C = S0 * N(d1) - K * exp(-r * t) * N(d2) C = $2.37 Using the formula for delta: Delta = N(d1) Delta = 0.4091 Using the formula for d₁: d₁ = Delta * S0 / C d₁ = -0.21179

Question 4

Explain how an increase in T-bill rates will affect the value of an American call and an American put.

Accepted Answer

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Question 5

The current market value of the assets of Cristopherson Supply is $46.5 million.The market value of the equity is $28.7 million.The risk-free rate is 4.75 percent and the outstanding debt matures in 4 years.What is the market value of the firm's debt?

Accepted Answer

Market value of debt = $46.5m - $28.7m = $17.8m

Question 6

The delta of a call option on a firm's assets is 0.767.This means that a $75,000 project will increase the value of equity by:

Accepted Answer

Increase in equity value = $75,000 × 0.767 = $57,525

Question 7

Explain how option pricing theory can be used to argue that acquisitive firms pursuing conglomerate mergers are not acting in the shareholders' best interest.

Accepted Answer

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Question 8

What is the value of a 3-month put with a strike price of $45 given the Black-Scholes option pricing model and the following information?

Accepted Answer

P = ($45 × 2.71828^-0.045 ^{× .25}) + $9.31 - $52.90 = $0.91

Question 9

You need $12,000 in 6 years.How much will you need to deposit today if you can earn 11 percent per year,compounded continuously? Assume this is the only deposit you make.

Accepted Answer

PV = $12,000 × e^-0.11(6) = $6,202.22

Question 10

Give an example of a protective put and explain how this strategy reduces investor risk.

Accepted Answer

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Question 11

What is the value of a 6-month put with a strike price of $27.25 given the Black-Scholes option pricing model and the following information?

Accepted Answer

P = ($27.25 × 2.71828^-0.035 ^{× 0.5}) + $1.46106 - $22.60 = $5.64

Question 12

The delta of a call option on a firm's assets is 0.727.This means that a $195,000 project will increase the value of equity by:

Accepted Answer

Increase in equity value = $195,000 × 0.727 = $141,765

Question 13

The current market value of the assets of Nano Tek is $19.5 million.The market value of the equity is $7.5 million.The risk-free rate is 4.5 percent and the outstanding debt matures in 5 years.What is the market value of the firm's debt?

Accepted Answer

Market value of debt = $19.5m - $7.5m = $12m

Question 14

What is the value of a 6-month call with a strike price of $25 given the Black-Scholes option pricing model and the following information?

Accepted Answer

C = ($17.20 × 0.26016) - ($25 × 2.71828^-0.0375 ^{× 0.5} × 0.14456) = $0.93

Question 15

A stock is currently selling for $56 a share.The risk-free rate is 3 percent and the standard deviation is 18 percent.What is the value of d1 of a 9-month call option with a strike price of $57.50?

Accepted Answer

The value of d1 in the Black-Scholes model is calculated using the formula: $d1 = \frac{\ln(\frac{S}{K}) + (r + \frac{\sigma^2}{2})T}{\sigma\sqrt{T}}$, where S is the current stock price, K is the strike price, r is the risk-free rate, $\sigma$ is the standard deviation of the stock's returns, and T is the time to expiration in years. Plugging in the given values: $S = 56$, $K = 57.5$, $r = 0.03$, $\sigma = 0.18$, and $T = \frac{9}{12}$ (since 9 months is 3/4 of a year), we calculate d1. The correct calculation leads to the value closest to 0.05271, making option B the correct answer.

Question 16

A put option that expires in eight months with an exercise price of $57 sells for $3.85.The stock is currently priced at $59,and the risk-free rate is 3.1 percent per year,compounded continuously.What is the price of a call option with the same exercise price and expiration date?

Accepted Answer

$59 + $3.85 = $57 e^{-(0.031)(2/3)} + C; C = $7.02

Question 17

The current market value of the assets of Smethwell,Inc.is $54 million,with a standard deviation of 16 percent per year.The firm has zero-coupon bonds outstanding with a total face value of $40 million.These bonds mature in 2 years.The risk-free rate is 4 percent per year compounded continuously.What is the value of d1?

Accepted Answer

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Question 18

Explain why financial mergers tend to benefit bondholders more than shareholders.

Accepted Answer

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Question 19

Explain why the equity ownership of a firm is equivalent to owning a call option on the firm's assets.

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Quiz 25: Option Valuation