Question 1

J&N, Inc. stock has a current market price of $46 a share. The one-year call on this stock with a strike price of $55 is priced at $0.05 while the one-year put with a strike price of $55 is priced at $8.24. What is the risk-free rate of return?

Accepted Answer

$55/(1 + r) = -$0.05 + $46 + $8.24; r = 1.49 percent

Question 2

The stock of Edwards Homes, Inc. has a current market value of $23 a share. The 3-month call with a strike price of $20 is selling for $3.80 while the 3-month put with a strike price of $20 is priced at $0.54. What is the continuously compounded risk-free rate of return?

Accepted Answer

($20 F1F1F1S1F1F1F10 e^-RF1F1F1S1^F1F1F10^0.25) = -$3.80 + $23 + $0.54$20 e^-0.25R = $19.74ln(e^-0.25R) = ln 0.987-0.25R = -0.013085R = 5.23 percent

Question 3

Today, you purchased 100 shares of Lazy Z stock at a market price of $47 per share. You also bought a one year, $45 put option on Lazy Z stock at a cost of $0.15 per share. What is the maximum total amount you can lose on these purchases?

Accepted Answer

Maximum loss = 100 ($45 - $47 - $0.15) = -$215

Question 4

Cell Tower stock has a current market price of $62 a share. The one-year call on Cell Tower stock with a strike price of $65 is priced at $7.16 while the one-year put with a strike price of $65 is priced at $7.69. What is the risk-free rate of return?

Accepted Answer

$65/(1 + r) = -$7.16 + $62 + $7.69; r = 3.95 percent

Question 5

A purely financial merger:

Accepted Answer

The answer of A purely financial merger:
...

Question 6

This morning, Krystal purchased shares of Global Markets stock at a cost of $39.40 per share. She simultaneously purchased puts on Global Markets stock at a cost of $1.25 per share and a strike price of $40 per share. The put expires in one year. How much profit will she earn per share on these transactions if the stock is worth $38 a share one year from now?

Accepted Answer

Profit = $40 - $39.40 - $1.25 = -$0.65

Question 7

Which one of the following statements is correct?

Accepted Answer

Shareholders might prefer a negative NPV project if it aligns with their risk preferences or strategic goals, despite the project not adding value in a traditional NPV sense.

Question 8

Todd invested $8,500 in an account today at 7.5 percent compounded continuously. How much will he have in his account if he leaves his money invested for 5 years?

Accepted Answer

FV = $8,500 F1F1F1S1F1F1F10 2.71828^0.075F1F1F1S1^F1F1F10⁵ = $12,367

Question 9

A firm has assets of $21.8 million and a 3-year, zero-coupon, risky bonds with a total face value of $8.5 million. The bonds have a total current market value of $8.1 million. How can the shareholders of this firm change these risky bonds into risk-free bonds?

Accepted Answer

To change the risky bonds into risk-free bonds, the firm can purchase a put option with a 3-year life and an $8.5 million face value. This option will give the firm the right to sell the bonds at a predetermined price (strike price) of $8.1 million in case the market value of the bonds falls below that price. This will protect the firm from potential losses due to a decline in the bond market. Moreover, purchasing put options with a total face value of $8.5 million will cover the full value of the risky bonds, ensuring that the firm's assets are fully protected. Option A and B involve purchasing call options, which do not provide protection against potential losses, but instead provide the right to buy the bonds at a predetermined price, which may not be beneficial if the bond prices fall. Option C involves purchasing a put option on the entire assets of the firm, which is unnecessary and may be expensive. Option D involves purchasing a put option with a $8.1 million face value only, which may not fully protect the firm's assets in case the market value of the bonds falls below that price. Therefore, option E is the best choice.

Question 10

Grocery Express stock is selling for $22 a share. A 3-month, $20 call on this stock is priced at $2.65. Risk-free assets are currently returning 0.2 percent per month. What is the price of a 3-month put on Grocery Express stock with a strike price of $20?

Accepted Answer

P = ($20/1.002³) + $2.65 - $22 = $0.53

Question 11

What is the value of d₂ given the following information on a stock?

Accepted Answer

d₂ = 0.63355 - [0.67 F1F1F1S1F1F1F10 (0.75^1/2)] = 0.0533

Question 12

You invest $4,000 today at 6.5 percent, compounded continuously. How much will this investment be worth 8 years from now?

Accepted Answer

FV = $4,000 F1F1F1S1F1F1F10 2.71828^0.065F1F1F1S1^F1F1F10⁸ = $6,728

Question 13

Wesleyville Markets stock is selling for $36 a share. The 9-month $40 call on this stock is selling for $2.23 while the 9-month $40 put is priced at $5.11. What is the continuously compounded risk-free rate of return?

Accepted Answer

($40 F1F1F1S1F1F1F10 e^-RF1F1F1S1^F1F1F10^0.75) = -$2.23 + $36 + $5.11$40 e^-0.75R = $38.88ln(e^-0.75R) = ln0.972-0.75R = -0.0284R = 3.79 percent

Question 14

A.K. Scott's stock is selling for $38 a share. A 3-month call on this stock with a strike price of $35 is priced at $3.40. Risk-free assets are currently returning 0.18 percent per month. What is the price of a 3-month put on this stock with a strike price of $35?

Accepted Answer

P = ($35/1.0018³) + $3.40 - $38 = $0.21

Question 15

Today, you are buying a one-year call on one share of Webster United stock with a strike price of $40 per share and a one-year risk-free asset that pays 4 percent interest. The cost of the call is $1.85 per share and the amount invested in the risk-free asset is $38.46. What is the most you can lose on these purchases over the next year?

Accepted Answer

Maximum loss = ($38.46 F1F1F1S1F1F1F10 1.04) - $38.46 + $0 - $1.85 = -$0.31

Question 16

Pure financial mergers:

Accepted Answer

The answer of Pure financial mergers:
...

Question 17

Today, you are buying a one-year call on Piper Sons stock with a strike price of $27.50 per share and a one-year risk-free asset which pays 3.5 percent interest. The cost of the call is $1.40 per share and the amount invested in the risk-free asset is $26.57. How much total profit will you earn on these purchases if the stock has a market price of $29 one year from now?

Accepted Answer

Profit = ($26.57 F1F1F1S1F1F1F10 1.035) - $26.57 + ($29 - $27.50) - $1.40 = $1.03

Question 18

What is the value of a 3-month call option with a strike price of $25 given the Black-Scholes option pricing model and the following information?

Accepted Answer

C = ($28.15 F1F1F1S1F1F1F10 0.74699) - ($25 F1F1F1S1F1F1F10 2.71828^-0.04F1F1F1S1^F1F1F10^0.25 F1F1F1S1F1F1F10 0.66642) = $4.53

Question 19

Given the following information, what is the value of d₂ as it is used in the Black-Scholes option pricing model?

Accepted Answer

d₂ = -0.65829 - [0.55 F1F1F1S1F1F1F10 (0.75^1/2)] = -1.1346

Question 20

The value of the risky debt of a firm is equal to the value of:

Accepted Answer

The value of the risky debt of a firm can be represented as the value of a risk-free bond minus the value of a put option. This is because the risky debt can be seen as a risk-free bond (assuming the firm will pay back the debt without default) minus the risk (represented by a put option) that the firm will default on its obligations.

Quiz 25: Option Valuation