Question 1

You invest $4,500 today at 6.5 percent,compounded continuously.How much will this investment be worth 8 years from now?

Accepted Answer

FV = $4,500 × 2.71828^0.065 ^{× 8} = $7,569

Question 2

A.K.Scott's stock is selling for $37 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 - $37 = $1.71

Question 3

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 4

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 = ($29.30 × 0.74699) - ($25 × 2.71828^-0.04 ^{× 0.25} × 0.66642) = $5.39

Question 5

Pure financial mergers:

Accepted Answer

The answer of Pure financial mergers:
...

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 $1.50 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 - $1.50 = -$0.90

Question 7

Grocery Express stock is selling for $22 a share.A 3-month,$20 call on this stock is priced at $2.85.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) + $2.85 - $22 = $0.73

Question 8

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 9

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 10

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 shareholders need to eliminate the risk associated with the bonds. The best way to do this would be to purchase a put option, which would give them the right to sell the bonds at a predetermined price. Since the bonds have a total current market value of $8.1 million, the shareholders should purchase a put option with a 3-year life and an $8.5 million face value, which will allow them to sell the bonds for a guaranteed price of $8.5 million at the end of the 3-year period. This will eliminate the risk associated with the bonds and convert them into risk-free bonds. Option E is the only choice that offers a put option with the appropriate terms.

Question 11

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 × 1.04) - $38.46 + $0 - $1.85 = -$0.31

Question 12

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 $5.63.What is the continuously compounded risk-free rate of return?

Accepted Answer

($40 × e^-R ^{× 0.75}) = -$2.23 + $36 + $5.63$40 e^-0.75R = $39.40ln(e^-0.75R) = ln0.985-0.75R = -0.0151R = 2.02 percent

Question 13

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

Accepted Answer

The value of risky debt can be thought of as the value of a risk-free bond minus the value of a put option. This is because the risky debt incorporates the possibility of default, which is similar to the holder of the debt having sold a put option on the firm's assets.

Question 14

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 × (0.75^1/2)] = -1.1346

Question 15

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 × 2.71828^0.075 ^{× 5} = $12,367

Question 16

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 4 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 × 1.04) - $26.57 + ($29 - $27.50) - $1.40 = $1.16

Question 17

A purely financial merger:

Accepted Answer

The answer of A purely financial merger:
...

Question 18

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

Accepted Answer

d₂ = 0.63355 - [0.58 × (0.75^1/2)] = 0.1313

Question 19

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 20

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 × e^-R ^{× 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

Quiz 25: Option Valuation