Chapter 13 What is the difference in the expected returns on

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Fundamentals of Derivatives Markets (McDonald)

Chapter 13 Corporate Applications

13.1 Multiple Choice Questions

1) We will assume that Nathans, Inc. has 3–year zero–coupon debt outstanding, which will pay

$200 at maturity. The assets are valued at $175, σ = 0.20, r = 0.04, and the company does not

pay a dividend. Using a Black–Scholes model, what is the value of the equity?

A) $23.05

B) $43.05

C) $63.05

D) $83.05

2) Jessie, Inc. has 4–year zero–coupon bonds outstanding, which will pay $1,000 at maturity.

The assets are valued at $900, σ = 0.25, r = 0.045, and the company does not pay a dividend.

Using a Black–Scholes model, what is the yield on debt?

A) 4.68%

B) 6.48%

C) 8.46%

D) 8.64%

3) Compute the yield on debt given a 10–year zero–coupon bond paying $500 at maturity.

Assume the asset value is $450, σ = 0.35, r = 0.06, and no dividend is paid.

A) 6.62%

B) 7.26%

C) 8.26%

D) 9.62%

4) What is the expected return on equity using the Black–Scholes formula, given a zero–coupon

bond that pays $250 at maturity in 4 years? Assume assets are worth $200, r = 0.05, σ = 0.30,

and no dividend is paid. The return on assets is 11.5%.

A) 10.27%

B) 14.27%

C) 18.27%

D) 22.27%

5) What is the difference in the expected returns on equity when using a Black–Scholes formula

versus a traditional weighted average formula? Assume rA = 0.12, rf = 0.06, asset value =

$170, equity value = $45, debt to value ratio = 0.55, and delta = 0.6500.

A) 1.00%

B) 1.20%

C) 1.40%

D) 1.60%

6) James, Inc. has zero–coupon outstanding debt maturing in 8 years. In rank of seniority, each

pays at maturity $20 million, $15 million, and $40 million. Assume asset value = $60 million,

r = 0.05, σ = 0.28, and no dividend is paid. What is the yield on the $15 million subordinate

debt?

A) 5.72%

B) 6.72%

C) 7.72%

D) 8.72%

7) Daniels, Inc. has assets valued at $2 million and 50,000 outstanding shares. A 5–year zero–

coupon bond exists, which pays $400,000 at maturity. The bond is convertible into 10,000

shares. Assume σ = 0.30, r = 0.055, and no dividend is paid. What is the value of the bond?

A) $402,672

B) $452,172

C) $415,022

D) $385,172

8) Willco, Inc. issues compensation options with the following terms. Strike = $45, price =

$42.00, σ = 0.48, r = 0.05, div = 0.02. What is the value of the option if it will be repriced at

$30? Assume 10 years to expiration.

A) $22.78

B) $24.65

C) $26.22

D) $30.46

9) Lechno, Inc. issues compensation options with the following terms. Strike = $65, price =

$63.50, σ = 0.22, r = 0.045, div = 0.015. What is the value of the option if it will be repriced at

$40? Assume 10 years to expiration.

A) $18.64

B) $22.22

C) $24.32

D) $26.84

10) A company issues an option grant with an outperformance feature, against the S&P 500.

Assume S&P 500 = 950, S = 22, k = 25, σ = 0.25, r = 0.06, and 5 years until expiration. The S&P

500 has a dividend yield of 2%, standard deviation of 18.0% and a 0.30 correlation coefficient

with the stock. What is the value of the outperformance feature?

A) $0.99

B) $1.31

C) $1.59

D) $1.72

11) A company issues an option grant with an outperformance feature, against the S&P 500.

Assume S&P 500 = 1100, S = 46, k = 45, σ = 0.30, r = 0.04, and 10 years until expiration. The

S&P 500 has a dividend yield of 2.5%, standard deviation of 20.0% and a 0.45 correlation

coefficient with the stock. What is the value of the outperformance option?

A) $11.92

B) $15.99

C) $19.75

D) $21.05

12) A company issues an option grant with an outperformance feature, against the S&P 500.

Assume S&P 500 = 1100, S = 46, k = 45, σ = 0.30, r = 0.04, and 10 years until expiration. The

S&P 500 has a dividend yield of 2.5%, standard deviation of 20.0% and a 0.45 correlation

coefficient with the stock. What is the value of the outperformance feature?

A) $2.25

B) $3.29

C) $4.11

D) $4.78

13) A company issues an option grant with an outperformance feature, against the S&P 500.

Assume S&P 500 = 1100, S = 46, k = 45, σ = 0.30, r = 0.04, and 10 years until expiration. The

S&P 500 has a dividend yield of 2.5%, standard deviation of 20.0% and a 0.45 correlation

coefficient with the stock. What is the value of the outperformance option?

A) $11.92

B) $15.99

C) $19.75

D) $21.05

14) In the case of an acquisition, with which of the following offer structures does the acquired

firm bear the most risk between the time the offer is accepted and the time it is

consummated?

A) Fixed stock offer

B) Floating stock offer

C) Fixed collar offer

D) Floating collar offer

15) A firm with assets value at $20 million issues a 10 year zero–coupon bond with a par value of

$22 million. Using a put option approach, what is the value of an insurance contract on the

bond given r = .05, volatility is given as .18 and there is no dividend paid by the company?

A) $0.82 million

B) $1.27 million

C) $2.23 million

D) $2.98 million

16) A firm with assets value at $10 million issues a 4 year zero–coupon bond with a par value of

$15 million. Using a put option approach, what is the value of the defaultable bond given r =

.06, volatility is given as .15 and there is no dividend paid by the company?

A) $7.83 million

B) $8.05 million

C) $8.89 million

D) $9.41 million

17) A firm with assets value at $200,000 issues a 3 year zero–coupon bond with a par value of

$250,000. Using a put option approach, what is the value of an insurance contract on the

bond given r = .08, volatility is given as .23 and there is no dividend paid by the company?

A) $29,672

B) $31,582

C) $33,331

D) $42,195

18) A firm with assets value at $500,000 issues a 6 year zero–coupon bond with a par value of

$550,000. Using a put option approach, what is the value of the defaultable bond given r =

.07, volatility is given as .33 and there is no dividend paid by the company?

A) $75,970

B) $245,601

C) $285,406

D) $361,376

19) A firm with assets value at $350,000 issues a 5 year zero–coupon bond with a par value of

$400,000. Interest rates are 5% and the volatility of the company’s assets are determined to be

.29. If the company pays no dividend, what is the delta of the issued debt?

A) .307

B) .324

C) .365

D) .396

20) A firm with assets value at $100,000 issues a 3 year zero–coupon bond with a par value of

$110,000. Interest rates are 4% and the volatility of the company’s assets are determined to be

.30. If the company pays no dividend, what is the change in the value of the firm’s debt if the

value of the assets increases by $20,000?

A) $ 6,930 decrease

B) $ 7,580 increase

C) $ 8,309 decrease

D) $ 9,029 increase

13.2 Short Answer Essay Questions

1) How does a reload option provide additional compensation compared to regular

compensation options?

2) Why does a company sell a put when issuing compensation options?

3) What feature of reload options prevents the use of a Black–Scholes valuation?

4) What three components exist in the value of an “outperform stock option”?

5) The use of collars in acquisitions serves the purpose of addressing what two issues in an

offer?

13.3 Class Discussion Question

1) In advance of class, direct students to review material on portfolio diversification. In class,

assign one student the task of writing the portfolio standard deviation formula on the board.

Lead a discussion on the similarities between exchange options and portfolio diversification.

Ask the class how the Markowitz theory they learned previously is applied in exchange

options. See how many people can identify the risk reduction aspect of exchange options.