Deck 13: Corporate Applications

Question 1

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

Answer 1

C

Question 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%

Answer 2

B

Question 3

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%

Answer 3

B

Question 4

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

Question 5

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

Question 6

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

Question 7

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 companyʹs assets are determined to be
)30. If the company pays no dividend, what is the change in the value of the firmʹs 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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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 companyʹs 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

Question 13

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%

Question 14

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

Question 15

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

Question 16

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%

Question 17

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

Question 18

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

Question 19

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

Question 20

What is the difference in the expected returns on equity when using a Black-Scholes formula versus a traditional weighted average formula? Assume r_A = 0.12, r_f = 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%

Question 21

How does a reload option provide additional compensation compared to regular compensation options?

Question 22

What feature of reload options prevents the use of a Black-Scholes valuation?

Question 23

What three components exist in the value of an ʺoutperform stock optionʺ?

Question 24

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

Question 25

The use of collars in acquisitions serves the purpose of addressing what two issues in an offer?