Question

Handler Corp. has a zero coupon bond that matures in five years with a face value of $87,000. The current value of the company’s assets is $83,000 and the standard deviation of its return on assets is 42 percent per year. The risk-free rate is 5 percent per year, compounded continuously.

  

a.	What is the value of a risk-free bond with the same face value and maturity as the current bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the value of a put option on the company’s assets with a strike price equal to the face value of the debt? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c-1.	Using the answers from (a) and (b), what is the value of the company’s debt? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c-2.	Using the answers from (a) and (b), what is the continuously compounded yield on the company’s debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
d-1.	Assume the company can restructure its assets so that the standard deviation of its return on assets increases to 51 percent per year. What is the new value of the debt? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
d-2.	What is the new continuously compounded yield on the debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
e-1.	If the company restructures its assets, how much will bondholders gain or lose? (A loss should be indicated by a minus sign.
e-2.	If the company restructures its assets, how how much will stockholders gain or lose? (A loss should be indicated by a minus sign.

Answer 1

a)
Value of a risk-free bond = $87,000 x e^–.05(5)	$                          67,755.67
b)
Using Black-Scholes model
S0 = underlying price	$83,000
X = strike price	$87,000
σ = volatility (% p.a.)	0.42
σ^2 = variance (% p.a.)	0.1764
r = continuously compounded risk-free interest rate (% p.a.)	0.05
q = continuously compounded dividend yield (% p.a.)	0
t = time to expiration (years in %)	5
Value of Equity =
d1 = [ln($83,000/$87,000) + (.05 + .42^2/2) × 5] / (.42 × sqrt(5)	0.6887
d2 =.7163 – (.42 × sqrt(5) =	-0.2504
N(d1) =	0.7545
N(d2) =	0.4011
Value of Equity = 83000 x .7545 - 67,755.67x .4011	$35,444.83
Price of the put option =  $67,755.67 + $35,444.83 - $83,000	$                          20,200.50
c- 1)
Value of Debt (Risky Bond ) = $67,755.67 - $20,200.50	$                          47,555.17
C-2
Continuously compounded yield on the company’s debt:
Return on debt: $47,555.17 = $87,000 x exp(–R x 5)		0.54661
.54661 = exp(–R(5)
Return on debt  = –(1/5)x ln(.54661) =	12.08%
d-1)
Value of a risk-free bond = $87,000 x e^–.05(5)	$                          67,755.67
Using Black-Scholes model
S0 = underlying price	$83,000
X = strike price	$87,000
σ = volatility (% p.a.)	0.51
σ^2 = variance (% p.a.)	0.2601
r = continuously compounded risk-free interest rate (% p.a.)	0.05
q = continuously compounded dividend yield (% p.a.)	0
t = time to expiration (years in %)	5
Value of Equity =
d1 = [ln($83,000/$87,000) + (.05 + .51^2/2) × 5] / (.51 × sqrt(5)	0.7424
d2 =.7424 – (.51 × sqrt(5) =	-0.3980
N(d1) =	0.7711
N(d2) =	0.3453
Value of Equity = 83000 x .7711 - 67,755.67x .3453	$40,602.24
Price of the put option =  $67,755.67 + $40602.2 - $83,000	$                          25,357.90
d- 1)
Value of Debt (Risky Bond ) = $67,755.67 - $25,357.90	$                          42,397.76
d-2
Continuously compounded yield on the company’s debt:
Return on debt: $42,397.76= $87,000 x exp(–R x 5)		0.48733062
.48733 = exp(–R(5)
Return on debt  = –(1/5)x ln(.48733) =	14.38%
e-1
Bondholders lose (42,397.76 - 47.555.17)	$                           (5,157.41)
stockholders gain ($40,602.24 - $35,444.83)	$5,157.41