Question

Kasimov Corp. has a zero coupon bond that matures in five years with a face value of $94,000. The current value of the company’s assets is $90,000, and the standard deviation of its return on assets is 35 percent per year. The risk-free rate is 3 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.)

  

Value of risk-free bond

$

  

b.	What is the value of a put option on the firm’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.)

  

Price of the put option

$

  

c-1	Using the answers from (a) and (b), what is the value of the firm’s debt? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Value of firm's debt

$

   

c-2	What is the continuously compounded yield on the company’s debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Return on debt

%

  

d-1	Assume the company can restructure its assets so that the standard deviation of its return on assets increases to 44 percent per year. What happens to the value of the debt? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Value of debt

$

  

d-2	What is the new continuously compounded yield on the debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Return on debt

%

  

e-1	If the company restructures its assets, how much will bondholders gain or lose? (A loss should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Bondholders' gain/loss

$

e-2	If the company restructures its assets, how much will stockholders gain or lose? (A loss amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Stockholders' gain/loss

$

Answer 1

(a) Continuously Compounded Risk-Free Rate = 3% per annum, Bond Tenure = 5 years and Face Value = $ 94000

Let the Value of the Risk -Free Bond be V(Risk Free)

Therefore, V (Risk Free) = 94000 / EXP(0.03 x 5) = $ 80906.55 approximately

(b) Put Option Strike Price = Face Value of Debt = K = $ 94000, Underlying Asset Value = S = $ 90000, Risk Free Rate = r = 3% per anum, Option Tenure = Bond Tenure = t = 5 years, Standard Deviation = s = 35%

Let the price of the put option be P

Using Black Scholes Model, P = N(-d2) x K x e^(-r x t) - S x N(-d1) where d1 = [ln(S/K) + {r + (s)^(2)/2} x t] / s x (t)^(0.5) and d2 = d1 - s x (t)^(0.5)

N(-d1) = 0.298954 and N(-d2) = 0.60072

P = 94000 x EXP(-0.03 x 5) x 0.060072 - 90000 x 0.298954 = $ 21696.32259 or $ 21696.32

(c1) Value of Firm's Debt = V(Risk Free) - P = 80906.55 - 21696.323 = $ 59210.227 or $ 59210.23 approximately

(c2) Market Value of Debt = D(MV) = $ 59210.227, Face Value of Debt = D(FV) = $ 94000, Debt Tenure = t = 5 years and let the continuously compounded cost of debt be kd

Therefore, D(MV) = D(FV) / EXP (kd x t)

59210.23 = 94000 / EXP[kd x 5]

LN(94000 / 59210.23) = kd x 5

kd = 0.09244 or 9.244 % or 9.24% approximately

NOTE: Please raise separate queries for solutions to the remaining sub-parts.