Question

I am re-posting this question because I never received the correct answer. - This is all the information it gives me.

Brozik Corp. has a zero coupon bond that matures in five years with a face value of $77,000. The current value of the company’s assets is $73,000, and the standard deviation of its return on assets is 36 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.)

  

Value of risk-free bond

$

  

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.)

  

Price of put option

$

  

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.)

  

Value of company's debt

$

   

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.)

  

Return on debt

%

       

d-1.	Assume the company can restructure its assets so that the standard deviation of its return on assets increases to 45 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.)

  

Value of debt

$

  

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.)

  

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 how much will stockholders 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.)

  

Stockholders' gain / loss

$

Answer 1

a. Risk free rate = 5% continuosly compounded

Value of risk free bond = 77000*exp(-0.05*5) = $ 59967.66

b.

Firm assets(S) = $ 73000

Debt face value(X) = $ 77000

Standard Deviation = 36%

Risk Free rate = 5%

d1 = [ln(73000/77000) + (0.05 + 0.36^2/2)*5]/[0.36*sqrt(5)] = 0.6468

d2 = 0.6468-(0.36*sqrt(5)) = -0.1582

N(d1) = 0.7411

N(d2) = 0.4372

Equity = $73000*(0.7411) - ($77,000*exp(-0.05*5))*(0.4372) = $ 27886.50

Debt = $73000- $27886.50= $ 45113.50

PUt option value = p=Xe^–rTN(–d₂)–S₀N(-d₁)

= $ 14854.16

Yield on debt = (77000/45113.50)^0.2-1 = 11.28%

d. If standard deviation increases to 45%

d1 = [ln(73000/77000) + (0.05 + 0.45^2/2)*5]/[0.45*sqrt(5)] = 0.6986

d2 = 0.6986-(0.45*sqrt(5)) = -0.3077

N(d1) = 0.7576

N(d2) = 0.3792

Equity = $73000*(0.7576) - ($77,000*exp(-0.05*5))*(0.3792) = $ 32566.08

Debt = $73000- $32566.08= $ 40433.92

Yield on debt = (77000/40433.92)^0.2-1 = 13.75%

e. Gain to shareholders = 32566.08-27886.50 = 4679.58

Loss to bondholders = 40433.92-45113.50 = -4679.58