Question

Brozik Corp. has a zero coupon bond that matures in five years with a face value of $83,000. The current value of the company’s assets is $79,000, and the standard deviation of its return on assets is 42 percent per year. The risk-free rate is 4 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 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.)

  

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

Brozik Corp. has a zero coupon bond that matures in five years with a face value of $83,000. The current value of the company’s assets is $79,000, and the standard deviation of its return on assets is 42 percent per year. The risk-free rate is 4 percent per year, compounded continuously.

Face value of debt, FV = $ 83,000, Risk free rate, r_f = 4% = 0.04, compounded continuously, T = time to maturity = 5 years

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.)

  the value of a risk-free bond with the same face value and maturity as the current bond = PV of FV = $ FV.e^-r_fT = $ 83,000 x e^{-0.04 x 5} = $ 67,954.65

Value of risk-free bond: $ 67,954.65

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.)

We will have to work it out using the Black Scholes Formula. Price of the put option is given by p. The symbols have their usual meanings in the world of derivative.

I have done this in excel. Against every calculation, I have also shown the formula used so that you can understand the mathematics.

Price of put option, p = $ 21,343.30

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.)

Company's debt = the value of a risk-free bond with the same face value and maturity as the current bond - p = $ 67,954.65 (calculated in part a) - $ 21,343.30 (calculated in part b) = $ 46,611.36

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.)

Market value of debt = 46,611.36 = Face Value of debt x e^-YT = 83,000 x e^-Y5

Hence, yield = Y = 1/5 x ln(83,000 / 46,611.36) = 11.54%

Return on debt: 11.54%

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.)

Value of debt $ 41,528.24

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 13.85% (Please see the last output in the table above)

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.)

Gain / (Loss) = Value of debt after restructuring - value of debt prior to restructuring =  41,528.24 -  46,611.36 = - 5,083.11

  

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   $   
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