Question

North Technology Inc. has a zero-coupon bond that matures in five years with a face value of $60,000. The current value of the company’s asset is $57,000 and the standard deviation of its rate of return on assets is 50% per year. The continuously compounded risk-free rate of interest is 6%.

1. What are the market values of the company’s debt and equity?

2, What is the yield on North Technology’s debt?

3. What is the value of shareholders’ limited liability?

4. Suppose the company can re-structure its balance sheet so that the standard deviation of its return on assets increases to 60% per year. Assuming all other things remaining the same, who (shareholders vs. bondholders) benefits from the restructuring and why? What are the magnitude of loss/gain to each type of stakeholders? Show your calculations. (Need detailed explanation)

Answer 1

Firm assets(S) = $ 57000

Debt face value(X) = $ 60000

Standard Deviation = 50%

Risk Free rate = 6%

d1 = [ln(57000/60000) + (0.06 + 0.50^2/2)*1]/[0.50*sqrt(5)] = 0.7815

d2 = 0.7815-(0.50*sqrt(5)) = -0.3366

N(d1) = 0.7827

N(d2) = 0.3682

Equity = $57000*(0.7827) - ($60,000*exp(-0.06*5))*(0.3682) = $ 28248.84

Debt = $57000- $28248.84= $ 28751.16

2. Yield on Debt = (60000/28751.16)^(1/5)-1 = 15.85%

3. Shareholders limited liability = 28751.16

4. Foloowing the above calculations:

Equity = 31888.24

Debt = 25111.66

Equity value increases with the restructuring as due to higher volatility, debtholders demand higher rate of return.

Gain to equity holder = (31888.24-28248.84)/28248.84 = 12.88%

Loss to debt holders = (25111.66-28751.16)/28751.16 = -12.66%