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 rate of return on assets is 50% per year. The continuously compounded risk-free rate of interest is 6%.

a) What are the market values of the company’s debt and equity?

b) What is the yield to maturity on North Technology’s debt?

c) What is the value of shareholders’ limited liability?

d) 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 magnitudes of loss/gain to each type of stakeholders? Show your calculations.

Answer 1

d1 = ln{($57,000 / $60,000) + (.06 + .602 /2) *5 } / .60*√5

d1= .8562

d2 = .8562 - (.60 * ​​​​​​√5)

d2 = -.4854

N(d1) = .8041 N(d2) = .3137

We find the new equity value (putting this value in Black-Scholers model)

EB = $57,000 (.8041) - ($60,000 - .06(5))(.3137)

EB = $31,890.02

The value of new debt is the firm:

DB = $57,000 - $31,890.02

DB = $25,109.98

  

Values	standard deviation 50%	Standard deviation 60%	Gain / (loss)
Values	$28,247.79	$31,890.02	$3,642.28
Values	$28,752.26	$25,109.98	($3,642.28)

$3,642 ($31,890.02 - $28,247.79) value transfer from bondholders to stockholders, which is preferred by the stockholders as a result with the higher standard deviation of 60%per year.

This is why stockholders would prefer higher risk project since they would increase the value of equity.