A firm wants to raise $30m to invest in a project. After the $30m invest- ment,

Question

A firm wants to raise $30m to invest in a project. After the $30m invest-

ment, the firm will have a total asset value of $100m. The risk-free rate

is 10%, and the volatility of the return on assets is 20%.

(a) If the firm wants to issue 10-year debt (zero-coupon), what face value

do they need to set?

(b) Now imagine that the bond has been issued (with a face value that

you found in the previous part), but that the stockholders can choose

an action that changes the nature of the cash flows. Namely, the

shareholders can: (1) do nothing, (2) take an action that will imme-

diately reduce the value of the assets from $100m to $99m and at the

same time raise the volatility to 30%. Will the shareholders take this

action?

(c) If the bondholders anticipated this possibility when they were of-

fered to invest in the company, what do you expect they would have

demanded as a face value?

(d) Would the shareholders have an incentive to include a covenant pro-

hibiting the action in part (b) above?

Explanation / Answer

(a)

Zero coupon bond face value = F / (1+r)t

F = face value of bond

r = rate or yield

t = time to maturity

$30 million = F / (1+0.10)10

F = 78 million

(b)

The shareholders will not take this return as it will reduce the assets.

(c) No they would not have demanded as a face value

(d) Yes, they have an incentive to include a covenant prohibiting the action as it will impact their returns in future

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