Question

Consider a single period binomial setting where the risk-free interest rate is zero, and there are no taxes. A firm consists of a machine that will produce cash flows of $200 if the economy is good and $87 if the economy is bad. The good and bad states occur with equal probability. Initially, the firm has 100 shares. Assume that outstanding debt with a face value of $80 is due at the end of the period. Suppose the firm unexpectedly announces that it will issue additional debt. This debt will be the same seniority with respect to existing debt and will have a face value of $40. The firm will use the entire proceeds to repurchase some of the outstanding shares. What is the price that the firm should offer in order to make existing shareholders to be indifferent between selling and not selling?

Select one:

a. 0.7

b. 0.945

c. 0.745

d. 0.9

Answer 1

$87 * 0.5 + $200 * 0.5 = $144 in expected equity. Minus the $80 of probably soon to be insolvent-debt, means we have ourselves $64 in equity, divided by 100 mostly worthless shares, gives us $0.64 Debased American Puppet Currency per share.
Well, the idiot who gave the debt to the firm didn't think of making it senior, so his dumbass now has to split the $87 with the other guy evenly like a tool:

$40 * .5 + $43.5 * .5 = $41.75.

So its worth $41.75.

First we know that they will take this $41.75 and buy back n worthless shares at an overvalued price we will call p. We also know that the remaining value of the equity in each scenario is as follows:

0.5 * 200 - 100 + 0.5 * 0 = $0

The firm will be worth $0 in any situation