Mini Case $5\mathrm{.}4$

Great Minds $($GM$)$ has risk$-$free debt outstanding with a current value of $10$ million and $1$ million

shares outstanding. The correct price for these shares is either $15$ or $13$ per share. Investors view both

possibilities as equally likely, so the shares currently trade for $14.$ GM must raise $40$ million to build

a new production facility. Because the firm would suffer a large loss of both customers and engineering

talent in the event of financial distress, managers believe that if GM borrows the $40$ million, the present

value of financial distress costs will exceed any tax benefits by $0\mathrm{.}5$ million. At the same time, because

investors believe that managers know the correct share price, GM faces a lemons problem if it attempts

to raise the $40$ million by issuing equity.

a$.$ Suppose that if GM issues equity, the share price will remain at $14.$ To maximize the long$-$

term share price of the firm once its true value is known, would managers choose to issue equity

or borrow the $40$ million if

I$)$ they know the correct value of the shares is $13?$

II$)$ they know the correct value of the shares is $15?$

$($Hint: When the firm raises equity or debt, the balance sheet of the firm is updated with an increase in

cash and a corresponding increase in equity or debt.

Total assets of the firm $=$ Existing assets $+$ New cash

Total debt and equity $=$ Existing debt $+$ Existing equity $+$ New equity $($debt$)$

Since the managers know the correct value of the shares, they know the true value of existing assets of

the firm. The long$-$term share price is calculated as true value of equity at the moment divided by the

total number of shares outstanding.$)$

b$.$ Given your answer to part $($a$),$ what should investors conclude if GM issues equity? What will

happen to the share price?

c$.$ Given your answer to part $($a$),$ what should investors conclude if GM issues debt? What will

happen to the share price in that case?

d$.$ How would your answers change if the present value of tax benefits will exceed any financial

distress costs by $1$ million?