A company currently has $$100$ million market value of equity, $$20$ million market value of debt, and $$15$ million cash balance.

Currently, the company has $5$ million equity shares outstanding.

The current cost of capital is $15\%.$

If the company increases its debt to $$30$ million, the cost of capital decreases to $12\%.$

a$)$ What is the annual savings in the cost of financing?

b$)$ What is the present value of the annual savings, assuming the savings grows perpetually at the rate of $3\%?$

c$)$ What is the present value of the annual savings, assuming the savings are only valid for $10$ year? Additionally, assume the savings do not grow during this $10-$year period?

d$)$ Suppose the company use the extra debt to issue more equity at the "rational" stock price. Using the same assumptions as in part $($c$)$ above, estimate the share price after the stock buyback. Assume transactions of partial shares are possible.

a$.$

a$)$ $$2\mathrm{.}85$ million; b$)$ $$28\mathrm{.}5$ million; c$)$ $$19\mathrm{.}4$ million; d$)$ $$23\mathrm{.}88$

b$.$

a$)$ $$2\mathrm{.}85$ million; b$)$ $$25\mathrm{.}91$ million; c$)$ $$16\mathrm{.}1$ million; d$)$ $$23\mathrm{.}22$

c$.$

a$)$ $$3\mathrm{.}5$ million; b$)$ $$25\mathrm{.}91$ million; c$)$ $$17\mathrm{.}8$ million; d$)$ $$24\mathrm{.}35$

d$.$

a$)$ $$2\mathrm{.}90$ million; b$)$ $$26\mathrm{.}9$ million; c$)$ $$16\mathrm{.}8$ million; d$)$ $$25\mathrm{.}18$