Halprin is an unlevered firm that is currently evaluating a plan to issue new debt and repurchase some outstanding stock, keeping the size of the firm unaffected.

Because interest expenses are tax$-$deductible, the firm value would increase, but the probability of bankruptcy would also increase. The CFO estimates that the present value of any bankruptcy cost is $$5$ million, and she has provided the following table showing the probability of bankruptcy as a function of the amount of new debt that the firm might take on:

Value of debt

$($$ million$)$ Probability of bankruptcy

$30\%$

$61\%$

$93\%$

$128\%$

$1518\%$

$1838\%$

$2180\%$

The stock has a beta of $1,$ and the firm's marginal tax rate is $28\%.$

The risk$-$free rate is $4\%$ and the market risk premium,

E

$($

r

M

$)$

$$

r

f

$,$ is $5\%.$

Attempt $1/99$ for $10$ pts$.$

Part $1$

What is the firm's current cost of capital?

$9\%$

Correct $$

Cost of equity:

E

$($

r

Equity

$)$

$=$

r

f

$+$

$\backslash$beta

$($

E

$($

r

M

$)$

$$

r

f

$)$

$=$

$0\mathrm{.}04$

$+$

$1$

$$

$0\mathrm{.}05$

$=0\mathrm{.}09$

Since the firm is currently unlevered, i$.$e$.,$ all capital comes from equity, the cost of capital is equal to the cost of equity.

Attempt $9/99$ for $10$ pts$.$

Part $2$

What is the net benefit from debt at the optimal capital structure, i$.$e$.,$ the benefit from debt minus the expected cost of bankruptcy $($in $ million$)?$

$2+$ decimals