COST OF CAPITAL Coleman Technologies is considering a major expansion program that has been proposed by the company's information technology group. Before proceeding with the expansion, the company must estimate its cost of capital. Suppose you are an assistant to Jerry Lehman, the financial vice president. Your first task is to estimate Coleman's cost of capital. Lehman has provided you with the following data, which he believes may be relevant to your task.

$$The firm's tax rate is $25\%.$

$$The current price of Coleman's $12\%$ coupon, semiannual payment, noncallable bonds with $15$ years remaining to maturity, is $$1,153\mathrm{.}72.$ Coleman does not use short$-$term, interest$-$bearing debt on a permanent basis. New bonds would be privately placed with no flotation cost.

$$The current price of the firm's $10\%,$ $$100\mathrm{.}00$ par value, quarterly dividend, perpetual preferred stock is $$111\mathrm{.}10.$

$$Coleman$\text{'}$s common stock is currently selling for $$50\mathrm{.}00$ per share. Its last dividend $($D$0)$ was $$4\mathrm{.}19,$ and dividends are expected to grow at a constant annual rate of $5\%$ in the foreseeable future. Coleman's beta is $1\mathrm{.}2,$ the yield on T$-$bonds is $7\%,$ and the market risk premium is estimated to be $6\%.$ For the bond$-$yield$-$plus$-$risk$-$premium approach, the firm uses a risk premium of $4\%.$

$$Coleman$\text{'}$s target capital structure is $30\%$ debt, $10\%$ preferred stock, and $60\%$ common equity.

To structure the task somewhat, Lehman has asked you to answer the following questions:

$1.$What is the firm's cost of preferred stock?

$2.$Coleman's preferred stock is riskier to investors than its debt, yet the preferred's yield to investors is lower than the yield to maturity on the debt. Does this suggest that you have made a mistake? $($Hint: Think about taxes.$)$