During the last few years, Jana Industries has been too constrained by the high cost of capital to make many capital investments. Recently, though, capital costs have been declining, and the company has decided to look seriously at a major expansion program proposed by the marketing department. Assume that you are an assistant to Leigh Jones, the financial vice president. Your first task is to estimate Jana$$s cost of capital. Jones has provided you with the following data, which she believes may be relevant to your task:

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

The current price of Jana$$s $12\%$ coupon, semiannual payment, noncallable bonds with $15$ years remaining to maturity is $$1,153\mathrm{.}72.$ There are $70,000$ bonds. Jana 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$ par value, quarterly dividend, perpetual preferred stock is $$116\mathrm{.}95.$ There are $200,000$ outstanding shares. Jana would incur flotation costs equal to $5\%$ of the proceeds on a new issue.

Jana$$s common stock is currently selling at $$50$ per share. There are $3$ million outstanding common shares. Its last dividend

$($D$0)$was $$3\mathrm{.}12,$ and dividends are expected to grow at a constant rate of $5\mathrm{.}8\%$ in the foreseeable future. Jana$$s beta is $1\mathrm{.}2,$ the yield on T$-$bonds is $5\mathrm{.}6\%,$ and the market risk premium is estimated to be $6\%.$ For the own$-$bond$-$yield$-$plus$-$judgmental$-$risk$-$premium approach, the firm uses a $3\mathrm{.}2\%$ risk premium.

Jana$$s preferred stock is riskier to investors than its debt, yet the preferred stock$$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.$)$