Radiator Products Company (RPC) is at its optimal capital structure of 75 percen

Question

Radiator Products Company (RPC) is at its optimal capital structure of 75 percent common equity and 25 percent debt. RPCs WACC is 12.50 percent. RPC has a marginal tax rate of 40 percent. Next years dividend is expected to be $2.50 per share, and RPC has a constant growth in earnings and dividends of 5 percent. The cost of common equity used in the WACC is based on retained earnings, while the before?tax cost of debt is 10 percent. What is RPCs current equilibrium stock price?

      a.    $12.73      b.    $17.23      c.    $25.83      d.    $20.37      e.23.70

Explanation / Answer

Step 1: Calculate the Cost of Common Equity

The cost of common equity will be calculated with the use of formula for WACC. The formula for WACC is:

WACC = After Tax Cost of Debt*Weight of Debt + Cost of Equity*Weight of Equity

__________

Substituting the information provided in the question in the above formula, we get,

12.50 = 10*(1-.40)*25% + Cost of Equity*75%

Rearraging the values, we get,

Cost of Equity = (12.50 - 1.50)/75% = 14.67%

_____________________

Step 2: Calculate Current Equilibirium Stock Price

We will use Gordon's constant dividend growth model to calculate the price. The formula is:

Current Equilibirium Stock Price = D1/(Cost of Equity - Growth Rate)

__________

Here, D1 = 2.50, Cost of Equity = 14.67% (from step 1) and Growth Rate = 5%

Using these values in the above formula for price, we get,

Current Equilibirium Stock Price = 2.50/(14.67% - 5%) = $25.85 which is closest to $25.83 (which is Option C)

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