Question

The CFO of Lenox Industries hired you as a consultant to help estimate its cost of capital. You have obtained the following data: (1) rd = yield on the firm’s bonds = 7.00% and the risk premium over its own debt cost = 4.00%. (2) rRF = 5.00%, RPM = 6.00%, and b = 1.25. (3) D1 = $1.20, P0 = $35.00, and g = 8.00% (constant). You were asked to estimate the cost of equity based on the three most commonly used methods and then to indicate the difference between the highest and lowest of these estimates. What is that difference?

a. 1.13%
b. 1.50%
c. 1.88%
d. 2.34%
e. 2.58%

Answer 1

To calculate the cost of equity using DDM, CAPM, and BYPRP, the estimates were 11.43%, 12.5%, and 11% respectively. The difference between the highest and lowest estimates is 1.5%, which corresponds to option (b).

The goal is to calculate the cost of equity for Lenox Industries using three different methods and then determine the difference between the highest and lowest estimates. The three methods to estimate the cost of equity are the Dividend Discount Model (DDM), the Capital Asset Pricing Model (CAPM), and the Bond Yield Plus Risk Premium (BYPRP) approach.

Using DDM, the formula is ke = (D1 / P0) + g, where:

• D1 = Next year's expected dividend = $1.20
• P0 = Current price of the stock = $35.00
• g = Growth rate of dividends = 8%

So, ke (DDM) = ($1.20 / $35.00) + 0.08 = 0.03429 + 0.08 = 11.43%.

Using CAPM, the formula is ke = rRF + (b * RPM), where:

• rRF = Risk-free rate = 5%
• b = Beta of the stock = 1.25
• RPM = Risk premium of the market = 6%

So, ke (CAPM) = 5% + (1.25 * 6%) = 5% + 7.5% = 12.5%.

Using BYPRP, the formula is ke = rd + risk premium, where:

• rd = Yield on the firm’s bonds = 7%
• risk premium = Risk premium over firm's own debt cost = 4%

So, ke (BYPRP) = 7% + 4% = 11%.

The difference between the highest estimate (CAPM at 12.5%) and the lowest estimate (BYPRP at 11%) is 1.5% (12.5% - 11% = 1.5%). Therefore, the answer is (b) 1.50%.