Question

4. The cost of retained earnings

If a firm cannot invest retained earnings to earn a rate of return (greater than or equal to, Less than) the required rate of return on retained earnings, it should return those funds to its stockholders.

The cost of equity using the CAPM approach

The current risk-free rate of return (rRFrRF) is 3.86% while the market risk premium is 6.63%. The D’Amico Company has a beta of 0.78. Using the capital asset pricing model (CAPM) approach, D’Amico’s cost of equity is (9.997%, 9.4815, 9.03, 10.836) .

The cost of equity using the bond yield plus risk premium approach

The Hoover Company is closely held and, therefore, cannot generate reliable inputs with which to use the CAPM method for estimating a company’s cost of internal equity. Hoover’s bonds yield 11.52%, and the firm’s analysts estimate that the firm’s risk premium on its stock over its bonds is 3.55%. Based on the bond-yield-plus-risk-premium approach, Hoover’s cost of internal equity is:

16.58%

18.08%

15.07%

18.84%

The cost of equity using the discounted cash flow (or dividend growth) approach

Tyler Enterprises’s stock is currently selling for $32.45 per share, and the firm expects its per-share dividend to be $2.35 in one year. Analysts project the firm’s growth rate to be constant at 5.72%. Estimating the cost of equity using the discounted cash flow (or dividend growth) approach, what is Tyler’s cost of internal equity?

12.96%

16.20%

17.50%

13.61%

Estimating growth rates

It is often difficult to estimate the expected future dividend growth rate for use in estimating the cost of existing equity using the DCF or DG approach. In general, there are three available methods to generate such an estimate:

•	Carry forward a historical realized growth rate, and apply it to the future.
•	Locate and apply an expected future growth rate prepared and published by security analysts.
•	Use the retention growth model.

Suppose Tyler is currently distributing 45% of its earnings in the form of cash dividends. It has also historically generated an average return on equity (ROE) of 24%. Tyler’s estimated growth rate is (23.45, 79, 24.55, 13.2) %.

Answer 1

If a firm cannot invest retained earnings to earn a rate of return GREATER THAN the required rate of return on retained earnings, it should return those funds to its stockholders.

Using CAPM, Cost of Equity = Risk free return + beta*market risk premium

= 3.86% + 0.78*6.63%

= 9.0314%

i.e. 9.03%

Cost of Equity using bond yield plus risk premium

= Bond yield + risk premium

= 11.52% + 3.55%

= 15.07%

Price = Expected Dividend/(Cost of Equity – Growth Rate)

32.45 = 2.35/(Cost of Equity – 5.72%)

Cost of Equity = 12.96%

Growth rate = ROE*Retention Ratio

= 24%*50%

= 13.2%