Cost of Retained Earnings

Cost of retained earnings (k_s) is the return stockholders require on the company's common stock.

There are three methods one can use to derive the cost of retained earnings:

a)     Capital-asset-pricing-model (CAPM) approach
b)     Bond-yield-plus-premium approach
c)     Discounted cash flow approach


CAPM Approach

 To calculate the cost of capital using the CAPM approach, you must first estimate the risk-free rate (r_f), which is typically the U.S. Treasury bond rate or the 30-day Treasury-bill rate as well as the expected rate of return on the market (r_m).

The next step is to estimate the company's beta (b_i), which is an estimate of the stock's risk. Inputting these assumptions into the CAPM equation, you can then calculate the cost of retained earnings.

Formula

Example: 

For Newco, assume r_f = 4%, r_m = 15% and b_i = 1.1. What is the cost of retained earnings for Newco using the CAPM approach?

Answer:

ks = rf + bi (rm - rf) = 4% + 1.1(15%-4%) = 16.1%


b)    Bond-Yield-Plus-Premium Approach
 
To estimating the cost of retained earnings. Simply take the interest rate of the firm's long-term debt and add a risk premium (typically three to five percentage points):

Formula

k_s = long-term bond yield + risk premium


Example: bond-yield-plus-premium approach

The interest rate on Newco's long-term debt is 7% and our risk premium is 4%. What is the cost of retained earnings for Newco using the bond-yield-plus-premium approach?

Answer: k_s = 7% + 4% = 11%

c)     Discounted Cash Flow Approach

Also known as the "dividend yield plus growth approach". Using the dividend-growth model, you can rearrange the terms as follows to determine k_s.

Formula

ks = D1 + g;         P0 where: D1 = next year's dividend g = firm's constant growth rate P0 = price You must also estimate g, which can be calculated as follows: Formula

g = (retention rate)(ROE) = (1-payout rate)(ROE) Example: discounted cash flow approach  Assume Newco's stock is selling for $40; its expected return on equity (ROE) is 10%, next year's dividend is $2 and the company expects to pay out 30% of its earnings. What is the cost of retained earnings for Newco using the discounted cash flow approach? Answer: g must first be calculated: g = (1-0.3)(0.10) = 7.0% ks = 2/40 + 0.07 = 0.12 or 12%

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