3. 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) Capitalassetpricingmodel (CAPM) approach
b) Bondyieldpluspremium approach
c) Discounted cash flow approach
a) CAPM Approach
To calculate the cost of capital using the CAPM approach, you must first estimate the riskfree rate (r_{f}), which is typically the U.S. Treasury bond rate or the 30day Treasurybill 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 11.3
Example: CAPM approach
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:
k_{s} = r_{f }+ b_{i }(r_{m}  r_{f}) = 4% + 1.1(15%4%) = 16.1%
b) BondYieldPlusPremium Approach
This is a simple, ad hoc approach to estimating the cost of retained earnings. Simply take the interest rate of the firm's longterm debt and add a risk premium (typically three to five percentage points):
Formula 11.4
k_{s}= longterm bond yield + risk premium 
Example: bondyieldpluspremium approach
The interest rate on Newco's longterm debt is 7% and our risk premium is 4%. What is the cost of retained earnings for Newco using the bondyieldpluspremium approach?
Answer:
k_{s} = 7% + 4% = 11%
c) Discounted Cash Flow ApproachAlso known as the "dividend yield plus growth approach". Using the dividendgrowth model, you can rearrange the terms as follows to determine k_{s}.
Formula 11.5
k_{s }= D_{1} + g; Â Â Â Â Â Â Â P_{0}
where: 
Typically, you must also estimate g, which can be calculated as follows:
Formula 11.6
g = (retention rate)(ROE) = (1payout 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 = (10.3)(0.10) = 7.0%
k_{s} = 2/40 + 0.07 = 0.12 or 12%
Exam Tips and Tricks Of the three approaches to determine the cost of retained earnings, be most familiar with the CAPM approach and the dividendyieldplusgrowth approach 

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