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  1. Explain three approaches that are used to estimate the cost of common equity.

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

a) CAPM Approach

To calculate the cost of capital using the CAPM approach, you must first estimate the risk-free rate (rf), 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 (rm).

The next step is to estimate the company's beta (bi), 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 

– CAPM

– Risk-free rate

- risk premium

Example: CAPM approach

For Newco, assume rf = 4%, rm = 15% and bi = 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

This is a simple, ad hoc 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 11.4

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:  ks = 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 ks.

Formula 11.5

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%

  1. Identify some problems with the capm approach.

The first problem, if a firm’s stockholders are not well diversified, they may be concerned with stand-alone risk rather than just market risk. In that case, the firm’s true investment risk would not be measured by its beta, and the CAPM procedure would understate the correct value of ks. Further, even if the CAPM method is valid, it is hard to obtain correct estimates of the inputs required to make it operational because (1) there is controversy about whether to use long-term or short-term Treasury yields for kRF, (2) it is hard to estimate the beta that investors expect the company to have in the future, and (3) it is difficult to estimate the market risk premium.

  1. Explain the two approaches that can be used to adjust for flotation costs.

The first approach simply adds the estimated dollar amount of flotation costs for each project to the project’s up-front cost. The estimated flotation costs are found as the sum of the flotation costs for the debt, preferred, and common stock used to finance the project. Because of the now-higher investment cost, the project’s expected rate of return and NPV are decreased.

The second approach involves adjusting the cost of capital rather than increasing the project’s cost. If the firm plans to continue to use the capital in the future, as is generally true for equity, then this second approach is better. The adjustment process is based on the following logic. If there are flotation costs, the issuing company receives only a portion of the total capital raised from investors, with the remainder going to the underwriter. When calculating the cost of common equity, the DCF approach can be adapted to account for flotation costs. For a constant growth stock, the cost of new common stock, ke, can be expressed as:

Cost of equity from new stock issues = ke =

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