This is “Cost of Common Stock”, section 12.4 from the book Finance for Managers (v. 0.1).
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New stock issues (IPOs) gain many headlines, as such companies are usually growing fast and require a large influx of capital. Secondary issues don’t get as much press, but are also a sign that companies are raising capital. But these are actually not the most common way of raising equity financing!
Because dividends are not required to be increased (or even paid!) when a company is doing well, the company can instead retain excess earnings and reinvest them (hence the item on the balance sheet). Most capital is raised through reinvesting earnings, instead of through issuing new stock, because issuing new stock incurs flotation costs. We will assume that the cost to the firm, r_{s}, is the same.
The cost of equity is the most difficult source of capital to value properly. We will present three basic methods to calculate r_{s}: the Dividend Discount Model (DDM), the Capital Asset Pricing Model (CAPM), and the Debt plus Risk Premium Model (D+RP).
In Chapter 10 "Stock Valuation", we explored the DDM model.
Equation 12.4 Cost of Common Stock
$${r}_{s}=\frac{{\text{D}}_{1\text{}}}{{\text{P}}_{0}}\text{}+\text{g}$$P_{0} is the price of the share of stock now, D_{1} is our expected next dividend, r_{s} is the required return on common stock and g is the growth rate of the dividends of common stock. This model assumes that the value of a share of stock equals the present value of all future dividends (which grow at a constant rate). This equation states that the cost of stock equals the dividend expected at the end of year one divided by the current price (dividend yield) plus the growth rate of the dividend (capital gains yield).
Falcons Footwear has 12 million shares of common stock. The stock is currently selling for $60/share. It pays a dividend of $3 this year and the dividend is growing at 4%. What is r_{s}?
First we must calculate D_{1}. D_{1} = D_{0}*(1+g) = $3*(1+.04) = $3.12
$${r}_{s}=\frac{{\text{D}}_{1\text{}}}{{\text{P}}_{0}}\text{}+\text{g}=\text{}\frac{\$3.12}{\$60}+0.04=0.52+0.04=0.092=9.2\%$$If our stock isn’t currently paying dividends, then the equation reduces to our capital gains yield, which should be proportional to our expected long term growth rate.
We learned that the Capital Asset Pricing Model (CAPM) was a relationship between the return for a given stock and the nondiversifiable risk for that stock using beta (β). The basic equation (from Chapter 11 "Assessing Risk") is:
Equation 12.5 CAPM Equation
Required return on stock = risk free rate + (market risk premium)*(Beta of stock)Equation 12.6 Market Risk Premium
market risk premium = expected market return − risk free rateWhere R_{F} is the risk free rate, R_{M} is the market return or the return on the market portfolio and β is beta. If our company has yet to issue stock, then beta will need to be estimated (perhaps by looking at a public competitor’s).
Falcons Footwear wants to calculate r_{s} using the CAPM. They estimate the risk free rate (R_{F}) to be 4%. The firm’s beta is 1.3 and the market return is 9%.
r_{s} = 0.04 + [0.09 − 0.04] * (1.3) = 0.105 = 10.5%If we know that, historically, our stock has traded at a particular premium to our cost of debt, we can use that relationship to estimate our cost of equity. If our stock isn’t publically traded, we can estimate based upon competitors or industry averages.
r_{s} = r_{d} + Risk PremiumWe know that current Falcons Footwear bonds are yielding 7%. If we know that comperable companies have cost of equity about 4% higher than their cost of debt, what is a good estimate of Falcons Footwear’s cost of equity?
r_{s} = 0.07 + 0.04 = 0.11 = 11%Each method has its strengths and weaknesses, and all are subject to the quality of the inputs. DDM is very sensitive to the estimation of the growth rate. CAPM depends upon an accurate estimate of the firm’s beta. D+RP assumes that the risk premium is accurate.
Often, the best method is to calculate all three results and make an informed judgment based on the results. If one result varies wildly from the other two, perhaps it is best omitted. Estimating the cost of equity is one of the most difficult tasks in finance, and it can end up being equal parts art and science.
Calculate r_{s} using CAPM given the following:
R_{F} = 5%, R_{M} = 4%, b = 1.4
Calculate r_{s} using Constant Growth Model given the following:
D1 = $5, Selling price is $35, Dividend is growing at 2%.