Cost of Capital

New stock issues (IPOs) gain many headlines, as such companies are usually growing fast and require a large influx of capital. Secondary issues do not get as much press but are also a sign that companies are raising capital. But these are not the most common ways of raising equity financing!

Because dividends are not required to be increased (or even paid!) when a company is doing well, it can 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, rs, 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 rs: the Dividend Discount Model (DDM), the Capital Asset Pricing Model (CAPM), and the Debt plus Risk Premium Model (D+RP).

Using the Dividend Discount Model (DDM)

We explored the DDM model.

Equation 12.4 Cost of Common Stock

\(r_s = \dfrac{D_1}{P_0} + g\)

P0 is the price of the share of stock now, D₁ is our expected next dividend, rs 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 stock cost 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).

Worked Example: Falcons Footwear – Constant Growth to calculate r_s

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 D₁ . D₁ = D₀^* (1+g) = $3^*(1+.04) = $3.12

\( r_s = \dfrac{D_1}{P_0} + g = \dfrac{$3.12}{$60}+0.04=0.52+0.04=0.092=9.2\% \)

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.

Using the Capital Asset Pricing Model (CAPM)

We learned that the Capital Asset Pricing Model (CAPM) was a relationship between the return for a given stock and the non-diversifiable risk for that stock using beta (β).

The basic equation) is:

Equation 12.5 CAPM Equation

Required return on stock = risk free rate + (market risk premium)*(Beta of stock)

\(r+s = R+F + [R+M − R+F] × β\)

Equation 12.6 Market Risk Premium

market risk premium = expected market return − risk-free rate

Where 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 must be estimated (perhaps by looking at a public competitor's).

Worked Example: Falcons Footwear - CAPM to calculate rs

Falcons Footwear wants to calculate rs using the CAPM. They estimate the risk-free rate (RF) 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%

Using the Debt plus Risk Premium Model (D+RP)

If we know that our stock has historically 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 publicly traded, we can estimate based on competitors or industry averages.

r_s = r_d + Risk Premium

Worked Example: Falcons Footwear - D+RP to calculate rs

We know that current Falcons Footwear bonds are yielding 7%. If we know that comparable companies have a 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%

Which Method Is Best?

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, it may be 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.

Final Thoughts on r_s

1. If a firm's only investors were common stockholders, then the cost of capital would be the required rate of return on equity.
   
   
2. The cost of retained earnings is the same as r_s.
   
   
3. The tax implications of common stock are also large. The company's dividends are not tax deductible (just like preferred stock dividends), and the company bears the full cost.