Calculating the Internal-Equity Cost of Capital

The cost of internal-equity capital to the firm is imputed to be the rate of return required by the

investors to purchase the firm’s stock. The imputed internal equity cost of capital can be

calculated in many ways, all of which have limitations in application. Two of the more common

methods, which we have discussed before, are

1. dividend growth model

2. capital asset pricing model

Dividend growth model—In theory, the internal-equity common stock’s value could be

calculated by discounting from now to infinity the stream of dividends at the investors’ required

rate of return. In practice, dividends cannot be estimated with confidence, therefore a simple

approach is to assume a constant dividend growth rate (g).

The basic formula used to represent a constant dividend stream to infinity is:

Pcs = D1/(kcs – g)

where D1, the next dividend, is related to D, the last dividend, by the following formula:

D1 = D(1 + g)

Rearranged algebraically to solve for kcs:

kcs = (D1/ NPcs) + g

or

kcs = [(D (1 + g))/ NPcs] + g

where:

Pcs = the imputed common stock price

kcs = the common stock after-tax cost of capital (not tax deductible)

D = the last common stock dividend

D1 = the next common stock dividend

g = the steady-state growth rate for dividends

Example

Echo Corporation common stock is currently selling for $22.00/share. Its present dividend is

$0.96/share, and its expected long-term dividend growth rate is 8.5%. What is Echo’s cost of

internal equity (kcs)?

Organize the data:

D1 = D(1 + g)

D1 = .96(1 + .085) = 1.0416

NPcs = $22.00

Formula:

kcs = (D1/NPcs) + g

Calculation:

kcs = (1.0416/22.00) + .085 = .1323

kcs = 13.23%

Capital asset pricing model—The second model for calculating internal common stock equity

is the capital asset pricing model (CAPM). It addresses the valuation of equity cost of capital

from the standpoint of the return required by stockholders for a given level of risk.

The return required for internal common stock equity is equal to risk-free return + a risk

premium that varies from stock to stock:

kcs = rrf + Bj(rm – rrf)

where:

Bj = beta and is normally estimated by historical values between a security’s return and

the market return

rrf = the risk-free rate and is usually estimated at the U.S. Treasury bill rate

rm = market risk

Example

Echo’s current beta value is 0.75. Treasury bills are currently yielding 5.5%, and the market

return is 14.3%. What is Echo’s internal cost of equity capital? Market return is 14.3%.

Organize the data:

rrf = –5.5%

Bj = .75

Formula:

kcs = rrf + Bj (rm – rrf) )

Calculation:

kcs = 5.5 + .75(14.3 – 5.5)

kcs = 12.1%