Cost of Equity Using Capital Asset Pricing Model (Calculation)

The value of an equity share is a function of cash inflows expected by the investors and the risk associated with the cash inflows. It is calculated by discounting the future stream of dividends at the required rate of return, called the capitalisation rote the required rate of return depends upon the element of risk associated with investment in shares. It will be equal to the risk-free rate of interest plus the premium for risk.

Thus, the required rate of return, K_e, for a share is:

K_e = Risk-free Rate of Interest + Premium for Risk

According to CAPM, the premium for risk is the difference between market return from a diversified portfolio and the risk-free rate of return. It is indicated in terms of beta co-efficient (b); i.e.

Risk-Premium = (Market Return of a diversified portfolio-Risk free return) b_i = b_i (R_m – R_f)

Thus, cost of equity, according to CAPM, can be calculated as below:

K_e = R_f + B_i (R_m – R_f)

Where, K_e = Cost of equity capital

R_f = Risk-free rate of return

R_m = Market return of a diversified portfolio

β_i = Beta co-efficient of the firm’s portfolio

Illustration 1:

You are given the following facts about a firm:

(i) Risk-free rate of return is 11 %.

(ii) Beta co-efficient, p, of the firm is 1.25.

Compute the cost of equity capital using Capital Asset Pricing Model (CAPM) assuming a market return of 15 per cent next year. What would be the cost of equity if Pi rises to 1.75.

Solution:

Illustration 2:

You are given risk free return and expected market return in respect of a number of projects as follows:

What is the required return on equity in each project under the Capital Asset Pricing Model? What generalisations can you make?

Solution:

Generalisations:

From the above it can be said that greater the beta, the higher is the risk and greater the risk premium which leads to higher required return on equity.