## Cost of Equity Share Capital (Ke)
Ke is the expectation of equity shareholders. It is the hardest cost to compute because equity has no fixed contractual payment and no redemption. So there are several methods — pick by the situation.
### Which method to use?
| Condition | Method |
|---|---|
| Dividend expected to stay constant | Dividend Price Approach |
| EPS expected to stay constant | Earnings Price Approach |
| Dividend & earnings grow at a constant rate | Growth Approach (Gordon's Model) |
| Future hard to forecast (look to the past) | Realized Yield Approach |
| Return depends on risk | CAPM |
### A. Dividend Price Approach (Dividend Valuation Model)
Assumes dividend per share stays constant forever.
$$K_e = \frac{D}{P_0}$$
D = expected dividend (D₁); P₀ = ex-dividend market price.
### B. Earnings Price Approach
Assumes EPS constant forever; nullifies the effect of changes in dividend policy.
$$K_e = \frac{E}{P}$$
E = current EPS; P = market price per share.
### C. Growth Approach / Gordon's Model
Earnings, dividends and share price all grow at the same constant rate g.
$$K_e = \frac{D_1}{P_0} + g$$
With floatation cost F on newly issued shares:
$$K_e = \frac{D_1}{P_0 - F} + g$$
where D₁ = D₀(1 + g) = next expected dividend.
Estimating the growth rate g:
- Average Method: $g = \sqrt[n]{\dfrac{D_0}{D_n}} - 1$ (D₀ = current dividend, Dₙ = dividend n years ago).
- Gordon's Growth Model: $g = b \times r$ (b = retention ratio, r = return on funds invested).
### D. Realized Yield Approach
Uses the average past return realized by shareholders as the expected future return. Based on the principle Cost to Company = Investors' Return. Computed from the investor's perspective (typical when shares are sold in the secondary market after a few years); Ke is the IRR of the relevant cash flows.
### E. Capital Asset Pricing Model (CAPM)
Describes the risk-return trade-off. Investors are compensated for (i) time value of money and (ii) risk.
$$K_e = R_f + \beta (R_m - R_f)$$
- R_f = risk-free rate
- β = beta coefficient (systematic risk)
- R_m = return on market portfolio
- (R_m − R_f) = market risk premium