# Cost of Equity

Cost of equity (also known as cost of common stock and referred to as K_{e}) is the minimum rate of return which a company must generate in order to convince investors to invest in the company's common stock at its current market price. It is alternatively referred to as required rate of return on equity.

Cost of equity is an important input in common stock valuation under different models. It is also used in calculation of the weighted average cost of capital.

## Formula

Cost of equity is estimated using either the dividend discount model or the capital asset pricing model.

### Cost of Equity - Capital Asset Pricing Model

$$ Cost\ of\ Equity\ (K_e)\\=Risk\ Free\ Rate+Beta\ Coefficient\times Market\ Risk\ Premium $$

Market risk premium (also called equity risk premium) equals market return minus the risk free rate.

$$ Market\ Risk\ Premium \\ = Market\ Return − Risk\ Free\ Rate $$

Risk free rate is the rate of return on 10-year Treasury Bond. Beta coefficient is a statistic that measures the systematic risk of a company's common stock while the market rate of return is the rate of return on the market. Return on some relevant benchmark index such as S & P 500 is a good estimate for market rate of return.

### Cost of equity - Dividend Discount Model

$$ Cost\ of\ Equity\ (DDM)\\=\frac{Next\ Year\ Dividend\ per\ Share}{Current\ Market\ Price}+\ Dividend\ Growth\ Rate $$

Dividends in next period equals dividends in current period multiplied by (1 + growth rate). Growth rate is normally taken as equal to the sustainable growth rate worked out as follows:

$$ Sustainable\ Growth\ Rate\\=(1-Dividend\ Payout\ Ratio)\times Return\ on\ Equity $$

Dividend discount model for estimation of cost of equity is useful only when the stock is dividend-paying. In reality, we have a lot of stocks that do not pay dividends. In such situations, the capital asset pricing model and some other more advanced models are used.

## Examples

### Example 1: Cost of Equity using CAPM

The yield on 5 year US treasury bonds as at 30 December 2012 is 0.72% (this data can be obtained from Bloomberg, Morningstar, etc.). From Yahoo Finance, we find that Caterpillar Inc.'s share price as at 30 December 2012 is $86.81 per share while it has a beta coefficient of 1.86. Trailing twelve months (TTM) return on S & P 500 is 11. 52%. Estimate the cost of equity.

Under the capital asset pricing model, the rate of return on short-term treasury bonds is the proxy used for risk free rate. We have an estimate for beta coefficient and market rate for return, so we can find the cost of equity:

Cost of Equity = Risk Free Rate + Beta Coefficient × (Market Rate of Return − Risk Free Rate)

Cost of Equity = 0.72% + 1.86 × (11.52% − 0.72%) = 20.81%

### Example 2: Cost of Equity using Dividend Growth Model

Caterpillar Inc.'s share price as at 30 December 2012 is $86.81 per share. Its last five year's average total dividends, return on equity and payout ratios are $1.6, 34.75% and 47.08%.

Before using the dividend discount model for estimating cost of equity, we need to make sure we have the required inputs which include the growth rate, dividends in next period and current market price.

We have the current market price ($86.81) and we need to estimate the growth rate and dividends in next period.

Growth Rate = (1 − 47.08%) × 34.75% = 18.39%

Dividends in Next Period = Dividends in Current Period × (1 + Growth Rate) = $1.6 × (1+18.39%) = $1.89

We have the required inputs which we can just punch into the following equation to get an estimate for cost of equity:

$$ Cost\ of\ Equity\ (DDM)\\=\frac{Dividend\ in\ Next\ Period}{Current\ Market\ Price}+Dividend\ Growth\ Rate\\=\frac{$1.89}{$86.81}+18.39\% \\= 20.57\% $$

Our estimates for cost for equity under both models are pretty close which adds credibility to our estimate. Financial analysts frequently use more than one models to estimate any statistic in order to obtain a range of possible values.