# Cost of Equity

Cost of equity (ke) is the minimum rate of return which a company must earn to convince investors to invest in the company's common stock at its current market price. It is also called cost of common stock or required return on equity.

Cost of equity is an important input in different stock valuation models such as dividend discount model, H- model, residual income model and free cash flow to equity model. It is also used in calculation of the weighted average cost of capital.

There are three methods commonly used to calculate cost of equity: the capital asset pricing model (CAPM), the dividend discount mode (DDM) and bond yield plus risk premium approach.

## Cost of equity - CAPM

In the capital asset pricing model, cost of equity can be calculated as follows:

Cost of Equity
= Risk Free Rate + Equity Risk Premium

Equity risk premium is the product of the stock's beta coefficient and the market risk premium.

Cost of Equity
= Risk Free Rate
+ Beta Coefficient × Market Risk Premium

Market risk premium equals market return minus the risk free rate.

Cost of Equity
= Risk Free Rate
+ Beta Coefficient × (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 a relevant benchmark index such as S & P 500 is a good estimate for market rate of return.

## Cost of equity - dividend discount model

Following is the formula for calculation of cost of equity under the dividend discount model:

 Cost of Equity = D1 + g P0

Where D1 is the dividend per share expected over the next year, P0 is the current stock price and g is the dividend growth rate. Dividends in next period equals dividends per share in current period multiplied by (1 + growth rate). Growth rate is equal to the sustainable growth rate which is the product of retention ratio and return on equity:

Sustainable Growth Rate
= Retention Rate × ROE

Sustainable Growth Rate
= (1 - Dividend Payout Ratio) × ROE

Dividend discount model for estimation of cost of equity is useful only when the stock is dividend-paying. But there are many stocks which do not pay dividends. In such situations, the capital asset pricing model and some other more advanced models are used.

## Bond yield plus risk premium approach

The bond yield plus risk premium approach is based on the observation that the required return on equity is higher than the yield required on debt because equity is riskier than debt. Hence, it starts with the after-tax cost of debt for a company and adds an appropriate risk premium to account for the increased risk.

This can be expressed in the form of following equation:

Cost of Equity (BYPRP) = Pre-tax Cost of Debt + Risk Premium

Pre-tax cost of debt equals the yield to maturity on the company's debt and the risk premium can be obtained from historical data i.e. the difference between realized return on equity and bond yield.

## Unlevered cost of equity

Sometimes you might be interested in finding the unlevered/ungeared cost of equity. It is the cost of equity under the assumption that the company has no debt in its capital structure. It can be calculated using capital asset pricing model by substituting the equity beta coefficient with asset beta (also called unlevered beta).

Unlevered Cost of Equity
= Risk Free Rate + Asset Beta × Market Risk Premium

## Example: 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
= 0.72% + 1.86 × (11.52% − 0.72%)
= 20.81%

## Example: Cost of equity using dividend discount model

Caterpillar Inc.'s share price as at 30 December 20X2 is \$86.81 per share and its average total dividends, return on equity and payout ratios for the last 5 years 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 equals the product of (1 - dividend payout ratio) and ROE.

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

Dividend per Share 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 = \$1.89 + 18.39% = 20.57% \$86.81

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