# Required Rate of Return

Required rate of return is the minimum return in percentage that an investor must receive due to time value of money and as compensation for the risks of the investment. There are multiple models to work out required rate of return on equity, preferred stock, debt and other investments.

The most basic framework is to estimate required rate of return based on the risk-free rate and add inflation premium, default premium, liquidity premium and maturity premium, whichever is applicable.

The formula for the general required rate of return can be written as:

$$Required\ return\ =\ r_f +\ IRP+DRP+LRP+MRP$$

Where,
rf is the real risk-free rate is the rate of return on Treasury inflation-protected securities.
IRP stands for inflation risk premium, the compensation for inflation risk;
DRP stands for default risk premium, the compensation for risk of investment loss due to default;
LRP stands for liquidity risk premium, the compensation for illiquidity and lack of marketability and
MRP stands for maturity risk premium, the compensation for higher interest rate risk and reinvestment risk that results from longer maturities.

## Required return on equity (i.e. common stock)

The required return on equity is also called the cost of equity. There are three common models to estimate required return on common stock: the capital asset pricing model, the dividend discount model and the bond yield plus risk premium approach.

The capital asset pricing model estimates required rate of return using the following formula:

$$Required\ Return\ on\ Equity\ (CAPM)\\=r_f+\beta\times(r_m-r_f)$$

Where rf is the nominal risk-free rate, β is the beta coefficient, a measure of systematic risk and rm is the return on the broad market index such as S&P 500. (rm – rf) is the called the market risk premium.

The dividend discount model estimates required return on equity using the following formula:

$$Required\ Return\ on\ Equity\ (DDM)=\frac{D_1}{P_0}+g$$

Where D1 is the dividend per share next year, P0 is the current price of the stock and g is the growth rate of dividends which equals the product of retention rate and return on equity (ROE).

The bond yield plus risk premium approach adds a certain equity risk premium (based on historical analysis) to the yield on a company’s publicly-traded bonds.

## Required return on preferred stock

Required return on preferred stock equals the ratios of preferred dividends per share (D) to the current price of the preferred stock (P0):

$$Required\ Return\ on\ Preferred\ Stock=\frac{D}{P_0}$$

## Required return on debt

Required return on debt (also called cost of debt) can be estimated by calculating the yield to maturity of the bond or by using the bond-rating approach.

The yield to maturity is the internal rate of return of the bond i.e. the rate that equates the current price of the bond to its future cash flows based on the following equation:

$$P_0=\frac{c}{m}\times F\times\frac{1-\left(1+\frac{YTM}{m}\right)^{n\times m}}{\frac{YTM}{m}}\\+\frac{F}{\left(1+\frac{YTM}{m}\right)^{n\times m}}$$

Where c is the coupon rate, m is the number of coupon payments per year, F is the face value i.e. principal amount, n is the number of years till maturity and YTM is the yield to maturity.

Where the debt is not publicly traded, the required return on debt can be inferred from the yield to maturity of other marketable bonds which carry the same bond rating as the bond under consideration.

The build-up approach can also be used to estimate required return on debt. It involves adding inflation, default, liquidity and maturity premia to the real risk free rate.

Written by Obaidullah Jan