Cost of Equity

The cost of equity capital is the return that needs to be offered to investors to induce them to buy and hold the equity shares in a company. This return is determined by the returns available on similar securities of the same risk class.

The capital asset pricing model gives a required rate of return for any asset if it is possible to obtain its beta (measure of its systematic or non-diversifiable risk) and the equity risk premium demanded by investors above the risk free rate of return for accepting the risk associated with investing in shares, generally.

Some risks are unique to the particular share. The impact of these variables is known as diversifiable risk (also referred to as firm, unique or unsystematic risk).

Some risk variables will affect all shares, to a greater or lesser extent. The impact of these variables is known as non-diversifiable risk (also referred to as market or systematic risk).

The reduction in standard deviation of the returns on the portfolio comes about because security returns generally do not vary with perfect positive correlation.

Because most shares are held by highly diversified institutions, market returns are dominated by the actions of fully diversified investors. These investors ensure that the market does not reward investors for bearing some unsystematic risk.

A share‟s sensitivity to general market movements is its beta value. A beta of 1.0 indicates that the share tends to produce returns that move broadly in line with the market index. A beta greater than 1.0 indicates that the share displays amplified movements relative to the market.

Beta can measure the systematic risk of any asset – so shares, debt instruments, and indeed any asset can have a beta.

The required return from any risky investment is described by the Capital Asset Pricing Model – the CAPM.

For share j, under the CAPM, the required return is: rj = rf + Beta(rm – rf)

Since the required return for equity is the same as the cost to the firm kE, kE = rf + Beta(rm – rf) This is the CAPM formula.

The CAPM formula can be shown on a graph as the Security Market Line , which shows the rise in expected returns as beta increases.

Market (equity) risk premium (rm – rf) or RP, is the extra return demanded by investors in equities generally above the risk free rate. Historical data on equity and government bond returns reveal the equity risk premia above the risk free rate are generally in the range of between 3% and 6% per annum.

Any measure of the equity risk premium will be sensitive to: - the period covered by the study. - the proxy for the risk-free rate (short-dated or long-dated government securities?); - the analyst‟s view of the riskiness of the average share relative to rf. - the market and currency.

To obtain the risk-free rate we ideally need to satisfy two conditions: - There is a zero default risk. - When intermediate cash flows are earned on a multi-year investment there is no uncertainty about reinvestment rates. In practice, finance directors and analysts use a long-term government rate on all the cash flows of a project that has a long-term horizon. Also, the bond used is one with coupons.

The slope of the characteristic line is the beta for the share. This relationship between rj and rm can be expressed thus for a generic share j: - Betaj = Covariance of security with the market / Variance of the market; or- Betaj = Correlation of security with the market x (Standard Deviation of security / Standard Deviation of the market)

Criticisms of CAPM: - It relies on the identification of a market portfolio to calculate both the equity (or market) risk premium and beta. In theory, this consists of a representative sample of all possible assets on which a return can be generated by an investor - identifying such a portfolio is almost impossible. - What data should be used to measure beta? Changing the time period the periodicity or the market proxy will change the measured beta. - Can the past be used to predict the future? Betas change, sometimes considerably, over time. - CAPM is a one period model – it assumes the variables (rf, beta, rm – rf ) will be stable for the period of the cash flows to be valued.

Assumptions that were used to derive the CAPM: -investors are rational and risk averse; -all investors have identical investment horizons; -all investors have identical perceptions regarding the expected returns, volatilities and correlations of available risky investments; -information has no cost and there are no barriers to information: investors come to identical conclusions regarding expected risks and returns given identical information; -there are no transaction costs or taxes; -investors can borrow and lend at the risk-free rate; -there is no dominant player in the market; and -no one transaction will move the market price of an asset.

Early (1970s) measurements of the Securities Market Line suggest that it is flatter than is predicted by the theory - beta risk requires some compensation, but not as much as suggested by the model. Also at a zero beta, investors seem to receive more than the rf. Studies in the 1990s concluded that a rise in beta does not lead to a higher return - many academics and practitioners have drawn the conclusion that beta is „dead‟ as relevant factor in adjusting required returns.

Arbitrage pricing theory (APT) uses a number of factors (each with betas and each with risk premiums), which relate to unexpected changes in economic quantities.

Expected returns = risk free rate + Beta1(r1 – rf) + Beta2(r2 – rf) ….+βn(rn– rf)

Beta is used for: -Assessing the risk of a portfolio; -Identifying whether a fund manager‟s performance is the result of good management or excessive risk taking; -Identifying „mispriced‟ shares, and; -To evaluate investment projects as well as to value shares. The Gordon growth model method for estimating the cost of equity capital is kE = d1/P + g