Determining the appropriate cost of capital

When undertaking NPV analysis it is important to use an appropriate discount rate, that is, to choose an interest rate that is commensurate with the risk of a project. Choosing an inappropriate discount rate can lead to the acceptance of a project that should have been rejected (or conversely the rejection of a project that should have been accepted).

In the survey by Graham and Harvey cited in section 5.7, 73.49% of respondents used the capital asset pricing model (CAPM) to determine the estimate the cost of capital.

Algebraically the CAPM can be expressed as:

E(Ri) = Rf + β[E(Rm) – Rf]

which in words means that the expected return on an asset (or portfolio) is equal to the riskfree rate (Rf) plus the asset (or portfolio) beta multiplied by the market risk premium [E(Rm) – Rf].

Credit Suisse produce an annual report entitled “Credit Suisse Global Investment Returns Yearbook”. The 2017 edition is in the public domain. Page 45 of this report details the risk premium, [E(Rm) – Rf], for the United Kingdom over the period 1900–2016 and finds it to be 4.4%. Over the more recent period of 1967–2016, equities have beaten Treasury bills by 5.1%.

Richard Roll and Steven Ross challenged William Sharpe's CAPM. In their opinion, market risk is not the only risk that systematically affects all assets. They argued that factors such as interest rates, inflation, the position in the business cycle, and expectations about future economic performance all systematically affect assets. Moreover, just like the CAPM where assets were affected in different ways relative to the stock market, assets would have different sensitivities to these additional systematic factors. Sharpe's defence was that the stock market reflects all of these other factors. Roll and Ross's model is known as the arbitrage pricing theory (APT).

The APT states that the following risk–return relationship will result for security i.

E(Ri) = RF + βi,F1[E(RF1) – RF] + βi,F2[E(RF2) – RF] + … + βi,FH[E(RFH) – RF]

where:

βi,Fj = the sensitivity of security i to the j’th factor.

[E(RFj) – RF] = the excess return of the j’th systematic factor over the risk free rate – this can be thought of as the price for the j’th systematic risk.