Capital Budgeting: A Beta Way To Do It

Having looked at risk and return, markets and project valuation, this article examines how stock markets can price risk and help identify the appropriate return for a new investment project.

Elroy Dimson focuses mainly on the capital asset pricing model, a popular tool of modern finance which relates the expected return on an asset to its risk while giving a precise definition to what is meant by risk. Dimson highlights the difference between company-specific risk and overall equity market risk and goes on to explain the concept of beta, which measures market related risk and allows investors to position portfolios in an aggressive or defensive way.

In general the CAPM tell us that the required rate of retrun on an investment is equal to the risk free rate of interest plus a premium for risk, where the premium is equal to beta multiplied by the equity marker risk premium.

The author warns that use of a single company-wide discount rate can lead to inappropriate investment decisions.

An investment that is risk-free offers a known pay-off over some period in the future but, sadly, capital investments are not usually risk-free and this risk has to be properly assessed and accounted for.

The best known risk-free investments are government bonds. The government can be expected to honour its promises because it can always print sufficient money to meet its obligations, though of course there is then a risk of inflation.

In some countries, such as the UK and the US, the government also issues index-linked bonds, which provide an income and capital repayment uplifted in line with inflation.

The promised return, or redemption yield, on government bonds is published daily in the Financial Times and the Wall Street Journal. These bonds provide a guaranteed return that is known today. For example, at the time of writing one can earn a gross yield to redemption of around 7.6 per cent on conventional UK government bonds with a five- to 15-year maturity. These gross yields equate to a yield after personal tax of a little under 6 per cent. Nominal yields vary over time and across currencies and issuers.

Similarly, index-linked United Kingd-om government bonds provide a gross rede-mption yield of around 3.6 per cent for matu-rities running as far into the future as the year 2030. Net of pers-onal income tax, their yield is around 3 per cent.This yield is measured in real terms over and above the level of retail price inflation.

If a capital project is risk-free, it should be required to earn a rate of return that is at least equal to the risk-free rate of interest. If the project is located in the UK, and cash flows are projected in real (inflation-adjusted) terms, then the cash flows should be discounted at the risk-free real rate of interest. Following the discounted cash flow method, the project should be accepted if its net present value is positive.

Risky investments

So what discount rate should we use if a project is risky? If we want to know the wholesale price for copper, cocoa or crude oil, we look at the Commodities Prices section of the Financial Times. By analogy, to learn about the wholesale price for capital, we must look to the Stock Exchange.

For a capital investment project, such as building a new power station, we should find the required rate of return by reference to a similar investment on the stock market. To do this we need to examine what risk means in that market.

Figure 1 shows the range of returns (capital gain or loss plus reinvested dividends) on the US equity market since 1926.

Although returns of 10-20 per cent are the most common, the equity market has often given returns of 30-40 per cent, and has frequently given negative returns. Within Figure 1, we identify the years in which particular levels of return were achieved. The US equity market fell by more than 40 per cent in 1931 and rose by more than 50 per cent in 1933 and 1954.

These three extremes are shown in the left-hand and right-hand tails of the distribution.

Whereas equity investment is risky, treasury bills (essentially, government bonds with a maturity of under a year) are virtually risk-free. A histogram of the returns on treasury bills would show that in almost every year their return was between 0-10 per cent. The most extreme outliers were a few years at the beginning of the 1980s when UK treasury bills gave a return of a little above 10 per cent. Because we know the return over the life of a treasury bill when we buy it, we sometimes refer to the return on bills as the risk-free rate of interest.

Investors do not like to be exposed to risk unless they can expect to receive compen-sation for their exposure. An interesting comparison, then, is between the risky return on equities and the risk-free interest rate. The difference between these two rates of return is called the excess return or equity risk premium. It measures the additional return received from investing in shares rather than in treasury bills. If the excess return is, on average, positive, then investors are receiving a premium for exposure to equity market risk.

Figure 2 shows the arithmetic average risk premium for the UK, measured in real terms, and estimated over rolling 20-year periods ending in 1938, 1939 and so on.

Over the period from 1919 to date, the UK equity risk premium has averaged between 8-9 percentage points per year. Over the period since 1926, Ibbotson Associates estimate that US equities also provided an arithmetic average risk premium of between 8-9 percentage points. Similar figures are available for other countries. As explained in accompanying articles, they may be used with caution as a guide to expectations for the future.

Projects that are riskless, therefore, should have their cash flows discounted at the risk-free rate of interest.

If we expect the risk premium in the future to be similar to its average value in the past, then projects whose risk is the same as investing in the equity market should have their cash flows discounted at the risk-free rate plus, say, 8 per cent. A project with intermediate risk merits an intermediate discount rate.

Capital asset pricing model

To implement this approach we need to agree on a method for estimating the riskiness of an investment. Until the 1960s, this would have been difficult.

But in the early part of that decade there was an important breakthrough in the theory of finance.Building on work by Harry Markowitz and James Tobin, Bill Sharpe formulated the capital asset pricing model (CAPM), a simple yet elegant model that relates the expected return on an asset to its risk while giving a precise definition to what we mean by risk.

The key insight of the CAPM is that investors can expect a reward for an investments contribution to the risk of a portfolio. There can be no expected reward for exposure to risks that are easily diversified away. The required rate of return should be higher for investments that have a larger element of non-diversifiable risk.

Two types of risk

A portfolio invested in just one share is typically much more volatile than a diversified portfolio. By holding a large number of securities, investors can eliminate company-specific risk. However, there are limits to the power of diversification. Once the investor has holdings in every share in the market, the portfolio will still be quite risky. While diversification can eliminate company-specific risk, it cannot eliminate overall equity market risk.

Every share therefore fluctuates in value because of two elements of risk. The first is market risk the tendency of the share to move with general stock market movements. The second is specific risk, which encapsulates all events that are specific to individual companies while having nothing to do with general market-wide factors.

Investors do not like risk and need the prospect of higher returns before they will take it on. Since market risk cannot be avoided by diversification, investors require a higher return for exposure to market risk. In the CAPM, market risk is measured by beta.

A stock with a beta of 1.0 tends to move broadly in line with the equity market a share with a beta of 1.5 tends to move up or down by 1.5 per cent for each percentage point movement in the market.

The bar chart in Figure 3 lists recent estimates of beta for some well-known companies. Some companies have betas as high as 1.5 or even more and are an aggressive play on the equity market. If the market goes up, these shares can be expected to outperform in a bear market they can be expected to fall by more than average.

Other shares have betas of 0.5 or less and these defensive companies are likely to be resistant to a bear market while being left behind when share prices surge ahead. Most companies, however, have a beta that is close to the average of 1.0.

Required rates of return

To estimate the required rate of return for an investment, we therefore need to estimate the beta for a capital project. This is easier to do if the project essentially replicates, probably on a smaller scale, the companys existing business. It is also easier if the project is typical of an industry sector for which betas are published.

A capital project with a beta of zero would be riskless and its cash flows should be discounted at the risk-free rate of interest. An investment in an equity index fund would have the same risk as the market, namely a beta of 1.0.

This investment would have a required rate of return equal to the riskless rate of interest plus the expected equity market risk premium.

Suppose we are considering building a power station, for which we have estimated a beta of 0.6. This is the same as the beta of a portfolio that is 40 per cent invested in treasury bills and 60 per cent invested in the equity market.

The CAPM tells us that the required return should therefore be equal to the return on treasury bills plus 60 per cent of the expected market risk premium.

In general, the CAPM tells us that the required rate of return on an investment is equal to the risk-free rate of interest plus a premium for risk. The premium for risk is equal to beta multiplied by the equity market risk premium.

Most projects have a risk level that is different from the beta of their companys shares: using a single company-wide discount rate can lead to inappropriate investment decisions.

The relationship between the required rate of return and beta is indicated in Figure 4 by the sloping line labelled risk-adjusted cost of capital. The chart shows how the required rate of return increases as beta gets larger (see Box 1).

Project risk

Some companies use only a single company-wide discount rate even though they operate in businesses that embrace a wide range of risks. However, this can lead to inappropriate investment decisions.

Figure 4 shows why. The upward sloping risk-adjusted cost of capital line shows the required rate of return for projects with varying levels of beta.

Projects with an expected return that plots above this security market line should be accepted while those beneath should be rejected.

A high-risk proposal, such as Project A, would incorrectly be accepted by a company using a single, company-wide discount rate. On a risk-adjusted basis it should be rejected. A low-risk proposal, such as Project B, would be incorrectly rejected when compared with the companys overall cost of capital. On a risk-adjusted basis it should be accepted.

While there are other approaches to estimating the risk-adjusted cost of capital, the CAPM remains highly popular. It is widely used in company valuation, project appraisal and regulation.

The cost of capital can be estimated by arbitrage pricing theory, option pricing theory and the dividend growth model. But the CAPM is the most popular approach. n

Box 1: Using the CAPM

To use the CAPM to calculate the required rate of return, we need three items of data:

The risk-free interest rate, which may be obtained from the Currencies and Money page of the Financial Times.

The beta of the investment, which may be derived from London Business Schools Risk Measurement Service.

The equity market risk premium, which has historically averaged around 8 per cent.

With a real interest rate of, say, 3 per cent and an investment with a beta of 0.6, we would have a required rate of return that is equal to 7.8 per cent (3 + 0.6 x 8 per cent). With a beta of 1.0, the required rate of return would be 11 per cent (3 + 1.0 x 8 per cent).

Most projects have a risk level that is different from the beta of the companys shares. One reason for this is that many companies are financed partly with debt, which increases the riskiness of their shares. To estimate the riskiness of a capital investment project we therefore need to remove the effect of borrowing from the beta of the companys shares. The beta of the underlying business of the company is simply a weighted average of the beta of its equity and the beta of its debt. (The weights are the proportion of equity and the proportion of debt in the capital structure.) If we make the assumption that the companys debt is so safe as to make its beta virtually zero, then the beta of the companys underlying business is equal to the beta of its shares multiplied by the proportion of equity (at market value) in its capital structure.

Consider a company whose shares have a beta of 0.6. Assume the company is financed 83 per cent by equity and 17 per cent by debt. The beta of the underlying business would be equal to the beta of the shares multiplied by the proportion of equity. The company would have an asset beta of 0.5 (0.6 x 0.83). To estimate the cost of equity capital for a company we should use the beta of its shares. But to estimate the cost of capital for the underlying business, we should use its asset beta.

Box 2: Alternative approaches

The cost of capital is an opportunity cost. It is the return that could be obtained in the stock market from an investment of similar risk and maturity to the capital tied up in the project. Financial economics offers four approaches to estimating the cost of capital:

The capital asset pricing model. Despite recent criticism, the CAPM remains the most popular approach to estimating the cost of capital.

Arbitrage pricing theory, a competitor of the CAPM, developed in the 1970s. As explained in the article by Massoud Mussavian (Part 3 of Mastering Finance), the APT can be seen as an extended version of CAPM, with multiple sources of risk and return.

Option pricing theory, also developed in the 1970s. The article by Anthony Neuberger in Part 8 of Mastering Finance will explain how this approach is sometimes applied to valuing capital projects that have option-like characteristics.

The dividend growth model, originated in the 1930s and popularised in the 1950s. Its drawback is that it assumes a dividend growth rate that can be sustained indefinitely. It also ignores the riskiness of an investment.Some companies use accounting-based approaches for estimating the cost of capital. These seriously flawed methods include:

The dividend yield. This tends to understate the cost of capital because it ignores the capital gains anticipated by investors.

The p/e ratio or its reciprocal, the earnings yield. This ignores the expected growth in company earnings.

Return on capital. Some companies use this as a guideline but it is absurd to estimate a low cost of capital just because a business earns a low accounting rate of return.

Return on marginal project. Some companies rank projects from most to least attractive and accept those with the highest return. This is circular since projects cannot be ranked correctly unless one already knows the cost of capital.

Funding cost. When projects are valued using the interest rate payable by the company, the discount rate fails to reflect the full risk of the investment.

Past return on the companys shares. Use of the long-run return on a companys shares as a guide to the cost of capital implies that poorly performing companies have the lowest cost of capital. It is misleading.

Despite continued usage of inadequate methods for determining the cost of capital, more sophisticated businesses tend to use the CAPM.The APT tends to be used for utilities in the US, while option pricing theory is sometimes used for valuing natural resource investments such as mines.