 # Capital Budgeting, Capital Structure And the Capm

## Introduction

So far, our study of Markowitz efficiency, beta factors and the CAPM has concentrated on the stock market's analyses of security prices and expected returns by financial institutions and private individuals. This is logical because it reflects the rationale behind the chronological development of Modern Portfolio Theory (MPT). But what about the impact of MPT on individual companies and their appraisal of capital projects upon which all investors absolutely depend? If management wish to maximise shareholder wealth, then surely a new project's expected return and systematic risk relative to the company's existing investment portfolio and stock market behaviour, like that for any financial security, is a vitally important consideration.

In this Chapter we shall explore the corporate applications of the CAPM by strategic financial management, namely:

- The derivation of a discount rate for the appraisal of capital investment projects on the basis of their systematic risk.

- How the CAPM can be used to match discount rates to the systematic risk of projects that differ from the current business risk of a firm.

Because the model can be applied to projects financed by debt as well as equity, we shall also establish a mathematical connection between the CAPM and the Modigliani-Miller (MM) theory of capital gearing based on their "law of one price" covered in our SFM companion texts.

## Capital Budgeting and the CAPM

As an alternative to calculating a firm's weighted average cost of capital (WACC) explained in the SFM texts, the theoretical derivation of a project discount rate using the CAPM and its application to NPV maximisation is quite straightforward. A risk-adjusted discount rate for the jth project is simply the risk-free rate added to the product of the market premium and the project beta, given by the following expression for the familiar CAPM equation: The project beta (bj) measures the systematic risk of a specific project (more of which later). For the moment, suffice it to say that in many textbooks the project beta is also termed an asset beta denoted by bA.

We then derive the expected NPV by discounting the average net annual cash flows at the risk-adjusted rate from which the initial cost of the investment is subtracted, using a mathematical formulation that you first encountered in Part Two of the SFM texts. Individual projects are acceptable if:

NPV > 0

Collectively, projects that satisfy this criterion can also be ranked for selection according to the size of their NPV. Given: So far, so good; but remember that CAPM project discount rates are still based on a number of simplifying assumptions. Apart from adhering to the traditional concept of perfect capital markets (Fisher's Separation Theorem) and mean-variance analysis (Markowitz efficiency) the CAPM is only a single-period model, whereas most projects are multi-period problems.

According to the CAPM, all investors face the same set of investment opportunities, have the same expectations about the future and make decisions within one time horizon. Any new investment made now will be realized then, next year (say) and a new decision made.

Given the assumptions of perfect markets characterised by random cash flow distributions, there is no theoretical objection to using a single-period model to generate an NPV discount rate for the evaluation of a firm's multi-period investment plans. The only constraints are that the risk-free rate of interest, the average market rate of return and the beta factor associated with a particular investment are constant throughout its life.

Unfortunately, in reality the risk-free rate, the market rate and beta are rarely constant. However the problem is not insoluble. We just substitute periodic risk-adjusted discount rates (now dated r ) for a constant r into Equation (46) for each future "state of the world", even if only one of the variables in Equation (45) changes. It should also be noted that the phenomenon of multiple discount rates combined with different economic circumstances is not unique to the CAPM. As we first observed in Part Two of SFM, it is common throughout NPV analyses.

On first acquaintance, it would therefore appear that the application of a CAPM return to capital budgeting decisions provides corporate financial management with a practical alternative to the WACC approach. A particular weakness of WACC is that it defines a single discount rate applicable to all projects, based on the assumptions that their acceptance doesn't change the company's risk or capital structure and is marginal to existing activities. In contrast, the CAPM rate varies from project to project, according to the systematic risk of each investment proposal. However, the CAPM still poses a number of problems that must be resolved if it is to be applied successfully, notably how to derive an appropriate project beta factor and how to measure the impact of capital gearing on its calculation.

For these reasons, we shall defer a comprehensive numerical example of investment appraisal and the CAPM until you read the Exercises associated with this chapter, by which time we will have covered the issues involved.