Finance 567; Assignment 2 by Sanjeev Sabhlok; 24

Finance 567; Assignment 2 by Sanjeev Sabhlok; 24.5.93

INVESTMENT APPRAISAL DECISION

1. INTRODUCTION

The investment decision is perhaps the most important financial decision for a firm, as indicated by Brealey and Myers' Third Law: "There's more value to be gained by good investment decisions than by good financing decisions (Brealey,1988:451)". The investment decision, also called capital budgeting decision, is a decision of how much not to consume now so that more can be consumed in the future. This could be done either by lending or by producing, with the expectation of getting returns at least equal to the market's rate of return.

Now, for the sake of theoretical tractability, it is assumed for most of this paper that capital markets are perfect and complete and that there are no imperfections, including taxes. In such a situation, there would be no reason for any project to give a positive net return. In a perfectly competitive market, where all opportunities have been duly exploited, there would exist no potential for returns higher than the market rate of return. Only when a firm is competitive in a particular area for some particular reason will it be possible to have a project with net positive returns. Thus positive NPVs come from specific competitiveness. It is assumed in the rest of the discussion that the firm does have a competitive edge which could lead to returns higher than the market rate of return. We shall also consider the financing and dividend decisions as given. Further, in perfect capital markets, the Fisher separation principle allows the consumption and investment decisions to be considered independently so that the decision criterion for shareholders would be to "maximise the present value of lifetime consumption" (Copeland,1983: 18). As we are aware, in reality there could be other interests operating, and agency costs to be incurred. Hence "a best technique for rating investment projects is heavily dependent on the decision maker's objective" (Bogue and Roll,1974:601). But in this paper, we assume that agency costs are absent (Copeland,1983:20).

How much to invest today, is referred to as the capital widening decision and how long to invest it for is the capital deepening decision (Martin,1988:111). There are three types of investment decisions: (i) the usual investment decision, or the allocation of capital to investment proposals, (ii) the decision to reallocate capital, when an existing asset no longer justifies continued commitment of capital, and (iii) acquisitions and mergers, which are similar to other investment decisions in many ways.

2. THE DECISION CRITERIA

Selecting the correct technique for investment purposes is very important. "The use of an improper capital budgeting technique will result in aggregate errors which stock-holders will not be able to eliminate" (Bogue and Roll, 1974). The decision criterion for capital budgeting purposes should take into account all cash flows; these cash flows should be discounted at the opportunity cost of funds; the technique should be capable of selecting from a set of mutually exclusive projects; and finally, the value-additivity principle should hold (Copeland,1983:26).

2a)Traditional techniques:Sophisticated, or discounted cash flow (DCF) techniques, take into account the time value of money. These are the net present value (NPV), internal rate of return (IRR) and profitability index (PI) or benefit-cost ratio. The MIRR (modified internal rate of return) is also used (Brigham,1990:282). There are also numerous unsophisticated techniques, chief among these being the payback method, including discounted payback, and the average rate of return (ARR) on book value. While we do not deliberate on the unsophisticated techniques here, and while it will shortly be seen that the NPV is the "best" technique, it would not do to outright reject the use of other techniques. "The different measures provide different types of information to decision makers, and since it is so easy to generate the values for the measures, all should be considered in the decision process. For any specific decision, more weight might be given to one measure than another, but it would be foolish to ignore the information inherent in any of the methods" (Brigham,1990: 289).

The correct sophisticated (DCF) technique: Initially, the IRR was the method recommended to firms by theorists such as Dean (1951). But in the mid- and late 1950s, it was conclusively shown by Savage (1955) and Hirshleifer (1958) that NPV is the superior technique and that the IRR rule often breaks down. The IRR rule gives rise to the following problems:

a)Change in sign of cash flows (lending or borrowing): If a project offers positive cash flows (borrowing) followed by negative flows (lending), then the IRR rule breaks down (Brealey,1988:80).

b)More than one change in sign of cash flows (multiple roots, or rates of return): If there is more than one change in the sign of the cash flows, the project may have several IRRs, or no IRR at all (e.g. the oil-well pump problem). It must be mentioned here that the MIRR has overcome the multiple IRR problem (Brigham,1990: 283).

c)Mutually exclusive projects: The IRR rule often gives the wrong ranking of mutually exclusive projects which differ in economic life or in the scale of investment.

d)Term structure of interest rates: The IRR rule requires a comparison of the project's IRR with the opportunity cost of capital. But often the short run and long run opportunity costs differ. It then becomes difficult to determine a yardstick for evaluating IRR.

e)Reinvestment at the IRR (implicit reinvestment rate assumption). It is assumed that the time value of money is the IRR, i.e., investors can reinvest their money at the IRR for each project. But reinvestment should be considered only at the opportunity cost of capital. Hence this assumption under the IRR rule defies logic (Copeland,1983:32).

f)Combinations of mutually exclusive and independent projects: The IRR rule violates the value additivity principle when combinations of mutually exclusive and independent projects are taken (Copeland,1983:32).

In view of the above, NPV is treated as the correct decision criterion for DCF analysis in this paper.

2b)Strategic analysis:Many projects may give rise to real options, and require a strategic analysis. The DCF techniques are inaccurate in capturing the range of possibilities in such cases. For example, businesses with substantial growth opportunities or intangible assets have options on their investments (Myers,1984:135).

3. CASH FLOWS

Two variables determine the NPV: the expected future cash flows and the expected opportunity cost. At the heart of the NPV are the cash flows. If these are biased, then the NPV rule will fail (Brealey,1988:88). A cash flow is simply the difference between cash received and cash paid out. We are interested here in the after-tax cash flows for an all-equity firm, but the principles hold true even for a firm using leverage (Weston,1989:104).

3A Certain cash flows: Let the cash flows be known with certainty and assume that these flows are perpetual, i.e., there is no growth (Copeland,1983:37). Then the relevant (certain) cash flows are given by

CF =(_R-_VC-_FCC)(1-Óc) + Óc(_dep) - _I,

where, CF stands for cash flows for capital budgeting, _R represents revenues, _VC is variable costs of operations, _FCC is fixed cash costs, Óc is the corporate tax rate, _dep is depreciation, and _I is the investment.

It is to be noted that all additional, associated, cash flows that follow from project acceptance have to be included (incremental cash flows). Allocated accounting overheads are included if they result from an actual increase caused due to the project. Sunk costs are ignored.

3B Uncertain cash flows: In the case of uncertainty about future cash flows, the same formula as above applies. But what we get are forecasts of cash flows (usually the expected cash flows). Very often, the forecast errors are quite large (Brigham,1990:298). The way out is to ensure that all persons involved in forecasting use a common and consistent set of macroeconomic and other assumptions. Data on probability distributions of the estimates, and their standard errors is essential. Fortunately, most of the forecast errors are random (unbiased) and can be expected to cancel out. On the other hand, some studies have shown that cash flow forecasts are not unbiased, but are commonly over-optimistic (Brigham,1990:316). This consistent upward estimation of forecasts has to be tackled carefully. One way being adopted by firms is to keep track of the historically determined over-estimates, if any, made by different managers, and to include this information in their future forecasts. The second method is to ask from where do the positive net present values come from? What is the competitive advantage of the firm in that project? Additional points required to be considered are:

i)The cross-sectional relationships between cash flows.

ii)Correlations of cash flows over time: if the cash flows of year t are dependent on cash flows for year t-1, then the variance of the project cash flows becomes larger and the project riskier.

ii)Links between today's investments and tomorrow's opportunities have to be worked out. Tomorrow's opportunities often represent an option, and require separate analysis.

From the forecasts we get either of:

a)Expected cash flows, or E(CF): In this case, risk is taken into account by adjusting the discount rate (risk-adjusted return, or RADR).

b)Certainty equivalent cash flows or, CE(CF): In this case, risk is absorbed into the cash flows. It was shown by Rubinstein (1973), using the CAPM, that if is the market price of risk, i.e.,

= E(Rm) - Rf

VAR(Rm)

where E(Rm) is the expected market rate of return, Rf is the market's risk-free rate of return, and VAR(Rm) is the variance of Rm.

then, the CE(CF), or certainty equivalent cash flow is:

CE(CF) = E(CF) - COV(CF,Rm)

where COV(CF,Rm) is the covariance of the cash flow with the market rate of return (Copeland, 1983:196).

Both versions of the cash flow lead to equivalent results in the one-period case (Copeland,1983:195). But in the multiperiod case, Robichek and Myers (1966) showed that the CE technique is superior to the E(CR) and RADR technique. According to them, risk and time are logically distinct variables. The CE approach takes account of them separately, but the RADR approach lumps them together. The only problem is that "there is no practical way to estimate a risky cash flow's certainty equivalent. Each individual would have his or her own estimate, and these could vary significantly." (Brigham,1990:368). Therefore the CE method is not commonly used. We must note that if we use the CE method then the risk-free rate is used to determine the NPV.

4. DISCOUNT RATE

The cost of capital depends on the use to which it is put (Brealey,1988:173). Therefore, the required rate of return on a project will depend on the riskiness of its cash flows.

4A. CERTAIN CASH FLOWS: The following analysis holds when either the cash flows are known with certainty, or we have CE(CF). In these cases there is no further riskiness of cash flows and Rf is used to discount these cash flows. But we must take note of the following theoretical aspects.

4A.1Two period case:

a)Lending and borrowing rates are the same (equal to r): Let an individual have an endowment of (y0,y1) of incomes at the beginning and end of the period, and a series of utility curves U. Then, if only production is an opportunity to him, then he will consume an amount C0 which is exactly equal to the amount he produces in the first period, P0, and invest y0-C0, such that the marginal rate of substitution of his consumption is exactly equal to the marginal rate of transformation of his production opportunity set. If borrowing and lending is allowed (capital markets exist), then it can be shown that the individual can increase present consumption C0 and thus increase his utility, by borrowing down the market line at the interest rate r (Copeland, 1983: 11). "A very practical example is building a house and then borrowing on it through a mortgage so as to replenish current consumption income" (Hirshleifer,1958). The important thing in this process is that MRS = MRT = -(1+r), where r is the lending/ borrowing rate. This holds true for all investors. This process was demonstrated by Hirshleifer (1958). The Fisher separation theorem arises from this: if capital markets are perfect and complete, then all individuals will reach the same decision for wealth maximisation with reference to the market rate of return. In practice, it is assumed that the risk-free market rate of return, Rf, can sufficiently represent r.

(b)Borrowing rate greater than lending rate: When the capital markets are not perfect (there are transaction costs) , then borrowing and lending rates will differ. In this case the solution becomes more complicated, with three zones being created. Hirshleifer showed that in Zone I, the borrowing rate is the relevant rate, in Zone III the lending rate is relevant, and in Zone II, a rate somewhere between these two rates is relevant. The Fisher theorem breaks down in such a case, and the subjective preferences of individuals enter back into the picture. Thus, the complications introduced by transaction costs are difficult to quantify. Rf is used in this case too, as a convenient proxy, but we must remember that it may not be the correct discount rate, and the subjective utility functions of shareholders have to be considered too (if that is possible).

4A.2 Multiperiod case: Hirshleifer (1958) also showed that essentially it is possible to generalise the principles of investment analysis of a two-period case to the multiperiod case, with the market line becoming a hyperplane, and the indifference curves becoming indifference shells.

4B. UNCERTAIN CASH FLOWS: The determination of RADR is necessary when we use the mean cash flows E(CF). The effect of risk on the required rate of return (RRR) has to be considered. A project can have three kinds of risk: stand-alone risk, within-firm (corporate) risk, and market risk (Brigham,1990:341). An investor is usually interested only in the market (systematic) risk, which is the relative risk of the project with reference to the market, since unsystematic risk can be diversified away by the investors on the capital market. But when liquidation costs exist, then unsystematic, corporate, or total risk, is also relevant to the shareholders - since diversification can prevent the possibility of bankruptcy (Brigham,1990:376).

The WACC (weighted average cost of capital) is a useful starting point for estimating the appropriate discount rate. But the problem is that WACC considers the risk of the firm's existing projects, and not specifically that of the project under consideration. The WACC has to be adjusted for risk by considering the project's risk category in relation to the divisional/ company risk structure. Unfortunately, this is a subjective adjustment, and not theoretically sound. The correct way would be to determine the project's systematic risk or ßproj, and then apply the CAPM to determine the RRR. Theoretically, it would be possible to do even better, by applying the APM. We look into these two methods below. We also touch upon the APV technique.

4B.1 Arbitrage pricing model, or theory (APM/APT): In the APT, formulated in 1976 by Ross, the assumption made is that the RRR on any security is a linear function of the movement of a set of fundamental factors, which are common to all securities. The return R on an asset would be given by the following equation, when three factors are considered:

R=E(R) + ß1F1 + ßGNPFGNP + ßrFr + _

where F1, FGNP and Fr represent systematic risk because these factors affect many securities. The term _ is considered unsystematic risk because it is unique to each individual security (Ross,1990:311).

The k-factor model would read as:

Ri = E(Ri) + bi1F1 + ... + bikFk + _i

where Ri is the random rate of return on the ith asset, E(Ri) is the expected rate of return on the ith asset, bik is the sensitivity of the ith asset's return to the kth factor, Fk is the mean zero kth factor common to the returns of all assets under consideration, and _i is a random zero mean noise term for the ith asset (Copeland,1983:211).

The APT allows the consideration of a large number of fundamental factors which is not possible in the CAPM (Ross, 1990:453). Chen, Roll and Ross (1983) find industrial production, inflation, interest rate term structure, and the spread between low and high grade bonds to be important economic variables (Bower,1986). The predictive power of APM has been found to be superior to the CAPM in all tests. However, there is disagreement on the variables involved, and there are many complications in applying the APM. Therefore the APM is not commonly used for determining RADR.

4B.2 Capital asset pricing model, or CAPM: In case the market rate of return is considered to be the only relevant factor, then the APT leads us to the CAPM, which can then be considered as a special case of the APM. According to the CAPM, sensitivity to a single market index does as good a job as any multi-factor model since the different sensitivities of the asset to the collection of economic forces "net out."