> '` Fbjbj$$ 8FFFt6666<7d9$77777a8a8a88888888$&:h<8a8a8a8a8a88778a8a8a8a8778a8a88a8a8a87z7W6a8a88809a80=a80=a80=a8 a8a8a8a8a8a8a8a888a8a8a8a89a8a8a8a8 66~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-c) + c(_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, c 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.1 Two 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 proj, 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) + 1F1 + GNPFGNP + rFr + _
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."
4B.2.1 Single period case:
4B.2.1.1 All-equity case: In this case, the project as well as the firm are financed entirely by equity. The CAPM assumes perfect capital markets, well-diversified investors and homogeneous expectations and therefore works well under a "single period uncertainty" case, as shown by Rubinstein (1973). The CAPM requires the project to earn at least the rate of return required by the market on projects of equivalent risk (Weston,1989:437). Rubinstein considered that the new asset already exists and is valued in the market (Martin,1988: 292). He then showed that the RADR is given by:
E(Rproj) = Rf + [E(Rm) - Rf]proj.
where, Rproj is the RADR on the project, and proj is the project's beta (Weston,1989:441).
Projects with greater systematic risk will have greater betas, and their RADR will be higher. Here, we see that Rf and Rm are generally known, but the problem is the determination of proj, which we now look into, below.
a) When the project has the same risk as the company's existing assets, then the company's beta of assets is required. It is determined by regressing an accounting measure of return for the company (such as the return on assets) on an economy-wide index of returns (such as the average return on assets for non-financial corporations). There are complications associated with this approach, which we do not touch upon here.
b) When the project has different risk to that of the company then it is the asset beta of the project that counts. Since product markets do not have active secondary markets, finding proj from historical information is not usually feasible (Rao,1992:366). The techniques used therefore are (Brigham,1990:363):
i) In the pure play method, existing firms producing a single product similar to the project under consideration are sought out. The betas of these firms are determined through regression analysis, and can then be used as a proxy for proj.
ii) When such single-product, publicly traded firms suitable for the pure play approach are not available, then accounting beta method is used. Here a suitable proxy is chosen, such as the division of another firm, or a privately held firm which matches the project, and a time series regression of that division's earning power is run against the average earning power of a large sample of stocks (Brigham,1990:364). We note that accounting betas are not as good as market betas.
4B.2.1.1.2 When the firm has leverage: If the firm as well as the project include debt financing, then as a company increases its degree of debt financing, the investors require an additional financial risk premium. The RADR is then adjusted under the CAPM by the Hamada (1969) formula in case the classical tax system applies. Here the RADR, keL (the cost of equity to a leveraged firm) is the sum of risk-free rate, business risk premium and financial risk premium.
keL = Rf + (Rm - Rf)U + (Rm - Rf)L
where L is the beta of the levered firm and U is the beta of the unlevered firm. But we know that
L = U [1+(B/S)(1-T) (Hamada formula)
where B is the market value of debt, S is the value of shares of the levered firm, and T is the corporate tax rate. Therefore,
keL = Rf + (Rm - Rf)U + (Rm - Rf)U (1-T)(B/S)
In Australia, where the dividend imputation system prevails, if there is no earnings retention and no preferential treatment of capital gains, and if a comprehensive measure of income is used, then the CAPM takes the form which would apply if there were no taxes (Van Horne,1990: 257):
keL = Rf + (Rm - Rf)U + (Rm - Rf)U. B/S
or keL = Rf + (Rm - Rf)U (1+B/S)
4B.2.1.1.3 Liquidation costs (Total risk to the firm): Projects financed with debt could at times cause an impact on the total risk to the firm (corporate risk), by bringing about the possibility of bankruptcy. The diversification aspects of a proposed investment are relevant to its evaluation in such a case (Van Horne,1990:243). A project which has a diversification effect would have a lower RADR, at least from the point of view of the shareholders/ debtholders and perhaps the management. This diversification effect could be verified by correlating the project's cashflows/NPV with the rest of the firm's projects.
4B.2.2 Multiple period case: We know that the CAPM relates to a single period only; but investment analysis almost always considers more than one year/ period. Many problems arise when the CAPM is extended to more than one period. The future Rf, Rm, and even proj vary over time. Some projects are safer in youth than in old age, others are riskier. In particular, the extension of CAPM is safer when proj remains constant over time, than if it changes significantly. In the latter instance, it would be necessary to apply different betas (and consequently, different RADRs) over different future periods. Unfortunately, there is no practical method to estimate these changes, and the errors in estimates can increase over time. Hence when the CAPM is extended to the multiperiod case, we must realise that its power declines over time (Rao,1992:373).
In fact, Bogue and Roll (1974) showed that multiperiod capital budgeting is simply not possible if there are imperfect markets for physical capital. They also required the consideration, not only of the systematic risk in the usual CAPM sense, but also of the risk of fluctuations in the risk-free rate and the covariation risk of the intermediate value of the project (Copeland,1983:363). Fama (1977) reexamined Bogue and Roll's critique and found that certain uncertainties allowed by Bogue and Roll are inadmissible in the stationary CAPM context, which assumes the portfolio opportunity set to be nonstochastic. Therefore the only admissible form of uncertainty is in the expected cash flows at time t, assessed at time 1).
iv. Capital constraints/ rationing: There is some debate on this point, since it is felt that there is no real capital constraint in the real world. Internal (soft) constraints are more likely than external (hard) ones. If there is a one-period capital constraint, then the PVI can be used. For multiple period capital constraints, two types of programming techniques are applicable: linear programming in case the projects are divisible, and integer programming in case they are not (Weingartner,1963,1977). However, these techniques fail when uncertainty is introduced.
v. Replacement problem: Here the question is whether to continue with a machine or to replace it now. The existing machine would have maintenance costs, but would yield revenues and a salvage value. In such a case the AEC of the new machine has to be worked out and a comparison made with the cost of the old machine.
vi. Excess capacity costs: The spare capacity created by a project has to be charged to whosoever uses it, in order to value it properly (Brealey,1988:109).
vii. Fluctuating load requirements: In case of more than one machine being required to meet fluctuating load requirements, it is possible that the NPV of replacing one or a few machines may be greater than replacing all of them (Brealey,1988: 110).
viii.Treatment of inflation: Here, both the cash flows and the opportunity cost of capital have to include (or exclude) expectations of inflation. The problem is of course the estimation of the future inflation rate. Usually, the term structure of interest rates is considered, as it is felt to reflect expected inflation. Account must be also taken of the differing effects of inflation on various inflows/outflows.
6. NPV UNDER UNCERTAINTY
In case E(CF) and the RADR as derived using the CAPM are used, then, the present value of an expected cash flow E(CF) will be given by:
E(PV) = E(CF) _
1+ {Rf + [E(Rm) - Rf)]proj}
Subtracting the initial outlay I from PV, we get the E(NPV)= E(PV) - I. But E(NPV) can be deceptive. Therefore it is always worthwhile doing some more study into the viability of the project.
i) Sensitivity analysis: Here we consider the major variables determining a project's success and estimate how far the NPV would be altered by taking a very optimistic or a very pessimistic view of each of these variables, one at a time.
ii) Scenario analysis: In this the effect on the project of a few combinations of variables is examined.
iii) Monte Carlo simulation: For large projects, it is worthwhile to look at all possible combinations of variables. In this technique, a model of the project is determined. The probability distributions of each of the determinants of cash flow are then specified. The computer then gives random values to these variables and determines different cash flows, and the NPVs. This gives rise to a frequency distribution of returns.
The above analysis will give a more complete picture of the variability of the NPV, and depending on the risk-aversion of shareholders, a better decision can be taken.
7. PRACTICAL ISSUES WITH DCF TECHNIQUES:
7.i Capital budgeting techniques used by firms: In a study in the USA, Gitman and Forrester (1977:68) found that the most popular investment appraisal decision rule is the IRR (53.6%), followed by ARR (25%). The use of the NPV has been increasing over the years, from 9.8% in the Gitman study (1977), to 68% in the Pike (1988) study carried out in UK. Pike found that:
a) Almost 2/3rd of the sample prepare a capital budget which looks beyond two years.
b) 84% of the firms have investment manuals.
c) Capital budgeting is not regarded as a specialist function and only 26% of the firms employ personnel for capital budgeting.
d) 71% of the firms review and set hurdle rates for their projects.
e) 86% of the firms carry out formal risk analysis.
f) Firms seem to use a basket of techniques to decide on a project. They use the payback method in 92% of the cases, IRR in 75% of the cases and NPV in 68% of the cases. Many of the firms use computer models for their analysis.
h) It was also found that DCF methods have proved their worth to firms, inspite of their many unavoidable shortcomings.
7.ii DCF and the decline of American fortunes: M.E.Porter (1992) has criticised the DCF system of evaluation of projects as being a possible cause of the relative decline of American business in comparison to Japan. He feels that DCF methods have led US capital and financial markets toward a short-term gain orientation. Impatient investors force business managers to maximise short-term earnings rather than in long-term growth. However, Bernstein (1992) shows that investors are not only patient but pay a premium for stocks of research-oriented companies. The cause of the decline of the US lies elsewhere and not in DCF techniques/ financial markets. One tends to agree with Bernstein.
8. MERGERS AND ACQUISITIONS (M&A):
M&A also constitute an investment decision. The difference is that in M&A, prices are subject to bargaining, and it is difficult to measure incremental cash flows accurately (Van Horne,1990:219). For M&A activity to be beneficial, there must first be an economic gain. For this to happen, the two firms must be worth more together than apart (synergy). Gain = PVAB - (PVA + PVB) where PVAB is the present value of the merged firm, and PVA and PVB are respectively the pre-merger values of the firms A and B. In addition, the costs have to be worked out. One should go ahead only when the gains exceed the costs. When the acquisition is financed by cash, Cost = cash - PVB, and when it is financed by equity, the cost = PVAB - PVB. There are different models which take account of efficiency, information costs, agency problems, market power, tax deductability, etc., in mergers and acquisitions. Analysis of M&A activity is therefore an independent topic itself and will not be considered here further.
9. STRATEGIC REAL OPTIONS ANALYSIS
Under some uncertain situations, investment projects could have options embedded in them: e.g., flexible technologies and research and development projects. These are called "real" options, to distinguish them from financial options such as traded puts and calls. Real options last longer and are more complex than financial ones. They are distinguished by the time-series links between/within projects. Many of these also take the "American" form, whereby they can be exercised before the expiration date. Such a project's NPV can be quite different from one that has no such options embedded in it. Very often the embedded option can tip capital investment decisions one way or the other (Brealey,1988:495). Some of the common real options are (adapted from Kulatika, 1993):
i) Investment timing: A positive-NPV project is equivalent to an in-the-money call option. We would obviously like to exercise this option at the best time. Thus all projects have the option of being taken up now, or later. A lease for offshore exploration for oil could be more profitable in the future when oil prices rise (Myers, 1984).
ii) There is always an option to make follow-on investment if the immediate investment project succeeds (Brealey, 1988:495).
iii) Abandonment value: If a project fails, it is not necessary to continue with it. Instead, if there are active secondary markets for tangible second-hand goods, then the project can be sold at higher than salvage value. We must keep in mind that intangibles have usually a lower value than tangibles. The second-hand market gives the owner a put option (Myers,1984).
iv) Shutdown option: The option to shutdown could exist in some cases during low price periods.
v) Growth option: Sometimes a current investment could facilitate future investment opportunities. In such a case the current project would have a larger NPV than it would otherwise have had (Brealey,1988:469).
vi) Designed-in option: This could include the option to switch to cheaper inputs, to switch to a different outputs and to include future expansion requirements.
vii) Research and Development projects: The value of R&D is almost all option; so also is the value of other intangible assets.
viii)Takeovers/acquisitions: A firm could sometimes be acquired at premium, at a negative NPV, for purely strategic reasons, for opening up investment opportunities in the future.
This area was a part of financial strategy till recently and not amenable to quantitative analysis. But now, a mixture of DCF and option valuation models are capable of forging the missing link between finance theory and strategic planning.
Valuation of real options: Banz and Miller (1978) have shown a method of valuing such options. First, the problem is set up in a time state preference framework. Second, the Black and Scholes (1973) option pricing model is used to calculate the prices of the identified state contingent claims identified (Martin,1988:510). One problem is that many of these options are of the American type and the B-S model has limitations when dealing with these. Further, the absence of a secondary market for the underlying asset places serious limitations on the value of real options. However, the mere recognition of real options opens up areas for quantitative analysis not available earlier.
10. CONCLUSION
The manager of a firm has to recognise that projects of different types, and meeting different assumptions, require different approaches to investment analysis. Whereas the DCF techniques and the CAPM have serve fairly well in most cases, it is important to recognise that many projects have real options, and recognising this would reduce the chance of rejecting good projects. Mergers and acquisitions also require a special analysis. But we must remember that inspite of the theoretical advance made in asset pricing under uncertainty, there are limitations imposed by the very nature of uncertainty in the analysis, and subjective judgement has ultimately to be applied, once all available data is compiled. To that extent, investment appraisal takes on the features of an art, rather than a science.
But as Pike (1988) has found out, sophisticated techniques have come to stay inspite of these limitations, and are making a positive contribution in improving investment decisions.
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