The theoretical rationale for the NPV approach to investment appraisal - Essay Example

?Explain the theoretical rationale for the NPV approach to investment appraisal and compare the strengths and weaknesses of the NPV approach to two other commonly used approaches. Net Present Value Method The Net Present Value (NPV) is defined as “the present value of a project’s cash inflows minus the present value of its costs” (Brigham & Ehrhardt, 2010, p. 383). It is originally attributed to Irving Fisher in his 1930 book, The Theory of Interest. The most common application of the Fisher model of NPV is in deriving the value of the net contribution of a potential investment to shareholder value, or for budgeting purposes, when deciding among alternative projects when available capital is limited and may not be sufficient to finance all the projects. In fact, the NPV is a valuation method that may be used to decide situations for which a stream of future returns and future payments may be estimated. The power and allure of the NPV is that it serves so well the role of financial markets that allows individuals and corporations to transfer money between dates (MacMinn, 2005:1). By creating a rationale valuation tool linking money in two different points in time, it becomes possible for the individual to “save by transferring dollars from the present to the future,” while the corporation may “invest and finance the investment by transferring dollars from the future to the present” (p.l-2). However, for the model to work requires knowledge of the cost of capital from which the discount rate is derived. The NPV is derived by discounting all future cash inflows and outflows to the present. By “discounting” is meant calculating the equivalent value in the present of all future cashflows, assuming these cashflows appreciated over time by an annual compound rate such as the cost of money. This “discount rate” is that rate of return that an investment (of similar risk) in the financial markets may be expected to earn. Otherwise stated, if an amount equivalent to the net present value were invested today in a financial instrument of similar risk as the alternative or project being considered, the rate of return of which is equal to the expected return on the investment, then such amount would represent the same benefit that may be derived from th entire stream of future cash flows yielded by the instrument invested in. When the discount rate has been determined, the present value of a single sum N years in the future may be found by multiplying this single sum by the discount factor pertaining to the discount rate applied over N number of years. In mathematical terms: Where: PV = present value of the future single sum R = the future single sum N = the number of compounding periods from the present to the time the single sum is realized or expected i = the discount rate The discount factor is equivalent to the factor multiplied by the single sum to obtain the present value. It is denoted by the expression Discount factor (single sum, discount rate i, N periods) = Where there are more than one cash flow, the several cash flows together make up a cash flow stream. In this instance, the sum of the present values of the individual cash flows is equal to the present value of the entire cash flow stream. When the cash flow is an inflow (or revenue), then the cash flow is positive and its present value is also positive. When the cash flow is an outflow (or cost), then the cash flow is negative, and its present value is also negative. Therefore the sum of present values for the inflows and outflows nets out the costs from the revenues, resulting in the net present value. Illustrating the theoretical rationale of the NPV To illustrate the rationale of the NPV approach, assume that management has to choose from three possible investments A, B and C, each with a life of five years and none of which are mutually exclusive, with the following expected future cash inflows and outflows: The cash flows at year 0 (the present) represent the initial investments which are costs and therefore are denoted by the negative sign. The positive cash flows from one to five years thereafter represent the revenues expected to be earned per year. In this exercise, the investor is constrained to a maximum investible capital of $750, and therefore could not invest in all three alternatives, but possibly may invest in Alternatives A and B, or A and C, but not B and C under any situation. Assuming the cost of capital is 10 per cent, the investor has to now make a decision as to which investment alternative to invest in. Table 2: Solution for NPV illustrative problem Year Discount Factor Present Values A B C 0 1 -250 -500 -500 1 0.9091 0 90.91 272.73 2 0.8264 0 82.64 165.29 3 0.7513 75.13 75.13 75.13 4 0.6830 68.30 136.60 68.30 5 0.6209 62.09 186.28 62.09 NPV -44.48 71.56 143.54 In Table 2, the solution to the investment problem is summarized. The net present value was arrived at by obtaining the present value of each year, and then adding these amounts for the entire investment. The discount factor is computed pursuant to the mathematical formula earlier given. The discount factor is 1 for year 0 because the cash flow occurs at the present and its present value is itself the amount of the cash flow. Alternative A is not acceptable. The reason is that when the present value of costs and revenues are summed up, the NPV is negative. This means that although the sum of the actual cash flows are positive ($300 in revenues against $250 in costs), because the cash inflows occur late in the investment’s life, then the sum of their present values ($205.52) is much lower than the sum of their nominal values, and is unable to fully cover the initial investment of $250, yielding an NPV of -$44.48. Investors who put their money in this alternative will not be able to recover their initial investment, much less realize their objective of earning any returns. Alternative B is acceptable, because it has a positive NPV, meaning that it stands to recover the initial investment for the investor, while at the same time earning him positive cash flows. The same may be said of Alternative C, which also has a positive NPV. If an investor had $1,000 to invest then both alternative would be viable and the investor would stand to gain the most net positive returns by investing in both. However, the investor in this case has only $750 to invest, and therefore could not simultaneously invest in both B and C, and must therefore make a choice between them. Therefore, it is recommended that he invest in Alternative C, which has the higher NPV between them ($143.54 as against $71.56). It is interesting to note that the simple sum of cash flows, which is done for the method in calculating payback periods, does not work for the NPV. It will be noted that Alternatives B and C in the problem both have the same total cash inflows ($800) and outflows (-$500). What differs between them is the point in time during which the particular cash flows occur. For Alternative B, the stronger cash flows are realized farther back in time while for Alternative C, the stronger cash flows are closer to the present. Based on the time value of money, a cornerstone principle of NPV, cash flows that take place sooner are more valuable to the present than cash flows that take place later. The NPV has been and continues to be a valuation method of choice for investment analysis for several reasons. Firstly, it explicitly takes into account the time value of money, because as illustrated it is computed based on discounted cash flows. Secondly, because it uses cash flows, the firm’s choice of accounting methods does not affect the result arrived at. Thirdly, through its discounting process, the NPV explicitly includes the impact of the costs of raising finance. The result is therefore immediately a net positive contribution to (or net negative reduction in) shareholder wealth, and allows for ease and clarity in decision-making (Coombs, Hobbs, & Jenkins, 2005). The NPV also has its disadvantages. While it is theoretically sound to assume a cost of money, as in this case, it is in practice quite difficult to fix a realistic discount rate. While the process involves the cost of capital, arriving at the latter necessitates an estimation of the costs of the different elements of finance which may fluctuate because of the volatility of the financial markets. Furthermore, the NPV is an absolute amount and does not take into account the relative size of the project or investment (Coombs, et al, 2005). For the sake of argumentation, supposing that a proposed investment X requires $1,000,000 initial investment, and investment Y requires only $1,000, yet investment X yields an NPV of $1,000 while that of Y produces and NPV of $750, then the criterion for investment selection through NPV dictates that investment X be chosen because it has the higher NPV. It is apparent, though, that wise investors would find investment Y more attractive because it requires a small outlay and yields an NPV which, though numerically smaller, is a higher proportion of the investment capital than that of investment X. Finally, the length of time for the duration of the project and the likelihood that the expected cash inflows shall not be realised are likewise not accounted for. These elements introduce risks into the project that are not evident in the straightforward NPV calculation. If the life of project M is 10 years and that of project N is only 6, if the NPV of project M is only slightly higher than that of N then the NPV method justifies choosing project M, without considering that the earlier completion of project N has a lower risk and will allow for new projects to be considered earlier. Likewise, it is possible that the assumed stream of cash flows for one investment will be more certain than that of the other. This may result out of practical considerations such as the reliability of suppliers or outsources, or the regularity of demand for the product good or service created. A large reduction in risk may prove a more worthy investment despite a smaller NPV. Risk-Adjusted Present Valuation (RPV) As was mentioned in the preceding paragraph, one of the pitfalls of the classic NPV approach is that it does not explicitly take into account the risk of the different alternatives. Shimko (2001) points out two fundamental limitations of the NPV: (1) that when a risk premium is attached to the discount rate, it is implicitly assumed that the risk charges are proportional to the value of the asset, which is a misleading assumption; and (2) since NPV is arrived at by mathematical calculation of expected cash flows, the impact of diversifiable risk on asset valuation is ignored. In modern asset valuations, overlooking such limitations may critically undermine the decision making process. The problem with the first limitation, that of attaching a risk premium to the discount rate, is that in present financial markets, instruments such as swaps and other derivatives are able to disengage the risk from the initial investment (the value of the asset). Therefore, cash investment in modern day finance is not always bundled with the assumption of risk, and it may be argued that if a project were to need cash today, the proponent may find any number of suppliers willing to accept a narrow spread to the risk-free interest rate. Shimko argues that cash has become more of a commodity at present than it was in the past (p. 2). The second limitation has to do with the failure of the NPV to take into account the idiosyncratic risk involved in the investment. Idiosyncratic, or unsystematic, risk is that risk that affects a very diminutive group of assets, or even possibly just one asset in particular, which is not accounted for by the general market conditions, but by the unique circumstances pertaining to that security. In investment management, idiosyncratic risk could usually be diversified away, but for Shimko such risk should be addressed in the case of valuation of a single investment. According to this author, the Modigliani-Miller framework assumes that idiosyncratic risk need not be priced because investors can just diversify it away, but this assumption is true only if capital is available in unlimited quantities to any given firm at a fair price. In reality, however, capital available at reasonable price is always limited in the short term, which compels investors to factor in risk in their decision. If a project turns out bad, for instance, it may cause a firm to forego or put off other undertakings or pay a higher price on new debt, thus reducing the profit-making potential for which the project was undertaken in the first place. To forestall management from too quickly jumping to risky projects, risk should therefore be assigned a cost (p. 2). A method proposed by Shimko (2001) that may present a viable alternative to the classic NPV is the RPV, which is a risk-based approach to valuation. This method introduces the use of risk capital aside from just the cash capital used in NPV. Risk capital is defined as the maximum loss an investment may take over the span of one year, corresponding with the “worst case” cash flow that may occur at any time within the year. It also makes use of RAROC or risk adjusted return on capital which accounts for the return on risk capital. Mirroring the statistical processes used in practices on the trading floor, a statistical confidence interval is assumed that represents the worst case loss expected. From this description, it is apparent why the RPV is not at present a popular or favoured method for valuation, though it was proposed by Shimko in 2001, and possibly others before him. The RPV introduces many more parameters that are more difficult to estimate than just the cost of money. The RPV takes as its framework the trading practices in the financial markets, which, while allowing for more exactness than the NPV in the short term, is prone to interim volatilities that would have been smoothed out if a longer-term perspective were adopted, as the NPV does. The reference to the “worst case” loss within the year, in trading practice, refers to the deepest drop in security valuation as a result of market prices reacting to the bad news of any one particular day; however, even traders know that market shocks are erratic and often recover within a short period of time. Such “worst case” valuations have therefore little to do with assessing the long-term viability of a project. The RPV, therefore, may be a case of taking too much pains to calculate too many variables that in the long run may not significantly inform the investment decision. Ingersoll and Ross’ (1992) “Rule of Thumb” While Shimko’s RPV espouses a more complicated substitute for the NPV, the “rule of thumb” proposed by Ingersoll and Ross proposes an analytical formula for the value that includes the option to wait. The formula proposes an approximation for determining the cutoff hurdle rate at which a project should be undertaken (Ross, 1995, p 100). The formula is given by: Where: T = the duration of the project rT = the yield on a zero coupon bond with maturity T = the standard deviation of the interest rate Without going into the intricacies of the calculation, Ingersoll and Ross state that using this model, the optimal cutoff for deciding on pursuing a project is lower than the IRR at all times. This means that for an investment option to be undertaken, the project must be “in the money” (i.e., showing positive net gains) over the internal rate of return. The model is so conservative that in many cases the margin from the IRR at which the cutoff falls is in the order of half the interest rate itself (Ross, 1995). If the cutoff hurdle is not reached, then the option to wait becomes the better decision. The rule-of-thumb proposed by Ingersoll and Ross may indeed be simpler to calculate, however, it does not provide a criterion for choosing between alternative investments, or ranking investments according to attractiveness or viability. What it does provide is the criterion for accepting or holding off on a project investment, until the cutoff hurdle rate is achieved. In the matter, therefore, similar to the example for the NPV shown earlier, the rule of thumb will not provide a convincing method by which a clear decision may be made. Conclusion It is true that the NPV may have its shortcomings in that it tends to simplify the complex workings of the financial markets and, as a result, fails to capture specific and real phenomena such as unsystematic risk. The NPV also makes assumptions as far as the cost of capital is concerned which fail to reflect the realities of the market for any length of time. However, it may be seen that alternatives to the NPV have their own limitations as far as their practical application are concerned. Parameters introduced to improve the accuracy of the cost of money / rate of return / discount rate have a tendency to become too complicated and difficult to maneuver, although their usefulness are as limited as the temporary shocks in the financial markets. Other methods fail to provide decision criteria that are clear to the mind of the investor. On the other hand, attempts have been made to fine tune the NPV and enable it to allow for considerations of uncertainty (Lee, 1980). Thus preference and confidence of investors and analysts in the use of the NPV continues to serve its usefulness as a tool for making valid decisions, a feat which other models may come to reprise only in due time (Connor, 2006). References Brigham, E F & Houston, J F 2009 Fundamentals of Financial Management, 12th edition. South-Western Cengage Learning, Mason, OH Brigham, E F & Ehrhardt 2010 Financial Management Theory and Practice. South-Western Cengage Learning, Mason, OH Burksaitiene, D 2009 “Measurement Of Value Creation: Economic Value Added And Net Present Value.” Economics & Management, p709-714 Connor, T 2006 “Net present value: blame the workman not the tool.” Strategic Change, Jun/Jul2006, Vol. 15 Issue 4, p197-204; DOI: 10.1002/jsc.766 Coombs, H M; Hobbs, D; & Jenkins, D E 2005 Management Accounting: Principles and Applications. Fisher, I 1965 The Theory of Interest, Augustus M. Kelley, Publishers, New York, NY. (Reprinted from the 1930 edition.) Lee, J C 1980 “Deterministic Net Present Value As An Approximation Of Expected Net Present Value.” Journal of Business Finance & Accounting, Summer 80, Vol. 7 Issue 2, p245 MacMinn, R D 2005 The Fisher Model and Financial Markets. World Scientific Publishing Co. Pte. Ltd., London Ross, S A 1995 “Uses, Abuses, and Alternatives to the Net-Present-Value Rule.” Financial Management, Autumn 1995, vol. 24, issue 3, p. 96. Shimko, D C 2001 “NPV No More: RPV for Risk-Based Valuation,” Risk Capital Management Partners, New York, NY Read More