The risk adjustment procedures discussed in this section are appropriate when the firm believes that a project’s total risk is the relevant risk to consider in evaluating the project and when it is assumed that the returns from the project being considered are highly positively correlated with the returns from the firm as a whole. Therefore, these methods are appropriate only in the absence of internal firm diversification benefits, which might change the firm’s total risk (or the systematic portion of total risk).
Several different techniques are used to analyze total project risk. These include the net present value/payback approach, simulation analysis, sensitivity analysis, scenario analysis, the risk-adjusted discount rate approach, and the certainty equivalent approach. In addition, total project risk can be measured by calculating the standard deviation and coefficient of variation.
Net Present Value/Payback Approach
Many firms combine net present value (NPV) with payback (PB) when analyzing project risk. As noted in Chapter, the project payback period is the length of time required to recover the net investment. Because cash flow estimates tend to become more uncertain further intothe future, applying a payback cutoff point can help reduce this degree of uncertainty. For example, a firm may decide not to accept projects unless they have positive net present values and paybacks of less than some stated number of years.
The net present value/payback method is both simple and inexpensive but it suffers from some notable weaknesses. First, the choice of which payback criterion should be applied is purely subjective and not directly related to the variability of returns from a project. Some investments may have relatively certain cash flows far into the future, whereas others may not. The use of a single payback cutoff point fails to allow for this. Second, some projects are more risky than others during their start-up periods; the payback criterion also fails to recognize this.
Finally, this approach may cause a firm to reject some actually acceptable projects. In spite of these weaknesses, however, some firms feel this approach is helpful when screening investment alternatives, particularly international investments in politically unstable countries and investments in products characterized by rapid technological advances.Also, firms that have difficulty raising external capital and thus are concerned about the timing of internally generated cash flows often find a consideration of a project’s payback period to be useful.
Computers have made it both feasible and relatively inexpensive to apply simulation techniques to capital budgeting decisions. The simulation approach is generally more appropriate for analyzing larger projects. A simulation is a financial planning tool that models some event. When simulation is used in capital budgeting, it requires that estimates be made of the probability distribution of each cash flow element (revenues, expenses, and so on).
If, for example, a firm is considering introducing a new product, the elements of a simulation might include the number of units sold, market price, unit production costs, unit selling costs, the purchase price of the machinery needed to produce the new product, and the cost of capital. These probability distributions are then entered into the simulation model to compute the project’s net present value probability distribution. as we have already sen in previous topic ,net present value is defined as follows
Lwhere NCFt is the net cash flow in period t, NINV is the net investment, and k is the cost of capital. In any period, NCFt may be computed as follows:NCFt = [q(p) – q(c + s) – Dep](1 – T) + Dep – _NWC
where q is the number of units sold; p, the price per unit; c, the unit production cost (excluding depreciation); s, the unit selling cost; Dep, the annual depreciation; _NWC, the change in net working capital; and T, the firm’s marginal tax rate. Using Equation, it is possible to simulate the net present value of the project. Based on the probability distribution of each of the elements that influence the net present value, one value for each element is selected at random.
Assume, for example, that the Wilshire Company is performing a simulation analysis and that the following values for the input variables are randomly chosen: q = 2,000; p = $10; c = $2; s = $1; Dep = $2,000;*NWC = $1,200; and T = 40%, or 0.40. Inserting these values into Equation 11.1 gives the following calculations:
Assuming that the net investment is equal to the purchase price of the machinery ($10,000, in this example), that the net cash flows in each year of the project’s life are identical, except for year 5, when $6,000 of NWC is recovered, that k = 10%,1 and that the project has a 5-year life, the net present value of this particular iteration of the simulation can be computed as follows:
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