Cost/benefit analysis means comparing the cost of a proposed investment and the benefit that will be achieved from investment. Normally financial costs and benefits are considered in cost/benefit analysis but in some sophisticated analysis models intangible benefits are also taken into account.

When organizations evaluate the financial feasibility of investment decisions, the time value of money is an essential consideration. This is particularly true when a project involves cash flow patterns which extend over a number of years. This article discusses one way in which such multiperiod investments can be evaluated.

Assume an investment of $50,000 is expected to generate a net (after expenses) return of $15,000 at the end of 1 year and and equal return at the end of the following three years. Thus a $50,000 investment is expected to return $60,000 over a 4-year period. Because the net cash flows occur over a 4-year period, the dollars during the different periods cannot be considered equivalent. To evaluate this project properly, the time value of the different cash flows must be accounted for.

One approach to evaluate a project like this is to translate the flow of cash into equivalent dollars at a common base period. This is called a discounted cash flow method. For example, this project might be evaluated by restating the flow of cash in terms of their equivalent values at t = 0, the time of the investment. The original $50,000 is stated in terms dollars at t = 0. However, each of the $15,000 cash inflows must be restated in terms of its equivalent value at t = 0.

In order to discount all the flow of cash to a common base period, an interest rate must be assumed for the intervening period. Frequently this interest rate is an assumed minimum desired rate of return on investments. For example, management might state that a minimum desired rate of return on all investments is 10 percent per year. How this figure is obtained by management is another issue in itself. Sometime it is a reflection of known rate of return which can be earned on relative investments (e.g., bonds or money market funds).

Let's assume that the minimum desired rate of return for the project is 8 percent per year. Our discounted cash flow analysis will compute the net present value (NPV) of all the flow of cash associated with a project. The net present value is the algebraic sum of the present value of all cash flows associated with a project; cash inflows are treated as positive cash flows and cash outflows are treated as negative cash flows. If the net present value of all cash flows is positive at the assumed minimum rate of return, the actual rate of return from the project exceeds the minimum desired rate of return. If the net present value for all cash flows is negative, the actual rate of return from the project is less than the minimum desired rate of return.

In our example, we discount the four $15,000 figures at 8 percent. By computing the present value of these figures, we are, in effect, determining the amount of money we would have to invest today (t = 0) at 8 percent in order to generate those four cash flows. Given that the net cash return values are equal, we can treat this as the computation of the present value of an annuity. Using present value of a single sum table.

with n = 4 and i = 0.08.

A = 15,000 (3.31213)

= $49,681.95

This value suggests that an investment of $49,681.95 would generate an annual payment of 15,000 at the end of each of the following 4 years. In this example, an investment of $50,000 is required. The net present value of this project combines the present values of all cash at t = 0, or

NPV = Present value of cash inflows - Present value of cash outflow

Thus

NPV = $49,681.80 - $50,000

= - $318.20

This negative value indicates that the project will result in a rate of return less than the minimum desired return of 8n percent per year, compounded annually.