# The theoretical rationale for the NPV approach to investment appraisal

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