Accounting for risk in a net present value calculation
A company that distributes restaurant supplies is analyzing the feasibility of expanding their distribution capacity by opening a new distribution center. Management has specified that the startup costs for the new center must be recovered within three years, from the revenue generated by the center. The company's analysts have a good handle on the startup costs, but there is a fair amount of uncertainty in the revenue stream and some uncertainty in the operating costs of the new center. To determine the feasibility of opening the new distribution center, the analysts will carry out a net present value calculation, using simulation to account for uncertainty in revenue and operating costs.
The net present value (NPV) of a revenue stream is given by:
where R n is the revenue in year n, C n is the cost in year n, r is the discount rate and N is the number of years in the revenue stream. The term C 0 represents the startup costs.
Management's requirement that the startup costs must be recovered within three years means that the net present value of the stream of revenues and costs over the three year period must be greater than 0. The analysts will assume that revenues grow at a fixed rate, starting from an estimated revenue for the first year. The expression for the net present value is then given by:
where revenue is the projected first year revenue, opcost is the annual operating cost of the center (assumed to be constant), growth is the revenue growth rate, startcost is the startup cost and rate is the discount rate.