BUS601: Financial Management

Net present value helps companies choose between alternatives at a particular point in time by determining which produces the higher NPV. To determine the NPV, the initial investment is subtracted from the present value of cash inflows and outflows associated with a project at a required rate of return. If the outcome is positive, the company should consider investment. If the outcome is negative, the company would forgo investment.

We previously discussed the calculation for present value using the present value tables, where n is the number of years and i is the expected interest rate. Once the present value factor is determined, it is multiplied by the expected net cash flows to produce the present value of future cash flows. The initial investment is subtracted from this present value calculation to determine the net present value.

Recall that the Present Value of $1 table is used for a lump sum payout, whereas the Present Value of an Ordinary Annuity table is used for a series of equal payments occurring at the end of each period. Taking this distinction one step further, NPV requires use of different tables depending on whether the future cash flows are equal or unequal in each time period. If the cash flows each period are equal, the company uses the Present Value of an Ordinary Annuity table, where the present value factor is multiplied by the cash flow amount for one period to get the present value. If the cash flows each period are unequal, the company uses the Present Value of $1 table, where the total present value is the sum of each of the unequal cash flows multiplied by the appropriate present value factor for each time period. This concept is discussed in the following example.

Assume that your company, Rudolph Incorporated, is determining the NPV for a new X-ray machine. The X-ray machine has an initial investment of $200,000 and an expected cash flow of $40,000 each period for the next 10 years. The expected $40,000 cash flows from the new X-ray machine can be attributed to either additional revenue generated or cost savings realized by more efficient operations of the new machine. Since these annual cash flows of $40,000 are the same amount in each period over the ten-years this will be a stream of annuity amounts received. The required rate of return on such an investment is 8%. The present value factor (i = 8,  n = 10) is 6.710 using the Present Value of an Ordinary Annuity table. Multiplying the present value factor (6.710) by the equal cash flow ($40,000) gives a present value of $268,400. NPV is found by taking the present value of $268,400 and subtracting the initial investment of $200,000 to arrive at $68,400. This is a positive NPV, so the company would consider investment.

If there are two investments that have a positive NPV, and the investments are mutually exclusive, meaning only one can be chosen, the more profitable of the two investments is typically the appropriate one for a company to choose. We can also use the profitability index to compare them. The profitability index measures the amount of profit returned for each dollar invested in a project. This is particularly useful when projects being evaluated are of a different size, as the profitability index scales the projects to make them comparable. The profitability index is found by taking the present value of the net cash flows and dividing by the initial investment cost.

For example, Rudolph Incorporated is considering the X-ray machine that had present value cash flows of $268,400 (not considering salvage value) and an initial investment cost of $200,000. Another X-ray equipment option, option B, produces present value cash flows of $290,000 and an initial investment cost of $240,000. The profitability index is computed as follows.

Based on this outcome, the company would invest in Option A, the project with a higher profitability index of 1.342.

If there were unequal cash flows each period, the Present Value of $1 table would be used with a more complex calculation. Each year's present value factor is determined and multiplied by that year's cash flow. Then all cash flows are added together to get one overall present value figure. This overall present value figure is used when finding the difference between present value and the initial investment cost.

For example, let's say the X-ray machine information is the same, except now cash flows are as follows:

The Present Value of $1 table is used because, each year, a new "lump sum" cash flow is received, so the cash flow in each period is different. The cash flows are treated as one-time lump sum payouts during that year. The present value for each period looks at each year's present value factor at an interest rate of 8%. All the PVs are added together for a total present value of $219,990. The initial investment of $200,000 is subtracted from the $219,990 to arrive at a positive NPV of $19,990. In this case, the company would consider investment since the outcome is positive. (More complex considerations, such as depreciation, the effects of income taxes, and inflation, which could affect the overall NPV, are covered in advanced accounting courses.)