## 4. Net present value

Managers need to know the value of a multiyear project in terms of today’s dollars, which will be used to make the initial investment. The net present value is found by discounting all estimated future cash flows to present value, then comparing the initial cost of the project to the sum of the discounted cash flows. When applying this method, it is usually preferable to consider cash inflows on an after-tax basis. In addition, tax costs and savings due to different depreciation rates need to be considered as cash flows. We’ll now go over an example of how to find net present value.

Company X management requires a 12% return on all investments. The company is currently considering the following three investments:

 Initial Cost Year 1 Cash Inflows Year 2 Cash Inflows Year 3 Cash Inflows Year 4 Cash Inflows Year 5 Cash Inflows Investment A (100,000) 27,000 27,000 27,000 27,000 27,000 Investment B (100,000) 0 0 20,000 50,000 90,000 Investment C (100,000) 50,000 30,000 20,000 15,000 15,000

Present value factors are as follows:

 Number of Periods Discount Rate 1 2 3 4 5 12% 0.893 0.797 0.712 0.636 0.567

The first step is to discount all cash flows from the first chart. This is simply a matter of multiplying the annual cash flows by the relevant time value factors. For instance, the \$25,000 cash flow from Investment A in year 1 would be multiplied by 0.893; 0.893 represents a time value factor for year 1 at a rate of 12% and can be calculated as: 1/(1+12%)1. We can now reproduce the first chart, but this time with discounted amounts:

 Initial Cost Year 1 Cash Inflows Year 2 Cash Inflows Year 3 Cash Inflows Year 4 Cash Inflows Year 5 Cash Inflows Investment A (100,000) 24,111 21,519 19,224 17,172 15,309 Investment B (100,000) 0 0 14,240 31,800 51,030 Investment C (100,000) 44,650 23,910 14,240 9,540 8,505

By subtracting the initial cost from the sum of all discounted cash flows, we can find net present value. Under the constraints set by management, we can see that only Investment C should be made:

Investment A: 24,111 + 21,519 + 19,224 + 17,172 + 15,309 – 100,000 = (\$2,665)

Investment B: 14,240 + 31,800 + 51,030 – 100,000 = (\$2,930)

Investment C: 44,650 + 23,910 + 14,240 + 9,540 + 8,505 – 100,000 = \$845

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