NPV Definition
NPV is defined as the difference between Initial Cost Outlay and present value of expected cash inflows. A positive NPV value is acceptable where as an NPV of zero yields the internal rate of return. A negative value for NPV suggests that investment is not worthy of the money we are about to invest.
NPV Formula
NPV Example
Let us examine finding Net Present Value or NPV with an example investment proposal. Let us say we were offered a series of cash inflows at the end of each of the next four years as $5000, $4000, $3000, and $1000. And the Initial Cost Outlay for this proposal is $10,000 and the discount rate or return is 12%.
NPV Calculation @ 12%
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NPV
at
12%
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| Year | NET CASH FLOW | PVIF @ 12% | PRESENT VALUE |
|---|---|---|---|
| 1 | 5000 | 0.893 | $4,465 |
| 2 | 4000 | 0.797 | $3,188 |
| 3 | 3000 | 0.712 | $2,136 |
| 4 | 1000 | 0.636 | $636 |
| NPV = $425 | $10,425-10,000 | ||
NPV Calculation @ 15%
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NPV
at
15%
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| Year | NET CASH FLOW | PVIF @ 15% | PRESENT VALUE |
|---|---|---|---|
| 1 | 5000 | 0.870 | $4,350 |
| 2 | 4000 | 0.756 | $3,024 |
| 3 | 3000 | 0.658 | $1,974 |
| 4 | 1000 | 0.572 | $572 |
| NPV = -$80 | $9,920-$10,000 | ||
NPV Profile
Generally speaking NPV ( Net Present Value ) and IRR ( Internal Rate of Return ) metrics help us decide whether to accept or reject investment proposals. The following figure illustrates graphically both methods in our current example. This graph is called NPV Profile which points out the curvilinear relationship between NPV for a project and the discount rate. At a discount rate of zero, the NPV is just the total cash inflows minus the total cash outflows of the project. Assuming the conventional projects where total cash inflows surpass total cash outflows, the highest NPV will occur when the discount rate is zero. As the discount rate increases, the NPV profile slopes downwards to the right. At the point where NPV profile curve cuts off the x-axis on the graph, the NPV of the project is zero and this is the rate which is called internal rate of return or IRR which is the discount rate at which NPV is zero. Any discount rate exceeding IRR will yield a negative NPV.
Any required rate of return less than internal rate of return will be acceptable when using either method. Say the discount rate was 11.8% as the vertical line touching the NPV profile suggests that at this rate the NPV will be $500. As long as NPV is greater than zero, we will opt to accept the project using the NPV method. And using the IRR we will still accept the project since IRR of 14.8% is greater than the discount rate of 11.8%. In a nutshell, both NPV and IRR give us similar answers to accepting or rejecting an investment proposal.
