Week 8 NPV Method
Net Present Value (NPV) Method
This method calls for calculating the present value of all a project's expected future cash flows, adding them up, and subtracting the initial required cash outflow. If the result is positive or zero, the project is acceptable. If the result is negative, the project is unacceptable.
The NPV Formula:
NPV = the Sum of the Present Values of all the cash flows in the problem that will occur in the future minus the cash flow that occurs initially at time-zero. In other words:
| PV of cash flow at T - 1 | ||
| + | PV of cash flow at T - 2 | |
| + | PV of cash flow at T - 3 | |
| .... | ||
| + | PV of cash flow atT - n | |
| - | initial cost | |
| ___________________ | ||
| = | NPV of project | |
NPV is frequently used in business finance to evaluate alternatives, and Academicians consider the NPV method the most theoretically correct of all the capital budgeting decision making techniques because it will always give you the decision which maximizes the value of the firm.
We will spare you the economic explanation, but the important thing to remember is that the NPV is the amount by which the proposed investment will increase the value of the firm if the project is adopted. (If the NPV is negative it will decrease the value of the firm and therefore should be rejected.)
Important Note: This is an extremely important point because, as you will recall from your studies in week 1 of the course, the objective of business managers is to maximize the value of the firm. Since the NPV method produces the amount that will be added to or taken away from the value of the firm if the project is adopted it is the ideal tool for evaluating proposed investments.
An NPV Calculation Example
Let’s assume that Amalgamated Hat Rack is using the NPV method to evaluate the plastic extruder project. Amalgamated’s required rate of return for investments of this sort is 10%. Given that 10% required rate of return and the plastic extruder’s forecasted cash flows, here is the NPV analysis (in $000s):
| Year | Future Cash Flow |
PV of future cash flow * |
|||
| 1 | $18 | $18 / (1 + .10)1 | = | $16.364 | |
| 2 | $18 | $18 / (1 + .10)2 | = | $14.876 | |
| 3 | $18 | $18 / (1 + .10)3 | = | $13.524 | |
| 4 | $18 | $18 / (1 + .10)4 | = | $12.294 | |
| 5 | $18 | $18 / (1 + .10)5 | = | $11.177 | |
| 6 | $18 | $18 / (1 + .10)6 | = | $10.161 | |
| 7 | $18 | $18 / (1 + .10)7 | = | $ 9.237 | |
| Total PV of future cash flows | = | $87.632 | |||
| Minus initial investment | -$100,000 | ||||
| NPV | -$12.638 | ||||
*Using the PV of a lump sum formula,
which is the same as PV = FV/(1+r)n
Since the NPV is negative, the project is rejected. If it was adopted it would decrease the value of the firm by $12,638.
Important Note: Observe that the NPV analysis is dependent on the required rate of return. If the required rate of return were higher, the NPV would be lower and vice versa. In this example the required rate of return was 10%, but if it had been under about 6% then the NPV would turn positive and the project would be acceptable. This illustrates why lower interest rates are good for business and higher interest rates are bad for business. When interest rates are lower firms can accept more projects thus stimulating the economy with their increased activity. When interest rates rise, projects are squeezed out and the activity of firms slows down.
Problems with the NPV Method:
- The NPV is tough to explain (try it yourself--pick somebody out and try to explain it to them)
- The NPV results in a dollar figure rather than a percent figure (the dollar figure is not as intuitively appealing as, say, a percent rate). Therefore, despite the fact that the NPV method is theoretically the most superior evaluation tool, many people instinctively prefer the Internal Rate of Return (IRR) method that follows.