Now let’s suppose you have to choose which one of three projects to undertake. Project A gives you an immediate payoff of $100. Project B costs you $10 now and pays $115 a year from now. Project C gives you an immediate payoff of $119 but requires you to pay $20 a year from now. We will assume that r = 0.10.
In order to compare these three projects, you must evaluate costs and revenues that are expended or realized at different times. It is here, of course, that the concept of present value is extremely handy: by using present value to convert any dollars realized in the future into today’s value, you can factor out differences in time. Once differences in time are factored out, you can compare the three projects by calculating each one’s net present value, the present value of current and future revenues minus the present value of current and future costs. The best project to undertake is the one with the highest net present value.
Table 9A-1 shows how to calculate the net present value of each of the three projects. The second and third columns show how many dollars are realized and when they are realized; costs are indicated by a minus sign. The fourth column shows the equations used to convert the flows of dollars into their present value, and the fifth column shows the actual amounts of the total net present value for each of the three projects.
|
Project |
Dollars realized today |
Dollars realized one year from today |
Present value formula |
Net present value given r = 0.10 |
|---|---|---|---|---|
|
A |
$100 |
— |
$100 |
$100.00 |
|
B |
−$10 |
$115 |
−$10 + $115/(1 + r) |
$94.55 |
|
C |
$119 |
−$20 |
$119 − $20/(1 + r) |
$100.82 |
TABLE 9A-
For instance, to calculate the net present value of project B, you need to calculate the present value of $115 received one year from now. The present value of $1 received one year from now is $1/(1 + r). So the present value of $115 received one year from now is 115 × $1/(1 + r) = $115/(1 + r). The net present value of project B is the present value of current and future revenues minus the present value of current and future costs: −$10 + $115/(1 + r).
From the fifth column, we can immediately see that, at an interest rate of 10%, project C is the best project. It has the highest net present value, $100.82, which is higher than the net present value of project A ($100) and much higher than the net present value of project B ($94.55).
This example shows how important the concept of present value is. If we had failed to use the present value calculations and had instead simply added up the revenues and costs, we would have been misled into believing that project B was the best project and C was the worst one.