Present Value of Cash Flows Calculator

Present Value of Cash Flows Calculator

Unlike an annuity, in some cases future cash flows vary in size. In this post, we demonstrate a few common-sense methods for computing the value of a set of unequal future cash flows and use the present value of cash flows calculator. We'll describe three of these methods through the use of the following example.

Example

Computing the Present Value of a Set of Unequal Future Cash Flows

Suppose you expect to receive the following cash flows at the times indicated:

Time                 0                    1                    2                    3

Cash flow      $3000          $2000            $8000          $5000         

If the required return is 10%, what is the total present value of these cash flows?

The total present value of these cash flows can be calculated by calculating the present value of each cash flow and then adding them together:

                                          PV = 3000+1818.182+6611.570+3756.574= $15,186.326

This calculation is illustrated in figure 1

An alternative method for calculating the total present value of our set of unequal future cash flows is called the "rollback" method: Start with the most distant cash flow ($5000 at time 3) and discount it back one period (at 10%). Its value at t = 2 is $4545.45 (=5000/1.10). And this amount to the time 2 cash flow of $8000 to get $12,545.45. Discount this amount back one period. Its value at t = 1 is $11,404.96(= 12,545.45/1.10). And the time 1 cash flow to this amount to get $13,404.96. Discount this amount back one period. Its value is $12,186.33 (= 13,404.96/1.10). Finally, this amount plus the $3000 time 0 cash flow equals the total present value of $15,186.33. Figure 2 illustrates the rollback method of calculating a present value.

Finally, many financial calculators provide a third method for valuing this unequal set of future cash flows. Because calculators are not identical, you'll have to use your own calculator's manual to learn how to use this method. There is an important advantage to using this calculator feature: If you already know the present value, but don't know the discount rate, the calculator can automatically compute the expected return for the set of unequal cash flows. This can eliminate the hassle of very tedious trial-and-error calculations.

Valuing Cash Flows at Other Points Along the Time Line

Thus far, we've calculated a present value (t=0) or a future value at t=n. But suppose we want to know the total value of a set of cash flows at some other point in time. Calculating such a value directly may require extra care, but it uses the same formulas. If you already know the present or future value, calculating such values is quite straightforward. Our next example illustrates this process by building on our last example.

Figure 1

Computing the present value of a set of unequal future cash flows.

Figure 2

The rollback method for calculating a present value.