Question

Murray is planning a project that will cost $22,000. The annual cash inflow, net of income taxes, will be $5,000 a year for 7 years. The present value of $1 at 12% is as follows:

Period                                    Present Value of $1 at 12%

1                                                          .893

2                                                          .797

3                                                          .712

4                                                          .636

5                                                          .567

6                                                          .507

                        7                                                          .452

Using a rate of return of 12%, what is the present value of the cash flow generated by this project?

A. $34,180

B. $22,820

C. $35,000

D. $22,600

Answer 1

Solution:

The correct answer is Option (B). $22,820.

If the cash inflow, net of taxes, at the end of each of 7 years is $5,000, and if the discount
rate is 12%, the present value of this series of cash flows will be equal to the present value of
an ordinary annuity of $5,000 for 7 years at 12%. The interest factor for the present value of
an ordinary annuity is equal to the sum of the interest factors for the present value of $1 for
the same period.

The interest factor for an ordinary annuity of $5,000 for seven periods is 4.564.

The present value is $22,820 ($5,000 × 4.564).

The alternative is to calculate the present value of each $5,000 cash flow using the interest
factor for the present value of $1 at 12% for each of the periods one through seven. The sum
of these products is equal to the present value of an ordinary annuity of $5,000 for seven
periods at 12%.

$5,000 * 0.893 = $4,465
$5,000 * 0.797 = $3,985
$5,000 * 0.712 = $3,560
$5,000 * 0.636 = $3,180
$5,000 * 0.567 = $2,835
$5,000 * 0.507 = $2,535
$5,000 * 0.452 = $2,260

$5,000 * 4.564 = $22,820