Question

A new computer system will require an initial outlay of $24,500, but it will increase the firm's cash flows by $4,900 a year for each of the next 8 years. Calculate the NPV and decide if the system is worth installing if the required rate of return is 9%. Calculate the NPV and decide if the system is worth installing if the required rate of return is 14%. How high can the discount rate be before you would reject the project?

Answer 1

Installation of New Computer System

Initial outlay $24,500

Increase in cashflow $4900 for 8 yrs

a) Computation of NPV taking required rate as 9%

PV of cash inflows

Year Cash Flows PVIF (9%) PV

1 $4,900 0.917 $4,495

2 $4,900 0.842 $4,124

3 $4,900 0.772 $3,784

4 $4,900 0.708 $3,471

5 $4,900 0.650 $3,185

6 $4,900 0.596 $2,922

7 $4,900 0.547 $2,680

8 $4,900 0.502 $2,459

5.535 $27,121

NPV = PV of cash inflows - Initial investment

$(27,121 - 24,500) $2,621

Since the NPV is positive, the system is worth installing

when required rate of return is 9%

b) Computation of NPV taking required rate as 14%

PV of cash inflows

Year Cash Flows PVIF (14%) PV

1 $4,900 0.877 $4,298

2 $4,900 0.769 $3,770

3 $4,900 0.675 $3,307

4 $4,900 0.592 $2,901

5 $4,900 0.519 $2,545

6 $4,900 0.456 $2,232

7 $4,900 0.400 $1,958

8 $4,900 0.351 $1,718

4.639 $22,730

NPV = PV of cash inflows - Initial investment

$(22,730 - 24,500) ($1,770)

Since the NPV is negative, the system is not worth installing

when required rate of return is 14%

c) The discount rate can maximum go upto 11.815% post which the NPV would be

negative hence the project would be rejected

Here, I have used trial error method which means plugging in random rate as IRR

IRR is the interest rate at which the NPV of all the cash flows from a project equal zero

I have used random rates between 10% and 14% which results in PVIF equal to Cash outflow

PV of cash inflows

Year Cash Flows PVIF (11.815%) PV

1 . $4,900 0.894 $4,382

2 $4,900 0.800 $3,919

3 $4,900 0.715 $3,505

4 $4,900 0.640 $3,135

5 . $4,900 0.572 $2,803

6 $4,900 0.512 $2,507

7 $4,900 0.458 $2,242

8 $4,900 0.409 $2,005

5.000 $24,500

NPV = PV of cash inflows - Initial investment

$(24,500 - 24,500) $0