1 Compute the IRR for Project X and note whether the firm sh

1.      Compute the IRR for Project X and note whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 9 percent.

Time:

0

1

2

3

4

5

Cash flow:

?1,000

?75

100

100

0

2,000

A.      9 PERCENT, ACCEPT

B.       9 PERCENT, REJECT

C.       16.61 PERCENT, ACCEPT

D.      16.61 PERCENT, REJECT

Solution

The Answer is “C. 16.61 PERCENT, ACCEPT”

Step – 1, Firstly calculate NPV at Say 16%

Net Present Value [NPV] = Present Value of Annual cash flows – Initial Investment

= [ (-$75 x 0.862068) + (100 x 0.743162) + (100 x 0.640657) + ( 0 x 0.552291) + (2,000 x 0.4761130) ] – $1,000

= $1,025 – 1,000

= $25

Step – 2, NPV at 16% is positive, Calculate the NPV again at a higher rate, Say 17%

= [ (-$75 x 0.854700) + (100 x 0.730513) + (100 x 0.624370) + ( 0 x 0.533650) + (2,000 x 0.456111) ] – $1,000

= $983 – 1,000

= - $17

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 16% + $25 (17% - 16%)

             $25 - ( - $17)

IRR = 16% + 0.61% = 16.61%

DECISION

“The Internal Rate of Return [IRR] of the Project is 16.61% which is greater than the required rate of return of 9%. Therefore, the project proposal should be accepted”