Question

Consider two investments with the following sequences of cash flows:

n Project A Project B
0 -$167,000 -$158,500
1 $38,500 $90,300
2 $47,400 $47,500
3 $59,300    $16,000
    4 $29,900     $20,300
5 $57,300     $26,500

a) Compute the IRR for each investment.
b) At MARR = 9%, consider the acceptability of each project.
c) If A and B are mutually exclusive projects, which project would you select on the basis of the rate of return on incremental investment?

Answer 1

n	Project A	Project B
0	-167000	-158500
1	38500	90300
2	47400	47500
3	59300	16000
4	29900	20300
5	57300	26500

MARR = 9%, Life = 5 year

a. Calculating the IRR of individual projects using the trial and error method.

Project A

Let the rate of interest is 10%

Calculate PW at 10%

PW = -167,000 + 38500 (1+0.10) ^{– 1} + 47400 (1+0.10) ^{– 2} + 59300 (1+0.10) ^{– 3} + 29900 (1+0.10) ^{– 4} + 57300 (1+0.10) ^{– 5}

PW = 7,727

PW is positive. So increase the rate of interest to 12% and calculate PW

PW = -167,000 + 38500 (1+0.12) ^{– 1} + 47400 (1+0.12) ^{– 2} + 59300 (1+0.12) ^{– 3} + 29900 (1+0.12) ^{– 4} + 57300 (1+0.12) ^{– 5}

PW = -1,114

Using interpolation

IRR = 10% + [7,727 – 0 ÷ 7,727 – (-1,114)]*2% = 11.74%

Project B

Let the rate of interest is 10%

Calculate PW at 10%

PW = -158500 + 90300 (1+0.10) ^{– 1} + 47500 (1+0.10) ^{– 2} + 16000 (1+0.10) ^{– 3} + 20300 (1+0.10) ^{– 4} + 26500 (1+0.10) ^{– 5}

PW = 5,188

PW is positive. So increase the rate of interest to 12% and calculate PW

PW = -158500 + 90300 (1+0.12) ^{– 1} + 47500 (1+0.12) ^{– 2} + 16000 (1+0.12) ^{– 3} + 20300 (1+0.12) ^{– 4} + 26500 (1+0.12) ^{– 5}

PW = -682

Using interpolation

IRR = 10% + [5,188 – 0 ÷ 5,188 – (-682)]*2% = 11.76%

b. At MARR of 9%, both the projects are good as the IRR of both is more than the MARR. However, the Project B is marginally a better project as it has more IRR than project A.

c) If A and B are mutually exclusive projects, which project would you select on the basis of the rate of return on incremental investment?

n	Project A	Project B	ICF between A - B
0	-167000	-158500	-8500
1	38500	90300	-51800
2	47400	47500	-100
3	59300	16000	43300
4	29900	20300	9600
5	57300	26500	30800

Calculating the IRR of incremental cash flow between A – B using trial and error method

Let the rate of interest is 10%

Calculate PW at 10%

PW = -8500 -51800 (1+0.10) ^{– 1} -100 (1+0.10) ^{– 2} + 43300 (1+0.10) ^{– 3} + 9600 (1+0.10) ^{– 4} + 30800 (1+0.10) ^{– 5}

PW = 2,540

PW is positive. So increase the rate of interest to 12% and calculate PW

PW = -8500 -51800 (1+0.12) ^{– 1} -100 (1+0.12) ^{– 2} + 43300 (1+0.12) ^{– 3} + 9600 (1+0.12) ^{– 4} + 30800 (1+0.12) ^{– 5}

PW = -432

Using interpolation

IRR = 10% + [2,540 – 0 ÷ 2,540 – (-432)]*2% = 11.70%

On the basis of incremental cash flow

IRR of ICF of A – B is greater than MARR – Select A