Question

Consider two mutually exclusive investment projects, each with MARR = 8% as shown in figure

A.On the basis of the IRR criterion, which alternative would be selected?

B. Determine the discounted payback period for each project.

Project's Cash Flow
n	A	B
0	-$20,000	-$25,000
1	$6,000	$10,000
2	$2,000	$3,000
3	$11,000	$8,000
4	$4,000	$2,000
5	$5,000
6	$11,000
7	$2,000

Answer 1

Using IRR Criterion,

Let the IRR for Project A be a

So 0 = -20000 + 6000 / (1+a/100)^1 + 2000 / (1+a/100)^2 + 11000 / (1+a/100)^3 + 4000 / (1+a/100)^4 + 5000 / (1+a/100)^5 + 11000 / (1+a/100)^6 + 2000 / (1+a/100)^7

Solving for a, we get a = 21.65%

Let the IRR for Project B b b

so 0 = -25000 + 10000 / (1+b/100)^1 + 3000 / (1+b/100)^2 + 8000 / (1+b/100)^3 + 2000 / (1+b/100)^4

Solving for b, we get b = -3.88%

Since negative IRR cannot be considered as it means the project will never give a NPV od 0, so project 1 has to be selected.

b) Using MARR of 8%,

the Present Value of the Project A is

Period	Cashflow	PV at 8%
0	-20000	-20000
1	6000	5555.556
2	2000	1714.678
3	11000	8732.155
4	4000	2940.119
5	5000	3402.916
6	11000	6931.866
7	2000	1166.981

Value remaining at end of 4th year = -20000 + 5555.56 + 1714.68 + 8732.15 + 2940.12 = -1057.49

If we consider that 3402.92 is spread uniformly over the next year, so 1057.49 will be recovered in

-1057.49 / 3402.92 years = 0.31 years.

So the payback period is 4.31 years.

For Project B, the total earnings in actual dollars is less than the initial cost. So it will not have a payback period ever.

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