Question

1. Consider the investment projects given in the table below.
		Net Cash Flow of Project
	Year	A	B	C
	0	($1,500)	($5,000)	($2,200)
	1	$700	$3,000	$1,600
	2	$2,500	$4,500	$2,600
a. Compute the IRR for each project.
b. On the basis of IRR criteria, if all three projects are mutually exclusive
investments, which project should be selected at 15% MARR?
c. Create a set of decision statements for varying MARR from 0% to 60%.
(Do not provide statements if the result will be a loss

Answer 1

a) r = IRR

For A

initial investment = 1500

CF 1 = 700

CF 2 = 2500

Assume NPV = 0

NPV = [ CF1 / (1+r) ] + [ (CF2 / (1+r)²] - initial investment

0 =[ 700/ (1+r) ] + [ 2500 / (1+r)² ] - 1500

Multiply with (1+r)² on both sides

1500 (1+r)² = 700 (1+r) + 2500

15 (1+2r + r²) = 7 + 7r + 25

15 r² + 23r - 17 = 0

r = 0.545

IRR = 54.5%

For B

initial investment = 5000

CF 1 = 3000

CF 2 = 4500

Assume NPV = 0

NPV = [ CF1 / (1+r) ] + [ (CF2 / (1+r)²] - initial investment

0 =[ 3000/ (1+r) ] + [ 4500 / (1+r)² ] - 5000

Multiply with (1+r)² on both sides

5000 (1+r)² = 3000 (1+r) + 4500

50 (1+2r + r²) = 30 + 30r + 45

50 r² + 70r - 25 = 0

r = 0.295

IRR = 29.5%

For C

initial investment =2200

CF 1 = 1600

CF 2 = 2600

Assume NPV = 0

NPV = [ CF1 / (1+r) ] + [ (CF2 / (1+r)²] - initial investment

0 =[ 1600/ (1+r) ] + [ 2600 / (1+r)² ] - 2200

Multiply with (1+r)² on both sides

2200 (1+r)² = 1600 (1+r) + 2600

22 (1+2r + r²) = 16 + 16r + 26

22 r² + 28r - 20= 0

r = 0.5096

IRR = 50.96%

b) IF the IRR > or = MARR

than the project should be selected

All the should projects should be selected as their IRR value greater than MAR value of 15%