Question

The following 3 mutually exclusive projects are under consideration. Use Incremental IRR to determine which project should be undertaken if MARR = 18%.

year	Proj. A	Projc. B	Proj. C
0	$-500,000	$-350,000	$-700,000
1	$200,000	$100,000	$300,000
2	$200,000	$150,000	$300,000
3	$250,000	$200,000	$300,000
4	$250,000	$250,000	$300,000

Answer 1

Since the lowest investment is of project B, then incremental ROR analysis starts with project B and it first compares with project A.

So, incremental analysis between project A and B:

Incremental initial investment = -500000 + 350000 = -$150000

Incremental income in year 1 = 200000 - 100000 = $100000

Incremental income in year 2 = 200000 - 150000 = $50000

Incremental income in year 3 = 250000 - 200000 = $50000

Incremental income in year 4 = 250000 - 250000 = 0

So, if incremental ROR = R

Then,

150000 = 100000/(1+R) + 50000/(1+R)^2 + 50000/(1+R)^3

At R = 20%

PW of incremented cash inflows = 146990.7

At R = 18%

PW of incremented cash inflows = $151086.5

Using interpolation technique,

R = 18% + ((151086.5 - 150000)/(151086.5-146990.7))*(20% - 18%)

R = 18.5%

since incremental ROR of 18.5% is more than the MARR of 18%, then project A is selected and project B is rejected.

==

Now

incremental analysis between project A and C:

Incremental initial investment = -700000 + 500000 = -$200000

Incremental income in year 1 = 300000 - 200000 = $100000

Incremental income in year 2 = 300000 - 200000 = $100000

Incremental income in year 3 = 300000 - 250000 = $50000

Incremental income in year 4 = 300000 - 250000 = $50000

if incremental ROR = R

Then,

200000 = 100000/(1+R) + 100000/(1+R)^2 + 50000/(1+R)^3 + 50000/(1+R)^4

At R = 20%

PW of incremental cash inflows = $205825.6

At R = 22%

PW of incremental cash inflows = $199258.8

Using interpolation technique,

R = 20% + ((205825.6- 200000)/(205825.6 - 199258.8))*(22% - 20%)

R = 21.77%

Since incremental ROR is 21.77% is higher than the MARR of 18%, then project C is selected and project A is rejection.

Hence, it is the project C among all the three projects that will be selected on the basis of incremental ROR analysis.