Question

1. Consider the following three alternatives. Using incremental IRR analysis, determine which of these projects is the most desirable. Your MARR is 11%. Each of these projects (A&B) will last for eight years. (2 points)

	Do nothing	A	B
Capital investment	$0	$100	$130
Annual revenues	$0	$150	$130.78
Annual costs	$0	$123.62	$92

Answer 1

Incremental analysis between A & DN

incremental initial cost (A-DN) = 100 - 0 = 100

incremental annual revenue (A-DN) = 150 - 0 = 150

incremental annual cost (A-DN) = 123.62 - 0 = 123.62

Let i% be the IRR, then

-100 + (150-123.62) * (P/A,i%,8) = 0

(150-123.62) * (P/A,i%,8) = 100

(P/A,i%,8) = 100 / 26.38 = 3.790750

using trail and error method

When i = 20%, value of (P/A,i%,8) = 3.837160

When i = 21%, value of (P/A,i%,8) = 3.725576

using interpolation

i = 20% + (3.837160 - 3.790750) / (3.837160 - 3.725576)*(21%-20%)

i = 20% + 0.41% = 20.41%

As incremental IRR > MARR, option A should be selected

Incremental analysis between B & A

incremental initial cost (B-A) = 130 - 100 = 100

incremental annual revenue (B-A) = 130.78 - 150 = -19.22

incremental annual cost (B-A) = 92 - 123.62 = -31.62

Let i% be the IRR, then

-30 + (-19.22+31.62) * (P/A,i%,8) = 0

12.4 * (P/A,i%,8) = 30

(P/A,i%,8) = 30 / 12.4 = 2.419354

using trail and error method

When i = 38%, value of (P/A,i%,8) = 2.431508

When i = 39%, value of (P/A,i%,8) = 2.380103

using interpolation

i = 38% + (2.431508 - 2.419354) / (2.431508- 2.380103)*(39%-38%)

i = 38% + 0.23% = 38.23%

As incremental IRR > MARR, option B should be selected

Finally option B should be selected