Question

Consider the following alternatives:

	A	B	C
Initial Cost	$420	$780	$260
Uniform Annual Benefits	$59	$138	$49
Salvage Value	$120	$225	$75
Useful Life	10	10	10

Assume a MARR of 13%.

a) What is the IRR of Alternative A?

b) What is the IRR of Alternative B?

c) What is the IRR of Alternative C?

d) Of A, B, and C, only two meet or exceed the MARR. For those two, what is the DIRR between them?

e) Which Alternative should be selected?

Answer 1

	A	B	C
Initial Cost	$420	$780	$260
Uniform Annual Benefits	$59	$138	$49
Salvage Value	$120	$225	$75
Useful Life	10	10	10

a. IRR of Alternative A

MARR = 13%

Using the trial and error method

Calculating PW at 13%

PW = -420 + 59 (P/A, 13%, 10) + 120 (P/F, 13%, 10)

PW = -420 + 59 (5.4262) + 120 (0.2946) = -65

As the NPW is negative decrease MARR to 9% to get positive NPW

NPW at 9% = -420 + 59 (P/A, 9%, 10) + 120 (P/F, 9%, 10)

NPW at 9% = -420 + 59 (6.4177) + 120 (0.4224) = 9

Using interpolation, IRR = 9% + [9 – 0 ÷ 9 – (-65)]*4% = 9.4%

b. IRR of Alternative B?

Using the trial and error method

Calculating PW at 13%

PW = -780 + 138 (P/A, 13%, 10) + 225 (P/F, 13%, 10)

PW = -780 + 138 (5.4262) + 225 (0.2946) = 35

As the NPW is positive increase MARR to 15% to get negative NPW

PW = -780 + 138 (P/A, 15%, 10) + 225 (P/F, 15%, 10)

PW = -780 + 138 (5.0188) + 225 (0.2472) = -32

Using interpolation, IRR = 13% + [35 – 0 ÷ 35 – (-32)]*2% = 14%

c. IRR of Alternative C?

Using the trial and error method

Calculating PW at 13%

PW = -260 + 49 (P/A, 13%, 10) + 75 (P/F, 13%, 10)

PW = -260 + 49 (5.4262) + 75 (0.2946) = 28

As the NPW is positive increase MARR to 16% to get negative NPW

PW = -780 + 138 (P/A, 16%, 10) + 225 (P/F, 16%, 10)

PW = -780 + 138 (4.8332) + 225 (0.2267) = -6

Using interpolation, IRR = 13% + [28 – 0 ÷ 28 – (-6)]*3% = 15.4%

	A	B	C
Initial Cost	$420	$780	$260
Uniform Annual Benefits	$59	$138	$49
Salvage Value	$120	$225	$75
Useful Life	10	10	10
IRR	9.4%	14%	15.4%

d. From the above calculation it can be seen that only Alternative B and C can be compared to calculate the incremental IRR because their IRR is greater than MARR. The Alternative A has an IRR that is less than MARR, so it cannot be accepted.

	B	C	ICF of B - C
Initial Cost	-$780	-$260	-520
Uniform Annual Benefits	$138	$49	89
Salvage Value	$225	$75	150

Calculating PW of ICF of B – C at 13%

PW = -520 + 89 (P/A, 13%, 10) + 150 (P/F, 13%, 10)

PW = -520 + 89 (5.4262) + 150 (0.2946) = 7

As the NPW is positive increase MARR to 14% to get negative NPW

PW = -520 + 89 (P/A, 14%, 10) + 150 (P/F, 14%, 10)

PW = -520 + 89 (5.2161) + 150 (0.2697) = -15

Using interpolation, IRR of ICF of B – C = 13% + [7 – 0 ÷ 7 – (-15)]*1% = 13.3%

e. IRR of B – C is greater than MARR (13%) so select Alternative B.