Question

The government of a particular city is considering two mutually exclusive water purification systems for implementation. Doing nothing is not an option. Refer to the data below to determine which system should be selected, when MARR = 9% per year, and

1. Use the AW method
2. Use rate of return method

Please Solve number b only !! Use rate of return method

Alternative	System 1	System 2
Capital Investment	$100,000	$150,000
Annual revenues	$50,000	$70,000
Annual expenses	$22,000	$40,000
Market value at end of useful life	$20,000	$20,000
Useful life (years)	5	10
IRR	16.5%	15.1%

Answer 1

As only option B has been asked, below is incremental ROR analysis

System 1 will be reinvested at EOY 5

incremental initial cost (System 2 - System 1) = 150000 - 100000 = 50000

incremental annual revenue (System 2 - System 1) = 70000 - 50000 = 20000

incremental annual cost (System 2 - System 1) = 40000 - 22000 = 18000

incremental salvage value (System 2 - System 1) = 20000 - 20000 = 0

Incremental Savings at EOY 5 (System 2 - System 1) = 0 - (-100000 + 20000) = 80000

Let incremental IRR be i%, then

(20000 - 18000)*(P/A,i%,10) + 80000* (P/F,i%,5) = 50000

dividing by 1000

2*(P/A,i%,10) + 80* (P/F,i%,5) = 50

using trail and error method

When i = 14%, value of 2*(P/A,i%,10) + 80* (P/F,i%,5) = 2*5.216116 + 80* 0.519369 = 51.981724

When i = 15%, value of 2*(P/A,i%,10) + 80* (P/F,i%,5) = 2*5.018769 + 80* 0.497177 = 49.811676

using interpolation

i = 14% + (51.981724-50) /(51.981724-49.811676)*(15%-14%)

i = 14% + 0.91% ~ 14.91% (Approx)

As Incremental IRR > MARR, system 2 should be selected