Question

A shipping company must update its propulsion plant’s exhaust emissions system, thus cutting in half the amount of polluting sulfur dioxide exhausting to the atmosphere. Costs and benefits are provided below. Determine the ROR of the “increment.”

	Alternative One	Alternative Two
First Cost ($)	-50,000	-100,000
Annual cost ($/year)	0	0
Salvage value ($)	6,000	28,000
Service life (years)	3	6

Answer 1

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

Incremental savings at EOY 3 = 50000 - 6000 = 44000

Incremental salvage at EOY 6 = 28000 - 6000 = 22000

Let incremental ROR be i%, then

44000*(P/F,i%,3) + 22000*(P/F,i%,6) = 50000

dividing by 1000

44*(P/F,i%,3) + 22*(P/F,i%,6) = 50

using trail and error method

When i = 7%, value of 44*(P/F,i%,3) + 22*(P/F,i%,6) = 44*0.816298 + 22*0.666342 = 50.576640

When i = 8%, value of 44*(P/F,i%,3) + 22*(P/F,i%,6) = 44*0.793832 + 22*0.630170 = 48.792339

using interpolation

i = 7% + (50.576640-50)/(50.576640-48.792339)*(8%-7%)

i = 7% + 0.32% = 7.32% ~ 7.3%