Question

Compute the future worth of alternative P shown below, using an interest rate of 8% per year using LCM method

	P	Q
First cost, $	-23,000	-30,000
Annual operating cost, $ per year	-4,000	-2,500
Salvage value, $	3,000	1,000
Life, years	3	6

Answer 1

Compute the future worth of alternative P shown below, using an interest rate of 8% per year using LCM method

	P	Q
First cost, $	-23,000	-30,000
Annual operating cost, $ per year	-4,000	-2,500
Salvage value, $	3,000	1,000
Life, years	3	6

The life of the alternatives given is different. Hence convert the unequal life into equal life using the LCM method. The LCM of 3 years of P and 6 years of Q is 6 years. Therefore, the common life now is equal to 6 years. Alternative P has 6 years. So it is to be repeated 2 times to equal to the LCM.

As per the question, calculating the Future worth of Alternative P only

FW = -23,000 (F/P, 8%, 6) – 23,000 (F/P, 8%, 3) – 4,000 (F/A, 8%, 6) + 3,000 (F/P, 8%, 3) + 3,000

FW = -23,000 (1.5869) – 23,000 (1.2597) – 4,000 (7.3359) + 3,000 (1.2597) + 3,000

FW = -88,036