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

LCM method means least common multiple i.e when the project alternative has different life periods then we use least common multiple method. Here LCM is 6. So alternative P will be repeatedly use 1 time. There will be two times first cost. One is at period 0 and another is at the end of 3rd year or at the beginning of 4th year. At the end of 3rd year there is salvage value of 3000 and first cost is -23000. So net cash flow at the end of 3rd year and begining of 4th year is -20,000.

Future worth of alternative P = -23000(F/P, 8%,6) -4000(F/A, 8%,6) - 23000+3000(F/P, 8%, 3) +3000 = -23000(F/P, 8%, 6)-4000(F/A,8%,6) -20000(F/P,8%,3) +3000 = -23000(1.08)^6 -4000[{(1.08)^6 -1}/0.08}] -20000(1.08)^3 +3000 = -23000*1.5868 -4000*7.3359 -20000*1.2597+3000 = - 88,034. As cash flow is negative i.e why there is negative sign before this future worth. So future worth will be 88,034.( Ans).

Extra:- Future worth of alternative Q = -30,000(F/P,8%,6) -2500(F/A,8%,6) +1000 = -30,000(1.08)^6 - 2500*[{(1.08)^6 -1}/0.08] +1000 = -30,000*1.5868 -2500*7.3359 +1000 = -64,943.75 = -64,944(approx). So future worth is 64,944.

As Future worth is less for alternative Q because Q has less amount of negative cash flow. So alternative Q is best.