Question

How to perform Present Worth comparisons when the useful lives of both products are NOT equal by using the least common multiple technique.

Also, include new example problem

Answer 1

In case of alternatives having unequal lives, we take the LCM (Least common multiple) of the life years of the project and then use it to find PW of each alternative for that time period and then compare them. For example we have two alternatives X and Y X: First cost $20,000 Annual cost $9000 Salvage value $4000 Life 3 years Y: First cost $30,000 Annual cost $7000 Salvage value $6000 Life 6 years LCM of 3 and 6 is 6 Now, we find oW of each alternative X and Y over a 6-year time period. PW (X) 20000 - 9000(P/A,10%,6) -(9000+7000) (P/F,10%,3) + 4000(P/F,10%,6) PW (X) -$68,961 PW (Y) -30000 7000(P/A,10%,6) + 6000(P/F,10%,6) PW (Y) -$57,100 Since PW of Y is more than X, one will prefer Alternative Y