Question

A city government is considering two types of town-dump sanitary systems. Design A requires an initial outlay of $260,000 with annual operating and maintenance costs of $48,000 for the next 17 years. Design B calls for an investment of $160,000 with annual operating and maintenance costs of $67,000 per year for the next 17 years. Fee collections from the residents for both designs would be $75,000 per year. The interest rate is 5%, and no salvage value is associated with either system. In order to determine which system should be selected, calculate the incremental profitability index.

Answer 1

ANSWER:

In order to find the incremental profitability index we will first find the incremental net present worth and so we will subtract the desigb b from design a because the initial cost of design a is more.

initial outlay (a-b) = -$260,000 - (-$160,000) = -$260,000 +$160,000 = -$100,000

aoc (a-b) = -$48,000 - (--67,000) = -48,000 + $67,000 = $19,000

since fees is similar for both designs , therefore we won't consider it in calculating npw as the time period is also same that is 17 years and the interest rate of 5% is similar.

npw (a - b) = initial outlay(a-b) + aoc(a-b) (p/a,i,n)

npw (a - b) = -100,000 +19,000(p/a,5%,17)

npw(a-b) = -100,000 + 19,000 * 11.274

npw(a-b) = -100,000 + 214,206

npw(a-b) = $114,206

profitability index = npw (a-b) / initial investment(a-b)

pi = 114,206 / (-260,000 - (-160,000)

pi = 114,206 / (-260,000 + 160,000)

pi = 114,206 / (-100,000)

pi = -1.14206

hence the incremental profitability index is -1.14206.