Question

Polytech Checmical, Inc. must decide between two additives to improve the dry-weather stability of its low-cost acrylic paint. Additive A will have an equipment and installation cost of $125,000 and an annual cost of $55,000. Additive B will have an installation cost of $175,000 and an annual cost of $35,000. If the company uses a 8 year recovery period for paint products and a MARR of 20% per year, calculate the incremental rate return.

Answer 1

incrermental cost (Additive B - Additive A) = 175000 - 125000 = 50000

incremental annual cost (Additive B - Additive A) = -35000 - (-55000) = 20000 (annual Savings)

Let incremental IRR be i%, then

20000 * (P/A,i%,8) = 50000

(P/A,i%,8) = 50000 / 20000 = 2.5

using trail and error method

When i = 35%, (P/A,i%,8) = 2.598165

When i = 36%, (P/A,i%,8) = 2.540429

When i = 37%, (P/A,i%,8) = 2.484915

using interpolation

i = 36% + (2.540429 - 2.5) / (2.540429 - 2.484915)*(37%-36%)

i = 36% + 0.7283%

i = 36.73%

As incremental IRR > MARR,  Additive B should be selected