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The Chem-Tex Chemical company is considering two additives for improving the dry-weather stability of its low-cost acrylic paint. Additive A will have a first cost of $110,000 and an annual operating cost of $60,000. Additive B will have a first cost of $175,000 and an annual operating cost of $35,000. If the company uses a three-year recovery period for paint products and a MARR of 20% per year, which process is favored on the basis of an incremental rate of return analysis?

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Answer:

The preferred process is that with lower cost which is Additive A with a PV cost of   $236,388.89  

Explanation:

To determine the preferred process , we compare the present value of the two alternatives and select the lower of the two two cost.

This will be done as follows

Alternative one

Total PV = First payment + PV of annual operating cost

PV of Annuity =A × (1-(1+r)^(-n)/r

A- annual operating cost, r- 20%, n=3

PV of operating cost

= 60,000  × (1- 1.2^(-3))/0.2

=  $126,388.89

Total PV = $110,000 + $126,388.89

            =    $236,388.89  

Alternative Two

PV of operating cost

=    35,000 × (1-1.2^(-3))/0.2

=   73,726.85

Total PV = $175,000 + $73,726.85

               = $248,726.85

The preferred process is that with lower cost which is Additive A with a PV cost of  $236,388.89  

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