Question

Assume the cost of purchasing an exhaust filter for a certain factory is $6,000 and the filter needs to be replaced every three years. If the estimated benefit to society from the use of the filter is $3,000 for the first year and $1,900 for the next two years and the interest rate is 6%, then should we proceed with purchase of the filter? What if the market interest rate rises to 9%?

Answer 1

The present values of the benefits of the filter will be (3000/1+.06)+(1900/(1+.06)²)+(1900/(1+.06)³)

Solving this will give the present value as $6,116.38. Since the present value of the benefits of using the filter is greater than the cost of installing it, so the factory should purchase one.

If interest rate changes to 9%. So in the above equation, .06 will be changed to .09. Solving again with 9% interest rate will give the prsent values of teh benefits equal to (3000/1+.09)+(1900/(1+.09)²)+(1900/(1+.09)³) or $5,185.5. Since this is smaller than $6000, so at interest rate 9%, the owner should not buy the filter.