A retail outlet is being designed in a strip mall in Nebraska. For this outlet, the installed fiberglass insulation to protect against heat loss in the winter and heat gain in the summer will cost an estimated $90,000. The annual savings in energy due to the insulation will be $16,000 at EOY one in the 7-year life of the outlet, and these savings will increase by 15% each year thereafter. If the annual interest rate is 18%, is the cost of the proposed amount of insulation justified?

What is the present equivalent of energy savings?

The present equivalent of energy savings is $88,000 and since the amount is less than the cost of insulation, the cost of insulation is not justified.

Explanation:

the cost of installation is $90,000. the life of insulation is 7 years.

the interest rate, r is 0.18.

the cash flow series of energy savings is a geometric cash flow series. where the first cash flow, A is $16,000 and the geometric gradient is 0.15

The present equivalent of energy savings is given by:

P = A[ (1 + (1+g) ^n (1+i) ^-n) / (i-g) ]

= (16000) [ (1 + (1+0.15) ^7 (1+0.18) ^-7) / (0.18-0.15) ]

= $88,000

Therefore, The present equivalent of energy savings is $88,000 and since the amount is less than the cost of insulation, the cost of insulation is not justified.