The heat loss through the exterior walls of a certain poultr

The heat loss through the exterior walls of a certain poultry processing plant is estimated to cost the owner $3,500 next year. A salesman from Superfiber Insulation, Inc., has told you, the plant engineer, that he can reduce the heat loss by 80% with the installation of $22,000 worth of Superfiber now. If the cost of heat loss rises by $200 per year (uniform gradient) after the next year and the owner plans to keep the present building for 15 more years, what would you recommend if the interest rate is 8% per year?

Solution

The installation will reduce heat loss by 80% so we now pay only 20% of the cost after installation.

With no installation, the annual equivalent cost will be

AEC1 = 3500 + 200*(A/G, 8%, 15) = 3500 + 200*5.594 = $4618.90.

With installation the annual equivalent cost turns out to be

AEC2 = 22000(A/P, 8%, 15) + 3500*(20%) + 200*(20%)*(A/G, 8%, 15)

= 22000*0.11683 + 700 + 40*5.594 = $3494.

Since ACE2 > AEC1, we would install the equipment.