Question

The heat loss through the exterior walls of a certain poultry processing plant is estimated to cost the owner ​$2,800 next year. A salesman from Superfiber​ Insulation, Inc., has told​ you, the plant​ engineer, that he can reduce the heat loss by 85​% with the installation of​$16,500 worth of Superfiber now. If the cost of heat loss rises by ​$170 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 12​% per​ year?

Answer 1

Year	Cost ($)	Loss reduction ($)
1	2800	2380
2	2970	2524.5
3	3140	2669
4	3310	2813.5
5	3480	2958
6	3650	3102.5
7	3820	3247
8	3990	3391.5
9	4160	3536
10	4330	3680.5
11	4500	3825
12	4670	3969.5
13	4840	4114
14	5010	4258.5
15	5180	4403

Loss reduction = 0.85 x Cost

Cost of the machine = $16500

interest rate = 12% , time period = 15 years

PW = -16500 + 2380/(1 + 12%) +  2524.5/(1 + 12%)² + ... +  4403/(1 + 12%)¹⁵

PW = $4611.32

Since, PW is positive, the machine should be installed.