Question

A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,194.00 to install, $5,090.00 to operate per year for 7 years at which time it will be sold for $6,925.00. The second, RayCool 8, costs $41,661.00 to install, $2,079.00 to operate per year for 5 years at which time it will be sold for $9,068.00. The firm’s cost of capital is 5.54%. What is the equivalent annual cost of the AC360? Assume that there are no taxes.

Answer 1

AC360

+ve: cash-out flow (cost)

-ve: cash-in flow (sale)

Year 0 cash flow = 26194 (purchase)

Year 1-7 cash flow = 5090 (operating cost)

Year 7 additional cash flow = -6925 (AC sold)

NPV = 26194 + 5090/(1+5.54%)^1 + 5090/(1+5.54%)^2+...+ 5090/(1+5.54%)^7 - 6925/(1+5.54%)^7

NPV = 26194 + (5090/5.54%)*(1-1/(1+5.54%)^7) - 6925/(1+5.54%)^7

NPV = $50330.94

Annuity factor = (1/5.54%)*(1-1/(1+5.54%)^7) = 5.6748

Equivalent annual cost = NPV/annuity factor = $50330.94/5.6748 = $8869.17