Question

A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,454.00 to install, $5,152.00 to operate per year for 7 years at which time it will be sold for $7,182.00. The second, RayCool 8, costs $41,990.00 to install, $2,150.00 to operate per year for 5 years at which time it will be sold for $9,054.00. The firm’s cost of capital is 6.22%. What is the equivalent annual cost of the RayCool8? Assume that there are no taxes.

Can you show me how you solved even if it was done in excel. Thanks!

Answer 1

Solution :- Present value of operating cost incurred every year = Future value * [ 1 - (1 + r)-T ] / r.

= 2150 * [ 1 - (1 + 0.0622)-5 ] / 0.0622 [ r = Rate of interest i.e., 6.22 % or 0.0622, T = Time period i.e., 5 years ]

= 2150 * [ 1 - (1.0622)-5 ] / 0.0622

= 2150 * (1 - 0.73955) / 0.0622

= 2150 * 0.26045 / 0.0622

= 2150 * 4.1873 (This 4.1873 is cumulative present value factors for five year at 6.22 % interest rate)

= $ 9002.695

Present value of salvage value = Future salvage value / (1 + r)T

= 9054 / (1 + 0.0622)5

= 9054 / (1.0622)5

= 9054 / 1.35217

= $ 6695.90

Equivalent annual cost of RayCool8 unit = (Initial installation cost + Present value of operating cost incurred per year - Present value of salvage value) / Cumulative present value factors for five year at 6.22 % interest.

= (41990 + 9002.695 - 6695.90) / 4.1873

= 44296.795 / 4.1873

= $ 10578.84 (Rounded off to $ 10579).

Conclusion :- Equivalent annual cost of RayCool8 unit = $ 10579. (approx).