Question

A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,649.00 to install, $5,074.00 to operate per year for 7 years at which time it will be sold for $6,863.00. The second, RayCool 8, costs $41,963.00 to install, $2,147.00 to operate per year for 5 years at which time it will be sold for $8,950.00. The firm’s cost of capital is 6.41%. What is the equivalent annual cost of the AC360? Assume that there are no taxes.

Answer format: Currency: Round to: 2 decimal places.

Answer 1

Equivalent Annual Cost (EAC) of the AC360

Period	Annual Cash Flow ($)	Present Value factor at 6.41%	Present Value of Cash Flow ($)
1	-5,074	0.939761	-4,768.35
2	-5,074	0.883151	-4,481.11
3	-5,074	0.829951	-4,211.17
4	-5,074	0.779956	-3,957.50
5	-5,074	0.732973	-3,719.10
6	-5,074	0.688819	-3,495.07
7	1,789 [-5,074 + 6,863]	0.647326	1,158.07
TOTAL		5.501938	-23,474.24

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$23,474.24 - $26,649

= -$50,123.24 (Negative)

Equivalent Annual Cost (EAC) of the AC360

Equivalent Annual Cost (EAC) of the AC360 = Net Present Value / [PVIFA 6.41%, 7 Years]

= -$50,123.24 / 5.501938

= -$9,110.11 (Negative)

“Hence, the Equivalent Annual Cost (EAC) of the AC360 will be -$9,110.11 (Negative)”

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.