Question

A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,405.00 to install, $5,054.00 to operate per year for 7 years at which time it will be sold for $7,059.00. The second, RayCool 8, costs $41,142.00 to install, $2,019.00 to operate per year for 5 years at which time it will be sold for $8,951.00. The firm’s cost of capital is 5.81%. What is the equivalent annual cost of the RayCool8? Assume that there are no taxes.

Answer 1

Let us first find present value of salvage value of raycool 8

PV = FV/(1+r)^n

Here FV = 8951 , r = cost of capital = 5.81% , n = no of years = 5

PV = 8951/(1+5.81%)^5

=8951/(1+0.0581)^5

=8951/(1.0581)^5

=8951/1.326275

=6748.98$

Thus Equivalent annual cost of  RayCool8 = [(Initial cost - PV of salvage value)/PVIFA(r%,n)] + Annual operating cost

PVIFA(r%,n) = [1-(1/(1+r)^n / r ]

PVIFA(5.81%,5) = [1-(1/(1+5.81%)^5 / 5.81%]
=[1-(1/(1+0.0581)^5 / 0.0581]
=[1-(1/(1.0581)^5 / 0.0581]
=[1-0.75399 / 0.0581]
=0.24601/0.0581
=4.2342

Thus Equivalent annual cost of  RayCool8 [(41142-6748.85)/4.2342] + 2019

=34393.02/4.2342 +2019

=8122.62 + 2019

=10142.62 $