To find the equivalent annual cost (EAC) of the AC360, we need to calculate the total present value of all costs associated with the unit and then convert it into an equivalent annual cost over the 7-year period.
Given data:
Cost of installing AC360 (C1) = $26,762.00
Annual operating cost of AC360 (C2) = $5,169.00
Number of years (n) = 7
Resale value of AC360 after 7 years (R) = $6,993.00
Cost of capital (discount rate) = 6.345%
Step 1: Calculate the present value (PV) of all costs associated with the AC360.
PV(C1) = C1 / (1 + r)^1
PV(C1) = $26,762.00 / (1 + 0.06345)^1
PV(C1) = $26,762.00 / 1.06345
PV(C1) ≈ $25,149.78
PV(C2) = C2 / (1 + r)^1 + C2 / (1 + r)^2 + ... + C2 / (1 + r)^n
PV(C2) = $5,169.00 / (1 + 0.06345)^1 + $5,169.00 / (1 + 0.06345)^2 + ... + $5,169.00 / (1 + 0.06345)^7
Now, we calculate the sum using the formula for the present value of an annuity:
PV(C2) = $5,169.00 * [(1 - (1 + 0.06345)^(-n)) / 0.06345]
PV(C2) = $5,169.00 * [(1 - (1.06345)^(-7)) / 0.06345]
PV(C2) ≈ $31,539.85
PV(R) = R / (1 + r)^n
PV(R) = $6,993.00 / (1 + 0.06345)^7
PV(R) = $6,993.00 / 1.48647
PV(R) ≈ $4,711.40
Step 2: Calculate the total present value of all costs (TPV).
TPV = PV(C1) + PV(C2) - PV(R)
TPV = $25,149.78 + $31,539.85 - $4,711.40
TPV ≈ $51,978.23
Step 3: Calculate the equivalent annual cost (EAC).
EAC = TPV * r / (1 - (1 + r)^(-n))
EAC = $51,978.23 * 0.06345 / (1 - (1 + 0.06345)^(-7))
EAC ≈ $7,456.21
The equivalent annual cost of the AC360 is approximately $7,456.21.
Hope this helps.
willkiddhill