Answer :
The equivalent annual cost of the Econo-Cool Air Conditioner can be calculated by considering the initial purchase cost, the annual electricity bill, and the discount rate.
The initial cost of the air conditioner is $500. The annual electricity bill is $190. The air conditioner lasts for 7 years. The discount rate is 21%.
To calculate the equivalent annual cost, we need to consider both the present value of the initial cost and the present value of the annual electricity bill over the 7-year period.
Using the formula for present value of a single cash flow: PV = CF / (1 + r)ⁿ, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.
Calculating the present value of the initial cost:PVinitial= $500 / (1 + 0.21)⁰ = $500 (no discounting applied)
Calculating the present value of the annual electricity bill:
PVannual= $190 / (1 + 0.21)¹ + $190 / (1 + 0.21)² + ... + $190 / (1 + 0.21)⁷
Now, we can sum the present values of the initial cost and the annual electricity bills over the 7-year period and divide it by the number of years:
Equivalent annual cost = (PVinitial+ PVannual / 7
The equivalent annual cost takes into account the present value of both the initial cost and the annual expenses associated with owning the air conditioner. The discount rate allows us to adjust future cash flows to their present value. By calculating the present value of the initial cost and the present value of the annual electricity bill, we can determine the annual cost that would be equivalent to the total costs incurred over the 7-year period. Dividing this total by the number of years gives us the equivalent annual cost, which allows for a meaningful comparison with other s or alternatives.
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