To calculate the maximum amount the car wash can spend today on a new, energy-efficient hot water boiler while aiming for an 8% annual return on its investment, we need to perform a present value analysis. This analysis involves determining the present value of the electricity cost savings over the five-year period, taking into account the increasing electric rate and the desired 8% annual return.
Here are the steps to perform this analysis:
Step 1: Calculate the annual electricity cost savings
The car wash is expected to save 30,000 kilowatt-hours of electricity annually. In the first year, the electric rate is $0.25 per kilowatt-hour. So, the annual electricity cost savings for each year from year 1 to year 5 can be calculated as follows:
Year 1: $0.25 per kWh * 30,000 kWh = $7,500
Year 2: ($0.25 + $0.05) per kWh * 30,000 kWh = $9,000
Year 3: ($0.25 + 2 * $0.05) per kWh * 30,000 kWh = $10,500
Year 4: ($0.25 + 3 * $0.05) per kWh * 30,000 kWh = $12,000
Year 5: ($0.25 + 4 * $0.05) per kWh * 30,000 kWh = $13,500
Step 2: Calculate the present value of each year’s savings
To calculate the present value of each year’s electricity cost savings, we use the formula for calculating the present value of a future cash flow:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value (in this case, the savings for each year)
r = Discount Rate (8% or 0.08)
n = Number of years in the future
Let’s calculate the present value of savings for each year:
Year 1: PV1 = $7,500 / (1 + 0.08)^1 = $6,944.44
Year 2: PV2 = $9,000 / (1 + 0.08)^2 = $7,905.09
Year 3: PV3 = $10,500 / (1 + 0.08)^3 = $8,635.08
Year 4: PV4 = $12,000 / (1 + 0.08)^4 = $9,205.26
Year 5: PV5 = $13,500 / (1 + 0.08)^5 = $9,597.89
Step 3: Calculate the total present value of savings
To find the total present value of all five years of electricity cost savings, add up the present values for each year:
Total PV = PV1 + PV2 + PV3 + PV4 + PV5
Total PV = $6,944.44 + $7,905.09 + $8,635.08 + $9,205.26 + $9,597.89
Total PV = $42,287.76
So, the maximum amount the car wash can spend today for the new boiler, while aiming for an 8% annual return, is $42,287.76. This amount ensures that the car wash will recover its investment through electricity cost savings over the next five years, accounting for the increasing electric rate.
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