ount should be indicated by a minus sign.)
To calculate the equivalent annual cost (EAC) of the "Dimple-Max" equipment, we need to consider the initial cost, operating costs, salvage value, depreciation, and taxes.
The initial cost of the equipment is $125,000.
The operating costs per year are $9,600.
The equipment has a 6-year life, so the salvage value at the end of the project's life is $9,300.
The relevant discount rate is 9 percent.
The straight-line depreciation method is used, meaning the equipment is depreciated evenly over its 6-year life.
To calculate the annual depreciation, we subtract the salvage value from the initial cost and divide by the number of years:
Annual Depreciation = (Initial Cost - Salvage Value) / Number of Years
Annual Depreciation = ($125,000 - $9,300) / 6
Annual Depreciation = $115,700 / 6
Annual Depreciation = $19,283.33
To calculate the tax savings from depreciation, we multiply the annual depreciation by the tax rate:
Tax Savings = Annual Depreciation * Tax Rate
Tax Savings = $19,283.33 * 0.24
Tax Savings = $4,627.60
To calculate the net cash flow each year, we subtract the tax savings from the operating costs:
Net Cash Flow = Operating Costs - Tax Savings
Net Cash Flow = $9,600 - $4,627.60
Net Cash Flow = $4,972.40
To calculate the present value of the net cash flows, we discount each year's net cash flow using the discount rate:
Present Value = Net Cash Flow / (1 + Discount Rate)^Year
Present Value Year 1 = $4,972.40 / (1 + 0.09)^1
Present Value Year 1 = $4,972.40 / 1.09
Present Value Year 1 = $4,568.07
Present Value Year 2 = $4,972.40 / (1 + 0.09)^2
Present Value Year 2 = $4,972.40 / 1.1881
Present Value Year 2 = $4,183.47
Present Value Year 3 = $4,972.40 / (1 + 0.09)^3
Present Value Year 3 = $4,972.40 / 1.29503
Present Value Year 3 = $3,840.47
Present Value Year 4 = $4,972.40 / (1 + 0.09)^4
Present Value Year 4 = $4,972.40 / 1.41158
Present Value Year 4 = $3,524.47
Present Value Year 5 = $4,972.40 / (1 + 0.09)^5
Present Value Year 5 = $4,972.40 / 1.53862
Present Value Year 5 = $3,235.47
Present Value Year 6 = $4,972.40 / (1 + 0.09)^6
Present Value Year 6 = $4,972.40 / 1.6771
Present Value Year 6 = $2,964.47
To calculate the equivalent annual cost (EAC), we sum up the present values of the net cash flows and divide by the annuity factor:
EAC = (Present Value Year 1 + Present Value Year 2 + Present Value Year 3 + Present Value Year 4 + Present Value Year 5 + Present Value Year 6) / Annuity Factor
The annuity factor can be calculated using the formula:
Annuity Factor = (1 - (1 + Discount Rate)^(-Number of Years)) / Discount Rate
Annuity Factor = (1 - (1 + 0.09)^(-6)) / 0.09
Annuity Factor = (1 - 0.50835) / 0.09
Annuity Factor = 0.49165 / 0.09
Annuity Factor = 5.46278
EAC = ($4,568.07 + $4,183.47 + $3,840.47 + $3,524.47 + $3,235.47 + $2,964.47) / 5.46278
EAC = $22,316.42 / 5.46278
EAC = $4,086.47