Math Problem Statement
Problem 6-23 Equivalent Annual Cost Bridgton Golf Academy is evaluating new golf practice equipment. The "Dimple-Max" equipment costs $146,000, has a 4-year life, and costs $10,300 per year to operate. The relevant discount rate is 12 percent. Assume that the straight-line depreciation method is used and that the equipment is fully depreciated to zero. Furthermore, assume the equipment has a salvage value of $10,700 at the end of the project’s life. The relevant tax rate is 21 percent. All cash flows occur at the end of the year. What is the equivalent annual cost (EAC) of this equipment? (A negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Solution
To calculate the Equivalent Annual Cost (EAC) for the "Dimple-Max" equipment, we'll break the problem into steps.
Step 1: Calculate the initial cost, operating costs, and salvage value.
- Initial cost: $146,000
- Operating costs: $10,300 per year
- Salvage value: $10,700
- Life of equipment: 4 years
- Discount rate: 12%
- Tax rate: 21%
Step 2: Calculate the depreciation and the annual tax shield on depreciation.
Using the straight-line depreciation method, the annual depreciation is:
[ \text{Annual Depreciation} = \frac{\text{Initial Cost} - \text{Salvage Value}}{\text{Life of Equipment}}
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Math Problem Analysis
Mathematical Concepts
Finance
Equivalent Annual Cost
Depreciation
Discount Rate
Tax Shield
Formulas
Annual Depreciation = (Initial Cost - Salvage Value) / Life of Equipment
Tax Shield on Depreciation = Depreciation × Tax Rate
Present Value of Cash Flows
Equivalent Annual Cost (EAC) = Total Present Value / Annuity Factor
Theorems
Time Value of Money
Present Value of an Annuity
Suitable Grade Level
Undergraduate (Finance/Business)
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