Math Problem Statement
A firm that purchases electricity from the local utility for $350,000 per year is considering installing a steam generator at a cost of $280,000. The cost of operating this generator would be $260,000 per year, and the generator will last for five years. If the firm buys the generator, it does not need to purchase any electricity from the local utility. The cost of capital is 10%.
For the local utility option, consider five years of electricity purchases. For the generator option, assume immediate installation, with purchase and operating costs in the current year and operating costs continuing for the next four years. Assume payments under both options at the start of each year (i.e., immediate, one year from now,..., four years from now).
What is the net present value of the more attractive choice?
Please round your answer to the nearest dollar. Report the NPV of cost as a negative number.
Solution
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Math Problem Analysis
Mathematical Concepts
Present Value
Net Present Value (NPV)
Annuities
Cost of Capital
Formulas
Present Value of an Annuity: PV = C × [(1 - (1 + r)^-n) / r]
Net Present Value (NPV): NPV = Σ [C / (1 + r)^t] - Initial Investment
Theorems
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Suitable Grade Level
Graduate Level
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