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Answer to Question #30197 in Economics of Enterprise for anne geddes

Question #30197
A car is purchased for $40000 at a CCA rate of 20% (depreciation = CCA rate), corporate tax rate of 30%, current intrest rate is 12.2%, inflation is 2%, with a salvage value of $4000 after its 8 year service life:

a. What is the after-tax present worth of the car?
b. What is the Equivalent Annual Cost (EAC) of the car in its first year?
Expert's answer
In finance, the net present value (NPV) or net present worth (NPW) of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows of the same entity.
In the case when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV). NPV is a central tool indiscounted cash flow (DCF) analysis and is a standard method for using the time value of money to appraise long-term projects. Used for capital budgeting and widely used throughout economics, finance, and accounting, it measures the excess or shortfall of cash flows, in present value terms, once financing charges are met.

a. After-tax present worth (NPV) = $40,000*(1 - 0.3) = $28,000


In finance the equivalent annual cost (EAC) is the cost per year of owning and operating an asset over its entire lifespan.
EAC is often used as a decision making tool in capital budgeting when comparing investment projects of unequal lifespans. For example if project A has an expected lifetime of 7 years, and project B has an expected lifetime of 11 years it would be improper to simply compare the net present values (NPVs) of the two projects, unless neither project could be repeated.
EAC is calculated by dividing the NPV of a project by the present value of an annuity factor. Equivalently, the NPV of the project may be multiplied by the loan repayment factor.

b. EAC = NPV/A8,14.2
NPV = $28,000
A8,14.2 = (1 - 1/(1.142)^8)/0.142 = 4.61
EAC = $28,000/4.61 = 6,073.75

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