The capital budgeting director of Sparrow Corporation is evaluating a project, which costs $200,000, is expected to last for 10 years and produce after-tax cash flows, including depreciation, of $44,503 per year. If the firm's cost of capital is 14 percent and its tax rate is 40 percent, what is the project's IRR?
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A. B. C. D. E.A
$200,000 = $44,503(PVIFA(Irr,10))
PVIFA(Irr,10) = 4.49408 ;IRR = 18%.
To calculate the internal rate of return (IRR) for the project, we need to find the discount rate at which the present value of the project's cash flows is equal to the initial investment.
The cash flows provided in the question are after-tax cash flows, which means they already incorporate the effect of taxes and depreciation. Therefore, we can use these cash flows directly in our calculation.
Step 1: Calculate the annual after-tax cash flows
The project's annual after-tax cash flows are given as $44,503. Since these cash flows remain constant over the 10-year duration of the project, the annual cash flow is $44,503.
Step 2: Calculate the present value of cash flows
We need to discount each year's cash flow to its present value using the cost of capital.
PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... + CF10 / (1 + r)^10
PV = $44,503 / (1 + 0.14)^1 + $44,503 / (1 + 0.14)^2 + ... + $44,503 / (1 + 0.14)^10
PV = $44,503 / 1.14^1 + $44,503 / 1.14^2 + ... + $44,503 / 1.14^10
Using a financial calculator or spreadsheet, we can calculate the present value of the cash flows:
PV = $44,503 / 1.14^1 + $44,503 / 1.14^2 + ... + $44,503 / 1.14^10 ≈ $327,898.60
Step 3: Calculate the IRR
The IRR is the discount rate that makes the present value of cash flows equal to the initial investment. In this case, the initial investment is $200,000.
We can set up the following equation:
PV = $200,000
$327,898.60 = $200,000 / (1 + IRR)^1 + $200,000 / (1 + IRR)^2 + ... + $200,000 / (1 + IRR)^10
Using trial and error or a financial calculator, we find that the IRR is approximately 12%.
Therefore, the correct answer is C. 12%.