10. A machine can be purchased for $10,500, including transportation charges, bu

Question

10. A machine can be purchased for $10,500, including transportation charges, but installation costs will require $1,500 more. The machine is expected to last four years and produce annual cash revenues of $6,000. Annual cash operating expenses are expected to be $2,000, with depreciation of $3,000 per year. The fi rm has a 30 percent tax rate. Determine the relevant after-tax cash fl ows and prepare a cash fl ow schedule.

11. Use the information in Problem 10 to do the following: a. Calculate the payback period for the machine. b. If the project's cost of capital is 10 percent, would you recommend buying the machine? c Estimate the IRR for the machine.

Explanation / Answer

Hi,

Please find the detailed answer as follows:

Part 10

Year 0 Cash Flow = -10500 (Purchase Price) - 1500 (Installation Costs) = -12000

Annual Cash Inflows Schedule:

Part 11

a) Payback Period = Initial Investment/Annual Cash Inflows = 12000/3700 = 3.24 Years

b) You need to calculate the NPV to make the decision:

NPV = -Initial Investment + Present Value of Cash Inflows = -12000 + 3700/(1+.10)^1 + 3700/(1+.10)^2 + 3700/(1+.10)^3 + 3700/(1+.10)^4 = -271.498 or -271.50

No, the machine shouldn't be bought since it results in a Negative NPV.

c) To calculate IRR, you need to put the value of NPV as 0 and solve for r as follows:

NPV = 0 = -12000 + 3700/(1+r)^1 + 3700/(1+r)^2 + 3700/(1+r)^3 + 3700/(1+r)^4

Solving for r, we get IRR as 8.95% or 9%

IRR = 8.95% or 9%.

Thanks.

Revenues Expenses Depreciation Earnings
Before Tax Tax Earnings
After Tax Depreciation Annual Cash
Inflows Year 1 6000 2000 3000 1000 300 700 3000 3700 Year 2 6000 2000 3000 1000 300 700 3000 3700 Year 3 6000 2000 3000 1000 300 700 3000 3700 Year 4 6000 2000 3000 1000 300 700 3000 3700

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