\"A firm is considering purchasing a computer system. -Cost of system is $185,00

Question

"A firm is considering purchasing a computer system.
-Cost of system is $185,000. The firm will pay for the computer system in year 0.
-Project life: 4 years
-Salvage value in year 0 (constant) dollars: $25,000
-Depreciation method: five-years MACRS -Marginal income-tax rate = 39% (remains constant over time)
-Annual revenue = $143,000 (year-0 constant dollars)
-Annual expenses (not including depreciation) = $84,000 (year-0 constant dollars)
-The general inflation rate is 4.5% during the project period (which will affect all revenues, expenses, and the salvage value but not depreciation).
-The firm borrows the entire $185,000 at 11.8% interest to be repaid in 2 annual payments. The debt interest paid and the principal payment SHOULD NOT be changed by the inflation rate. Lending agencies set the interest rate of borrowing to account for the inflation rate. Calculate the effects of borrowing and include the debt interest paid and the principal repayment into the income statement and cash flow statement. Determine the INFLATION-FREE IRR' of the computer system. Enter your answer as a percentage between 0 and 100."

Explanation / Answer

Depreciation on assets in future periods are not cash flows per se but they do have cash benefits in the form of reduced taxes. So they are used in net cashflow calculation. Let us calculate NPV of this project by considering net cash inflows for each period.

5-year MACRS table

Net Cashflows post taxes = Cash Inflows- Cash Outflows - Income Tax

Income Tax = Net Income * Tax rate

Net Income = Cash Inflow - Cash Outflow - non-cash expenses(depreciation)

therefore Net Cashflows post taxes = (Cash inflow - Cash Outflow -Depreciation) * (1-tax rate) + Depreciation

All cashflows except loan payment and depreciation will increase by a factor of 1.045 every year

Cash outflow 1 would be annual expenses

Cash outflow 2 would be loan repayments which will be paid in 2 equal installments

Loan Payment = Principal Value * rate of interest / ( 1- (1+rate of interest)^-number of payment periods)

= $185000 * 0.118 /(1- 1.118-2) = $109176.5534

Let us see what the cash flow statement will be like for 4 years of useful life of computer system

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To calculate IRR, take cashflows of each year starting from year 0 and use excel function =IRR(cashflows, guess) to get the IRR value. Cashflow from year zero = -$185000

Alternative you can equate NPV to 0 at IRR rate of return and solve by trial and error. The equation will look like this: -$185000 -14588.1455/(1+IRR%) - $4207.716/(1+IRR%)2 + $54923.37/(1+IRR%)3 + $69416.33/(1+IRR%)4 = 0

Excel gives a value of IRR= -10.033%

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