Question

"A firm is considering purchasing a computer system.
-Cost of system is $182,000. The firm will pay for the computer system in year 0.
-Project life: 4 years
-Salvage value in year 0 (constant) dollars: $23,000
-Depreciation method: five-years MACRS
-Marginal income-tax rate = 41% (remains constant over time)
-Annual revenue = $154,000 (year-0 constant dollars)
-Annual expenses (not including depreciation) = $96,000 (year-0 constant dollars)
-The general inflation rate is 2.1% during the project period (which will affect all revenues, expenses, and the salvage value but not depreciation).
-The firm borrows the entire $182,000 at 7.1% 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."

Answer 1

Please refer below table for the income statement with inflation.

Income Statement
Year	1	2	3	4
Revenue	$1,54,000.00	$1,57,234.00	$1,60,535.91	$1,63,907.17
Expense	$96,000.00	$98,016.00	$1,00,074.34	$1,02,175.90
Gross Profit	$58,000.00	$59,218.00	$60,461.58	$61,731.27
Interest Payment	$12,922.00	$6,239.50	$0.00	$0.00
Depriciation	$72,800.00	$43,680.00	$26,208.00	$16,312.00
Operating Profit	-$27,722.00	$9,298.50	$34,253.58	$45,419.27
Other Income	$0.00	$0.00	$0.00	$21,128.01
PBT	-$27,722.00	$9,298.50	$34,253.58	$66,547.28
Tax	$0.00	$3,812.39	$14,043.97	$27,284.39
PAT	-$27,722.00	$5,486.12	$20,209.61	$39,262.90

Please refer below table for cash flow statement

Cash Flow Statement
Year	1	2	3	4
Cash flow from revenue	$1,54,000.00	$1,57,234.00	$1,60,535.91	$1,63,907.17
Cash flow from expense	$96,000.00	$98,016.00	$1,00,074.34	$1,02,175.90
Cash flow interest payment	$12,922.00	$6,239.50	$0.00	$0.00
Cash flow taxes paid	$0.00	$3,812.39	$14,043.97	$27,284.39
Cash flow other income	$0.00	$0.00	$0.00	$21,128.01
Cash flow from operations	$45,078.00	$49,166.12	$46,417.61	$55,574.90
Cash flow from financing	$87,908.17	$94,560.77	$0.00	$0.00
Net Cash Flow	-$42,830.17	-$45,394.66	$46,417.61	$55,574.90

Here PMT i.e. per period payment can be calculated with below formula;-

PMT = P*R / (1-(1+R)^-n

Now IRR can be calculated for any find of cash flow i.e. before tax, after tax, net income, net cash flow etc.

I have calculated IRR From below table (adjusted back to no inflation)

Cash Flow Statement
Year	1	2	3	4
Cash flow from revenue	$1,54,000.00	$1,54,000.00	$1,54,000.00	$1,54,000.00
Cash flow from expense	$96,000.00	$96,000.00	$96,000.00	$96,000.00
Cash flow interest payment	$12,922.00	$6,239.50	$0.00	$0.00
Cash flow taxes paid	$0.00	$3,313.01	$13,034.72	$25,754.56
Cash flow other income	$0.00	$0.00	$0.00	$23,000.00
	$45,078.00	$51,760.50	$58,000.00	$81,000.00
Cash flow from financing	$87,908.17	$94,560.77	$0.00	$0.00
Net Cash Flow	-$42,830.17	-$42,800.27	$58,000.00	$81,000.00

If now we calculate the IRR for above Net cash flow it will be 26%.

Thank You!!