Question

"A firm is considering purchasing a new milling machine and has collected the following information for its income statement and cash flow statement. However, this income statement was calculated as if there is no inflation! All dollars are expressed in constant (year-0) dollars. Recalculate the income and cash flow statement by assuming there is a general (average) inflation of 2.6% applied to revenue, O&M, and salvage value.
- The firm will pay back the loan in 2 years, and the annual loan payment is $26,571.
- The tax rate is 38%.
- The revenue for year 1 is $40,000 and $36,000 for year 2.
- O&M for year 1 is $8,000 and $11,000 for year 2.
- The interest paid on the debt is $2743 for year 1 and $1409 for year 2.
- The taxable income is $19,111 for year 1 and $14,897 for year 2.
- The income taxes are $7,262 for year 1 and $5,661 for year 2.
- The milling machine costs $71,000.
- The salvage value at the end of year 2 is $48,000.
Calculate the IRR of the cash flow based on actual dollars. Express your answer as a percentage between 0 and 100.
You should calculate the depreciation based on the information given in the problem, but do not refer to the MACRS table. You will also need to calculate the amount that is borrowed and that goes to the principal on the debt in years 1 and 2."

Answer 1

IRR is that rate at which P.V. of inflow equals P.V. of outflow.

First we find the depreciation figure: Revenue - O&M - Interest - Depreciation = Taxable Income

Yr 1: 40000 - 8000 - 2743 - x = 19111; depn = $10146

Yr 2: 36000 - 11000 - 1409 - x = 14897; depn = $8694

Here the figures given are in constant dollars (i.e without considering inflation) but we need to calculate IRR based on actual cash flow (i.e considering the inflation effect) so the figures need to be restated.

Yr 1: Restated figures: Revenue 41040; O&M 8208; No salvage

Net Inflow = 41040-8208-2743-10146 = 19943 - tax@38% = $12365

Outflow is the principal repayment of $ 26571 - 2743 = $23828

So net outflow of Yr 1 = 23828-12365 = $ 11463

Yr 2 : Restated figures: Revenue 36936; O&M = 11286; Salvage = 49248

Net inflow = 36936-11286-1409-8694 = 15547 - Tax@38% = $9639 PLUS salvage net off tax = $30534 [TOTAL INFLOW = 40173]

Outflow is the principal repayment of $26571 - 1409 = $ 25162

so net inflow in year 2 is 40173-25162 = $15011

Also the amount borrowed is 53142 (i.e. 26571*2) - 2743-1409 = 48990 i.e the actual cash outflow to purchase at beginning period is 71000-48990 = $22010.

Thus we need the rate that equates outflow at T0 of 22010, Outflow at T1 of 11463 and inflow at T2 of 15011 (ie rate at which P.V. of inflow = P.V. of outflow)

Therefore IRR = 39.45% (Using trial & error method)