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 4.7% applied to revenue, O&M, and salvage value.
- The firm will pay back the loan in 2 years, and the annual loan payment is $15,796.
- The tax rate is 39%.
- The revenue for year 1 is $36,000 and $27,000 for year 2.
- O&M for year 1 is $12,000 and $13,500 for year 2.
- The interest paid on the debt is $2427 for year 1 and $1264 for year 2.
- The taxable income is $12,713 for year 1 and $4,644 for year 2.
- The income taxes are $4,958 for year 1 and $1,811 for year 2.
- The milling machine costs $62,000.
- The salvage value at the end of year 2 is $47,000.
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

Cash Flow statement
		Year 0	Year 1	Year 2
1	Sales revenue	-	$37,692	$28,269
2	O&M cost	-	-12,564	-14,135
3	Interest cost	-	-2,427	-1,264
4	Income before tax	-	22,701	12,871
	[1-(2+3+4)]
5	Taxes at 39%	-	-4958	-4958
6	Net income	-	17,743	7,913
	[4-5]	-
7	Cash flow from operation	-	17,743	7,912.5
	[1-2-3-5]	-
8	Initial Investment	($62,000)	-	-
9	Salvage value			47000
10	Total cash flow	($62,000)	$17,743	$54,913
	[7+8+9]

IRR Calculation

The calculation of IRR is based on Net Present Value (NPV) being zero, thus:

NPV = 0; or

PV of future cash flows − Initial Investment = 0; or

	CF1	+	CF2					− Initial Investment = 0
	( 1 + r )1		( 1 + r )2

Where,
   r is the internal rate of return;
   CF₁ is the period one net cash inflow;
   CF₂ is the period two net cash inflow,

Assuming IRR at 12%
	PV(C0)	PV(C1)	PV(C2)
	-62000	= 17743/(1.12)^1	= 54913/(1.12)^2
	-62000	15842	43776
NPV {(PV(C0)+ PV(C0)+ PV(C0)}	-2382.1
Since negative NPV let’s assume lower IRR of 10%
	PV(C0)	PV(C1)	PV(C2)
	-62000	= 17743/(1.10)^1	= 54913/(1.10)^2
	-62000	16130	45382
NPV	-487.77
Since negative NPV let’s assume lower IRR of 9.5%	PV(C0)	PV(C1)	PV(C2)
	-62000	= 17743/(1.095)^1	= 54913/(1.095)^2
	-62000	16204	45798
NPV	1.28
Since NPV is close to zero, IRR is 9.5%

Principle payment
	Year 1	Year 2
Aggregate loan payment	15796	15796
Interest Payment	-2,427	-1,264
Principle payment	13369	14532