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 4.9% applied to revenue, O&M, and salvage value.
- The firm will pay back the loan in 2 years, and the annual loan payment is $11,808.
- The tax rate is 36%.
- The revenue for year 1 is $46,000 and $42,000 for year 2.
- O&M for year 1 is $12,000 and $13,100 for year 2.
- The interest paid on the debt is $1722 for year 1 and $895 for year 2.
- The taxable income is $22,275 for year 1 and $19,434 for year 2.
- The income taxes are $8,019 for year 1 and $6,996 for year 2.
- The milling machine costs $70,000.
- 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

A ) Calculate the IRR of the cash flow based on actual dollars. Express your answer as a percentage between 0 and 100.

	Particulars	Initial Outlay	Year1	Year2
A	Revenue		$ 46,000.00	$ 42,000.00
B	Less O&M		$ 12,000.00	$ 13,100.00
C	Less Interest expense		$    1,722.00	$        895.00
D	Less Depreciation (A-B-C-E)		$ 10,003.00	$    8,571.00
E	Taxable Income		$ 22,275.00	$ 19,434.00
	Less tax paid		$    8,019.00	$    6,996.00
	Income after Tax		$ 14,256.00	$ 12,438.00
	Incremental Cash Flow (Income after Tax + Non cash Exp)		$ 24,259.00	$ 21,009.00
	Salvage value			$ 48,000.00
		(70,000.00)	$ 24,259.00	$ 69,009.00

NPV = Cash outflow + (CF1/(1+IRR)^N)

Ideal IRR is when NPV is 0

hence doing trial and Error method for arriving at IRR

1 ) Lets try at IRR 0%

NPV = -70000+ (24259/(1.0)^1)+(69009/(1.0)^2 = 23268 . Since NPV is Positive IRR also should be Positive

2 ) Lets try at IRR 20%

NPV = -70000+ (24259/(1.20)^1)+(69009/(1.20)^2 = -1861.25. Since NPV is Negative IRR also should be below 20%

3 ) Lets try at IRR 18%

NPV = -70000+ (24259/(1.18)^1)+(69009/(1.18)^2 = 119. Since NPV is Positive. IRR also should be above18%

Since the positive amount is very close to 0 we can clearly say that IRR is ~18%

B ) Calculation of Depreciation as Below :

	Particulars	Year1	Year2
A	Revenue	$ 46,000.00	$ 42,000.00
B	Less O&M	$ 12,000.00	$ 13,100.00
C	Less Interest expense	$    1,722.00	$        895.00
D	Less Depreciation (A-B-C-E)	$ 10,003.00	$    8,571.00
E	Taxable Income	$ 22,275.00	$ 19,434.00
	Less tax paid	$    8,019.00	$    6,996.00
	Income after Tax	$ 14,256.00	$ 12,438.00

C) Calculation of Amount Borrowed and principal paid on debt in year 1 and 2

A	B	(A-B)
Repayment	Interest	Principal
$ 11,808	$ 1722	$ 10,086
$ 11,808	$ 895	$ 10,913

Total Principal Borrowed is $ 20999 ~ $21000 ($10086+$10913)