Question

Chinchilla Company is considering the purchase of a new machine for $57,000. The machine would generate an annual cash flow of $18,228 for five years. At the end of five years, the machine would have no salvage value. The company's cost of capital is 12 percent. The company uses straight-line depreciation with no mid-year convention. What is the internal rate of return for the machine rounded to the nearest percent, assuming no taxes are paid?

Answer 1

Internal rate of return is that interest rate that sets the present value of a project’s cash inflows equal to the present value of a project’s cost.

Now there are two methods either use :

1)See the present value table to look up the interest rate

$57,000/$18,228 = 3.127, which is the pv factor for n = 5, i= $18%

2)use Hit and trial method

Now in this method choose two interest rates with a difference preferably not more than 5% , the main thing in this method is to select two interest rate where we get one positive NPV and one negative NPV so as to get Desired IRR

So lets Choose One interest Rate As 15% and other 20% , we calculate each NPV as Follows:

	Amount	Year	Interest Rate	PV factor	Amount
Cash Outflow
Purchase of Machine	$57,000	0	15%	1	$57,000
Total(A)					$57,000
Cash Inflow
Annual Cash Flow	$18,228	1-5	15%	3.352	$61,100
Total(B)					$61,100
NPVx(B-A)					$4,100
	Amount	Year	Interest Rate	PV factor	Amount
Cash Outflow
Purchase of Machine	$57,000	0	20%	1	$57,000
Total(A)					$57,000
Cash Inflow
Annual Cash Flow	$18,228	1-5	20%	2.991	$54,520
Total(B)					$54,520
NPVy(B-A)					($2,480)

IRR=Lower Rate+[Lower Rate NPV/(Lower Rate NPV-Higher Rate NPV) * (High Rate-Low Rate)]

=15%+[4100/(4100-(2480) * (20%-15%)]

=15%+[4100/6580 * 5%]

=15%+3.11%

=18.11% or 18%(rounded off)