Question

Lou Barlow, a divisional manager for Sage Company, has an opportunity to manufacture and sell one of two new products for a five-year period. His annual pay raises are determined by his division’s return on investment (ROI), which has exceeded 22% each of the last three years. He has computed the cost and revenue estimates for each product as follows:

	Product A			Product B
Initial investment:
Cost of equipment (zero salvage value)	$	370,000		$	570,000
Annual revenues and costs:
Sales revenues	$	400,000		$	480,000
Variable expenses	$	180,000		$	214,000
Depreciation expense	$	74,000		$	114,000
Fixed out-of-pocket operating costs	$	88,000		$	68,000

The company’s discount rate is 20%.

Click here to view Exhibit 12B-1 and Exhibit 12B-2, to determine the appropriate discount factor using tables.

3. Calculate the internal rate of return for each product.

Answer 1

IRR is the rate of return at which PV of cash flow= Cash outflow

NPV is zero at IRR

depreciation is a non cash expense so it is not relevant here as it wont affect cashoutflow.

	A	B
sales	$400,000	$480,000
less: variable expenses	$180,000	$214,000
less: Fixed out-of-pocket operating costs	$88,000	$68,000
Cash inflow per year	$132,000[$400,000-180,000-88,000]	$198,000[480,000-214,000-68,000]

A

Suppose IRR = 10%

Year	Cash flow	PV factor	Present value
0	($370,000)	1	($370,000) [$370,000*1]
1-5	($132,000)	3.79079	$500,384[$132,000*3.79079]	As there is continuous cash flow for 5 years we will use annuity table 12B-2
		NPV	$130,384[$370,000-500,384]

Suppose IRR = 20%

Year	Cash flow	PV factor	Present value
0	($370,000)	1	($370,000) [$370,000*1]
1-5	($132,000)	2.99061	$394,761[$132,000*2.99061]	As there is continuous cash flow for 5 years we will use annuity table 12B-2
		NPV	$24,761[$370,000-394,761]

=

=0.10+0.12344

=22.34% [ ROUND OFF to 22% IF REQUIRED]

B:

Suppose IRR = 10%

Year	Cash flow	PV factor	Present value
0	($570,000)	1	($570,000) [$370,000*1]
1-5	($198,000)	3.79079	$750,576[$198,000*3.79079]	As there is continuous cash flow for 5 years we will use annuity table 12B-2
		NPV	$180,576

Suppose IRR = 20%

Year	Cash flow	PV factor	Present value
0	($570,000)	1	($570,000) [$370,000*1]
1-5	($198,000)	2.99061	$592,141[$198,000*2.99061]	As there is continuous cash flow for 5 years we will use annuity table 12B-2
		NPV	$22,141

=0.10+18,058/158,435

=0.10+0.1139

=21.40% [ round off to 21% if required]

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