Question

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.4 million. The equipment will be depreciated straight - line over 6 years to a value of zero, but, in fact, it can be sold after 6 years for $682,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.30 per trap and believes that the traps can be sold for $5 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 35%, and the required rate of return on the project is 8%. Year: 0 1 2 3 4 5 6 Thereafter Sales (millions of traps) 0 0.5 0.7 0.8 0.8 0.7 0.5 0 Suppose the firm can cut its requirements for working capital in half by using better inventory control systems. By how much will this increase project NPV? (Enter your answer in millions rounded to 4 decimal places.). Change in NPV= ?? million

Answer 1

			All cash flows are in millions of dollars
	Initial Investment	5.4	million
	salvage value after tax	443,300
	(682000 x (1-0.35))
	Year	0	1	2	3	4	5	6	Thereafter
	Sales units(in milions)	0	0.5	0.7	0.8	0.8	0.7	0.5	0
	x sales price per unit		$5	$5	$5	$5	$5	$5	$5
	Sales Revenue		$2.5000	$3.5000	$4.0000	$4.0000	$3.5000	$2.5000	$0.0000
	Working capital -10%	0.2500	0.3500	0.4000	0.4000	0.3500	0.2500	0.0000
	Change in NWC	-0.2500	-0.1000	-0.0500	0.0000	0.0500	0.1000	0.2500
	Production cost
	Year	0	1	2	3	4	5	6	Thereafter
	Sales units(in milions)	0	0.5	0.7	0.8	0.8	0.7	0.5	0
	x cost per unit		$1.30	$1.30	$1.30	$1.30	$1.30	$1.30	$1.30
	Production cost		$0.6500	$0.9100	$1.0400	$1.0400	$0.9100	$0.6500	$0.0000
	Revenues		$2.5000	$3.5000	$4.0000	$4.0000	$3.5000	$2.5000	$0.0000
	Expense		$0.6500	$0.9100	$1.0400	$1.0400	$0.9100	$0.6500	$0.0000
	Depreciation		0.9000	0.9000	0.9000	0.9000	0.9000	0.9000
	Pretax profit		$0.9500	$1.6900	$2.0600	$2.0600	$1.6900	$0.9500
	Tax at 35%		0.3325	0.5915	0.7210	0.7210	0.5915	0.3325
	After-tax profit		0.6175	1.0985	1.3390	1.3390	1.0985	0.6175
	Cash Flow from operations		1.5175	1.9985	2.2390	2.2390	1.9985	1.5175
	Cash Flow: capital invest.	-5.4						0.4433
	Cash Flow from WC	-0.2500	-0.1000	-0.0500	0.0000	0.0500	0.1000	0.2500
	Cash Flow from operations		1.5175	1.9985	2.2390	2.2390	1.9985	1.5175
	Total Cash Flow	-5.6500	1.4175	1.9485	2.2390	2.2890	2.0985	2.2108
	PVF at 8%	1	0.925926	0.857339	0.793832	0.73503	0.680583	0.63017
	Present Value	-5.65	1.3125	1.670525	1.77739	1.682483	1.428204	1.393179
	NPV	$        3.6143
Change in NWC requirement
	Year	0	1	2	3	4	5	6	Thereafter
	Sales units(in milions)	0	0.5	0.7	0.8	0.8	0.7	0.5	0
	x sales price per unit		$5	$5	$5	$5	$5	$5	$5
	Sales Revenue		$2.5000	$3.5000	$4.0000	$4.0000	$3.5000	$2.5000	$0.0000
	Working capital -10%	0.1250	0.1750	0.2000	0.2000	0.1750	0.1250	0.0000
	Change in NWC	-0.1250	-0.0500	-0.0250	0.0000	0.0250	0.0500	0.1250
	Cash Flow: capital invest.	-5.4						0.4433
	Cash Flow from WC	-0.1250	-0.0500	-0.0250	0.0000	0.0250	0.0500	0.1250
	Cash Flow from operations		1.5175	1.9985	2.2390	2.2390	1.9985	1.5175
	Total Cash Flow	-5.5250	1.4675	1.9735	2.2390	2.2640	2.0485	2.0858
	PVF at 8%	1	0.925926	0.857339	0.793832	0.73503	0.680583	0.63017
	Present Value	-5.525	1.358796	1.691958	1.77739	1.664108	1.394175	1.314408
	NPV	$        3.6758
	change in npv	$0.0616	final answer
	(3.6758 - 3.6143)