Question

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $6.3 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 $536,000. 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 $1.10 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 10%. Use the MACRS depreciation schedule.

Year:	0	1	2	3	4	5	6	Thereafter
Sales (millions of traps)	0	0.5	0.7	0.8	0.8	0.6	0.5	0

a. What is project NPV? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)
b. By how much would NPV increase if the firm depreciated its investment using the 5-year MACRS schedule? (Do not round intermediate calculations. Enter your answer in whole dollars not in millions.)

Answer 1

a]	[$ in millions]	0	1	2	3	4	5	6
	Sales [millions of traps]		0.5000	0.7000	0.8000	0.8000	0.6000	0.5000
	Sales revenue		$       2.5000	$        3.5000	$       4.0000	$       4.0000	$           3.0000	$        2.5000
	Production cost excluding depreciation		$       0.5500	$        0.7700	$       0.8800	$       0.8800	$           0.6600	$        0.5500
	Depreciation = 6.3/6 =		$       1.0500	$        1.0500	$       1.0500	$       1.0500	$           1.0500	$        1.0500
	NOI		$       0.9000	$        1.6800	$       2.0700	$       2.0700	$           1.2900	$        0.9000
	Tax at 35%		$       0.3150	$        0.5880	$       0.7245	$       0.7245	$           0.4515	$        0.3150
	NOPAT		$       0.5850	$        1.0920	$       1.3455	$       1.3455	$           0.8385	$        0.5850
	Add: Depreciation		$       1.0500	$        1.0500	$       1.0500	$       1.0500	$           1.0500	$        1.0500
	OCF		$       1.6350	$        2.1420	$       2.3955	$       2.3955	$           1.8885	$        1.6350
	Capital spending	$        6.3000
	Change in NWC	$        0.2500	$       0.1000	$        0.0500	$                 -	$      -0.1000	$         -0.0500	-0.2500
	After tax salvage value of the equipment = 0.536*(1-35%) =							0.3484
	FCF	$      -6.5500	$       1.5350	$        2.0920	$       2.3955	$       2.4955	$           1.9385	$        2.2334
	PVIF at 10% [PVIF = 1/1.1^t]	1	0.90909	0.82645	0.75131	0.68301	0.62092	0.56447
	PV at 10%	$      -6.5500	$       1.3955	$        1.7289	$       1.7998	$       1.7045	$           1.2037	$        1.2607
	NPV (Sum of PVs t0 to t6]	$        2.5430
b)	Depreciation under SLM		$ 10,50,000	$ 10,50,000	$ 10,50,000	$ 10,50,000	$     10,50,000	$ 10,50,000
	Depreciation under MACRS		$ 12,60,000	$ 20,16,000	$ 12,09,600	$    7,25,760	$       7,25,760	$    3,62,880
	Difference in depreciation [MACRS-SLM]		$    2,10,000	$     9,66,000	$    1,59,600	$ -3,24,240	$     -3,24,240	$ -6,87,120
	Tax shield on difference in depreciation at 35%		$       73,500	$     3,38,100	$       55,860	$ -1,13,484	$     -1,13,484	$ -2,40,492
	PVIF at 10% [PVIF = 1/1.1^t]	1	0.90909	0.82645	0.75131	0.68301	0.62092	0.56447
	PV of depreciation tax shield		$       66,818	$     2,79,421	$       41,968	$      -77,511	$         -70,465	$ -1,35,751
	Sum of PVs	$    1,04,481
	The NPV will increase by $104,481, if MACRS method is used for depreciation.