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 $584,000. 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 10%.

Year:	0	1	2	3	4	5	6	Thereafter
Sales (millions of traps)	0	0.6	0.7	0.8	0.8	0.7	0.4	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?

Answer 1

a]	[$ in millions]	0	1	2	3	4	5	6
	Sales [millions of traps]		0.6000	0.7000	0.8000	0.8000	0.7000	0.4000
	Sales revenue		$       3.0000	$        3.5000	$       4.0000	$       4.0000	$           3.5000	$        2.0000
	Production cost excluding depreciation		$       0.7800	$        0.9100	$       1.0400	$       1.0400	$           0.9100	$        0.5200
	Depreciation = 5.4/6 =		$       0.9000	$        0.9000	$       0.9000	$       0.9000	$           0.9000	$        0.9000
	NOI		$       1.3200	$        1.6900	$       2.0600	$       2.0600	$           1.6900	$        0.5800
	Tax at 35%		$       0.4620	$        0.5915	$       0.7210	$       0.7210	$           0.5915	$        0.2030
	NOPAT		$       0.8580	$        1.0985	$       1.3390	$       1.3390	$           1.0985	$        0.3770
	Add: Depreciation		$       0.9000	$        0.9000	$       0.9000	$       0.9000	$           0.9000	$        0.9000
	OCF		$       1.7580	$        1.9985	$       2.2390	$       2.2390	$           1.9985	$        1.2770
	Capital spending	$        5.4000
	Change in NWC	$        0.3000	$       0.0500	$        0.0500	$                 -	$      -0.0500	$         -0.1500	-0.2000
	After tax salvage value of the equipment = 0.584*(1-35%) =							0.3796
	FCF	$      -5.7000	$       1.7080	$        1.9485	$       2.2390	$       2.2890	$           2.1485	$        1.8566
	PVIF at 10% [PVIF = 1/1.1^t]	1	0.90909	0.82645	0.75131	0.68301	0.62092	0.56447
	PV at 10%	$      -5.7000	$       1.5527	$        1.6103	$       1.6822	$       1.5634	$           1.3340	$        1.0480
	NPV (Sum of PVs t0 to t6]	$        3.0907
b)	Depreciation under SLM		$       0.9000	$        0.9000	$       0.9000	$       0.9000	$           0.9000	$        0.9000
	Depreciation under MACRS		$       1.0800	$        1.7280	$       1.0368	$       0.6221	$           0.6221	$        0.3110
	Difference in depreciation [MACRS-SLM]		$       0.1800	$        0.8280	$       0.1368	$      -0.2779	$         -0.2779	$      -0.5890
	Tax shield on difference in depreciation at 35%		$       0.0630	$        0.2898	$       0.0479	$      -0.0973	$         -0.0973	$      -0.2061
	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		$       0.0573	$        0.2395	$       0.0360	$      -0.0664	$         -0.0604	$      -0.1164
	Sum of PVs	$        0.0896
	The NPV will increase by $0.0896 millions, if MACRS method is used for depreciation.
	CHECK:
	[$ in millions]	0	1	2	3	4	5	6
	Sales [millions of traps]		0.6000	0.7000	0.8000	0.8000	0.7000	0.4000
	Sales revenue		$       3.0000	$        3.5000	$       4.0000	$       4.0000	$           3.5000	$        2.0000
	Production cost excluding depreciation		$       0.7800	$        0.9100	$       1.0400	$       1.0400	$           0.9100	$        0.5200
	Depreciation MACRS		$       1.0800	$        1.7280	$       1.0368	$       0.6221	$           0.6221	$        0.3110
	NOI		$       1.1400	$        0.8620	$       1.9232	$       2.3379	$           1.9679	$        1.1690
	Tax at 35%		$       0.3990	$        0.3017	$       0.6731	$       0.8183	$           0.6888	$        0.4091
	NOPAT		$       0.7410	$        0.5603	$       1.2501	$       1.5196	$           1.2791	$        0.7598
	Add: Depreciation		$       1.0800	$        1.7280	$       1.0368	$       0.6221	$           0.6221	$        0.3110
	OCF		$       1.8210	$        2.2883	$       2.2869	$       2.1417	$           1.9012	$        1.0709
	Capital spending	$        5.4000
	Change in NWC	$        0.3000	$       0.0500	$        0.0500	$                 -	$      -0.0500	$         -0.1500	-0.2000
	After tax salvage value of the equipment = 0.584*(1-35%) =							0.3796
	FCF	$      -5.7000	$       1.7710	$        2.2383	$       2.2869	$       2.1917	$           2.0512	$        1.6505
	PVIF at 10% [PVIF = 1/1.1^t]	1	0.90909	0.82645	0.75131	0.68301	0.62092	0.56447
	PV at 10%	$      -5.7000	$       1.6100	$        1.8498	$       1.7182	$       1.4970	$           1.2737	$        0.9316
	NPV (Sum of PVs t0 to t6]	$        3.1803
	Difference in NPV = 3.1803-3.0907 =	$        0.0896