Question

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.7 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 $638,000. The firm believes that working capital at each date must be maintained at a level of 15% of next year’s forecast sales. The firm estimates production costs equal to $1.70 per trap and believes that the traps can be sold for $8 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	0.5	0.6	0.8	0.8	0.6	0.4	0

Using this schedule

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

Calculation of NPV using SLM depreciation:

35% Tax rate Calculation of annual depreciation Total Depreciation Cost Dep Rate Depreciation Year-1 $ 5,700,000 16.67% $ 950,000 Year-2 $ 5,700,000 16.67% $ 950,000 Year-3 $ 5,700,000 16.67% $ 950,000 Year-4 $ 5,700,000 16.67% $ 950,000 Year-5 $ 5,700,000 16.67% $ 950,000 Year-6 $ 5,700,000 16.67% $ 950,000 $ 5,700,000 $ $ 5,700,000 5,700,000 Calculation of after-tax salvage value Cost of machine Depreciation WDV Sale price Profit/(Loss) Tax Sale price after-tax $ 638,000 638,000 223,300 414,700 $ $ Calculation of annual operating cash flow No of units Selling price Operating ost Sale Less: Operating Cost Contribution Less: Depreciation Profit before tax Tax@35% Profit After Tax Add Depreciation Cash Profit after-tax Year-1 500,000 $ 8.00 $ 1.70 $ 4,000,000 $ 850,000 $ 3,150,000 $ 950,000 $ 2,200,000 $ 770,000 $ 1,430,000 $ 950,000 $ 2,380,000 Year-2 600,000 $ 8.00 $ 1.70 $ 4,800,000 $ 1,020,000 $ 3,780,000 $ 950,000 $ 2,830,000 $ 990,500 $ 1,839,500 $ 950,000 $ 2,789,500 Year-3 Year-4 800,000 800,000 $ 8.00 $ 8.00 $ 1.70 $ 1.70 $ 6,400,000 $ 6,400,000 $ 1,360,000 $ 1,360,000 $ 5,040,000 $ 5,040,000 $ 950,000 $ 950,000 $ 4,090,000 $ 4,090,000 $ 1,431,500 $ 1,431,500 $ 2,658,500 $ 2,658,500 $ 950,000 $ 950,000 $ 3,608,500 $ 3,608,500 Year-5 600,000 $ 8.00 $ 1.70 $ 4,800,000 $ 1,020,000 $ 3,780,000 $ 950,000 $ 2,830,000 $ 990,500 $ 1,839,500 $ 950,000 $ 2,789,500 Year-6 400,000 $ 8.00 $ 1.70 $ 3,200,000 $ 680,000 $ 2,520,000 $ 950,000 $ 1,570,000 $ 549,500 $ 1,020,500 $ 950,000 $ 1,970,500

Calculation of working capital movement 480,000 Working capital-opening Closing working capital Movement $ $ - 600,000 600,000 $ $ $ 600,000 720,000 120,000 $ $ $ 720,000 $ 720,000 $ 960,000 $ 240,000 $ 960,000 960,000 960,000 - $ $ $ $ 960,000 960,000 $ $ 720,000 $ (240,000) $ 12 720,000 $ 480,000 $ (240,000) $ (480,000) Calculation of NPV Year 10.00% Capital Working capital Operating cash Annual Cash flo PV factor Present values $ (5,700,000) $ (600,000) $ (6,300,000) 1.0000 $ (6,300,000) $ (120,000) $ 2,380,000 $ 2,260,000 0.9091 $ 2,054,545 $ (240,000) $ 2,789,500 $ 2,549,500 0.8264 $ 2,107,025 - $ 3,608,500 $ 3,608,500 0.7513 $ 2,711,119 $ 240,000 $ 3,608,500 $ 3,848,500 0.6830 $ 2,628,577 240,000 $ 2,789,500 $ 3,029,500 0.6209 $ 1,881,081 $ 414,700 $ 480,000 $ 1,970,500 $ 2,865,200 0.5645 $ 1,617,331 $ Net Present Value $ 6,699,679

Calculation of NPV using MACARS depreciation

35% Tax rate Calculation of annual depreciation Total Depreciation Cost Dep Rate Depreciation Year-1 Year-2 $ 5,700,000 $ 5,700,000 20.00% 32.00% $ 1,140,000 $ 1,824,000 Year-3 Year-4 Year-5 $ 5,700,000 $ 5,700,000 $ 5,700,000 19.20% 11.52% 11.52% $ 1,094,400 $ 656,640 $ 656,640 Year-6 $ 5,700,000 5.76% $ 328,320 $5,700,000 $ $ 5,700,000 5,700,000 Calculation of after-tax salvage value Cost of machine Depreciation WDV Sale price Profit/(Loss) Tax Sale price after-tax $ 638,000 638,000 223,300 414,700 $ Calculation of annual operating cash flow No of units Selling price Operating ost Sale Less: Operating Cost Contribution Year-1 500,000 $ 8.00 $ 1.70 $ 4,000,000 $ 850,000 $ 3,150,000 Year-2 600,000 $ 8.00 $ 1.70 $ 4,800,000 $ 1,020,000 $ 3,780,000 Year-3 800,000 $ 8.00 $ 1.70 $ 6,400,000 $ 1,360,000 $ 5,040,000 Year-4 800,000 $ 8.00 $ 1.70 $ 6,400,000 $ 1,360,000 $ 5,040,000 Year-5 600,000 $ 8.00 $ 1.70 $ 4,800,000 $ 1,020,000 $ 3,780,000 Year-6 400,000 $ 8.00 $ 1.70 $ 3,200,000 $ 680,000 $ 2,520,000 Less: Depreciation Profit before tax Tax@35% Profit After Tax Add Depreciation Cash Profit after-tax $ $ $ $ $ $ 1,140,000 2,010,000 703,500 1,306,500 1,140,000 2,446,500 $ $ $ $ $ $ 1,824,000 $ 1,956,000 $ 684,600 $ 1,271,400 $ 1,824,000 $ 3,095,400 $ 1,094,400 $ 3,945,600 $ 1,380,960 $ 2,564,640 $ 1,094,400 $ 3,659,040 $ 656,640 4,383,360 1,534,176 2,849,184 656,640 3,505,824 $ $ $ $ $ $ 656,640 $ 3,123,360 $ 1,093,176 $ 2,030,184 $ 656,640 $ 2,686,824 $ 328,320 2,191,680 767,088 1,424,592 328,320 1,752,912

Calculation of working capital movement 480,000 Working capital-opening Closing working capital Movement $ $ $ - 600,000 600,000 $ $ $ 600,000 720,000 120,000 $ $ $ 720,000 960,000 240,000 $ $ $ 960,000 960,000 - $ $ $ 960,000 $ 720,000 $ (240,000) $ 720,000 $ 480,000 $ (240,000) $ (480,000) Calculation of NPV Year Capital Working capital Operating cash $ (5,700,000) $ (600,000) $ (120,000) $ 2,446,500 $ (240,000) $ 3,095,400 - $ 3,659,040 240,000 $ 3,505,824 $ 240,000 $ 2,686,824 $ 414,700 $ 480,000 $ 1,752,912 10.00% Annual Cash flo PV factor Present values $ (6,300,000) 1.0000 $ (6,300,000) $ 2,326,500 0.9091 $ 2,115,000 $ 2,855,400 0.8264 $ 2,359,835 $ 3,659,040 0.7513 $ 2,749,091 $ 3,745,824 0.6830 $ 2,558,448 $ 2,926,824 0.6209 $ 1,817,327 $ 2,647,612 0.5645 $ 1,494,508 Net Present Value $ 6,794,209 NPV with MACARS NPV with SLM Increase in NPV $ 6,794,209 $ (6,699,679) $ 94,530