Better Mousetraps has developed a new trap. It can go into production for an ini
ID: 2716162 • Letter: B
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 $695,000. 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 $1.80 per trap and believes that the traps can be sold for $7 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 11%.
Use the MACRS depreciation schedule. (
Year: 0 1 2 3 4 5 6 Thereafter
Sales (millions of traps) 0 .6 .8 .9 .9 .5 .2 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.) NPV $ million
Explanation / Answer
Basic calculations Investment cost 6300000 Depreciation no of years 6 residual value 695000 Working capital 10% of next year sales Production cost per unit 1.8 Selling price 7 Tax rate 35% Cost of capital 11% Sales in Units (Million of Traps) 0.6 0.8 0.9 0.9 0.5 0.2 Sales in Units 600000 800000 900000 900000 500000 200000 Depreciation rate MACRS A Calculation of net present value (Amount in Dollars) Particulars 1 Years 1 2 3 4 5 6 2 Sales in Units (Million of Traps) 0.6 0.8 0.9 0.9 0.5 0.2 3 Sales in units (units*1000000) 600000 800000 900000 900000 500000 200000 4 Selling price per unit 7 7 7 7 7 7 5 Sales in value 4200000 5600000 6300000 6300000 3500000 1400000 6 Total revenue 4200000 5600000 6300000 6300000 3500000 1400000 7 Expenses 8 Production cost per unit 1.8 1.8 1.8 1.8 1.8 1.8 9 Total production cost ( No of units * Production cost per unit ) 1080000 1440000 1620000 1620000 900000 360000 10 Change in Working capital ( Note 2 ) 140000 70000 0 -280000 -210000 -140000 11 Depreciation ( Note 1 ) 1260000 2016000 1209600 725760 725760 362880 12 Total expenditure 2480000 3526000 2829600 2065760 1415760 582880 13 Profit (Total revenue - Total expenditure) 1720000 2074000 3470400 4234240 2084240 817120 14 Tax rate at 35 % on profits 602000 725900 1214640 1481984 729484 285992 15 Net profit after tax ( Profit - Tax ) 1118000 1348100 2255760 2752256 1354756 531128 16 ADD : Depreciation ( Non Cash expenditure ) 1260000 2016000 1209600 725760 725760 362880 18 Residual value on 6th year 695000 19 Net cash inflows ( Net profit after tax + Depreciation + Working capital of 6th year for year 6 ) 2378000 3364100 3465360 3478016 2080516 1589008 20 Present value discount factors at 11 % 0.9009 0.8116 0.7312 0.6587 0.5935 0.5346 21 Present value of cash inflows ( Net cash flows * Present value of discount factors 2142342 2730379 2533841 2291077 1234685 849549 22 Present value of cash inflows of 6 years 11781873 23 Present value of cash outflows a Cost of equipment 6300000 b Working capital investment 10 % of 1st sales ( 4200000*10%) 420000 c Total present value of working capital 6720000 6720000 d Net present value = Total present value of cash inflows - Total present value of cash outflows 5061873 Note 1 Cost of the equipment = 6300000 Depreciation method MACRS Depreciation schedule Years 1 2 3 4 5 6 Depreciation rate in percentage 20 32 19.2 11.52 11.52 5.76 Cost of the equipment 6300000 6300000 6300000 6300000 6300000 6300000 Depreciation 1260000 2016000 1209600 725760 725760 362880 Note 2 Working capital Years 0 1 2 3 4 5 6 Working capital expenditure 10 % of next year sales 420000 560000 630000 630000 350000 140000 Change in working capital ( Current year working capital requirement - previous working capital amount ) 140000 70000 0 -280000 -210000 -140000 Note Working capital is 10 % of sales of the next year, so in 0 year working capital is 10% of 1st year, also the same is capital cash outflow. Form 2nd year onwards only changes in the working capital from year to year has been considered as expenditure in calculations. If the firm cuts the working capital by 50 % A Calculation of net present value (Amount in Dollars) Particulars 1 Years 1 2 3 4 5 6 2 Sales in Units (Million of Traps) 0.6 0.8 0.9 0.9 0.5 0.2 3 Sales in units (units*1000000) 600000 800000 900000 900000 500000 200000 4 Selling price per unit 7 7 7 7 7 7 5 Sales in value 4200000 5600000 6300000 6300000 3500000 1400000 6 Total revenue 4200000 5600000 6300000 6300000 3500000 1400000 7 Expenses 8 Production cost per unit 1.8 1.8 1.8 1.8 1.8 1.8 9 Total production cost ( No of units * Production cost per unit ) 1080000 1440000 1620000 1620000 900000 360000 10 Change in Working capital ( Note 2 ) 70000 35000 0 -140000 -105000 -70000 11 Depreciation ( Note 1 ) 1260000 2016000 1209600 725760 725760 362880 12 Total expenditure 2410000 3491000 2829600 2205760 1520760 652880 13 Profit (Total revenue - Total expenditure) 1790000 2109000 3470400 4094240 1979240 747120 14 Tax rate at 35 % on profits 626500 738150 1214640 1432984 692734 261492 15 Net profit after tax ( Profit - Tax ) 1163500 1370850 2255760 2661256 1286506 485628 16 ADD : Depreciation ( Non Cash expenditure ) 1260000 2016000 1209600 725760 725760 362880 18 Residual value on 6th year 695000 19 Net cash inflows ( Net profit after tax + Depreciation + Working capital of 6th year for year 6 ) 2423500 3386850 3465360 3387016 2012266 1543508 20 Present value discount factors at 11 % 0.900900901 0.811622433 0.731191381 0.658730974 0.593451328 0.5346 21 Present value of cash inflows ( Net cash flows * Present value of discount factors 2183333 2748843 2533841 2231132 1194182 825222 22 Present value of cash inflows of 6 years 11716555 23 Present value of cash outflows a Cost of equipment 6300000 b Working capital investment 10 % of 1st sales ( 4200000 * 5% ) 240000 c Total present value of working capital 6540000 6540000 d Net present value = Total present value of cash inflows - Total present value of cash outflows 5176555 Note 2 Working capital Years 0 1 2 3 4 5 6 Working capital expenditure 5 % of next year sales 210000 280000 315000 315000 175000 70000 Change in working capital ( Current year working capital requirement - previous working capital amount ) 70000 35000 0 -140000 -105000 -70000
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