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	0.6	0.8	0.9	0.9	0.5	0.2	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

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