Question

BETTER MOUSETRAPS HAS DEVELOPED A NEW TRAP. IT CAN GO INTO PRODUCTION FOR AN INITIAL INVESTMENT IN EQUIPMENT OF 6 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 $500,000. 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 COST EQUAL TO $1.50 PER TRAP AND BELIEVES THAT THE TRAPS CAN BE SOLD FOR $4 EACH. SALES FORECASTS ARE YEAR 1 0.5, YEAR 2 0.6, YEAR 3 1.0, YEAR 4 1.0, YEAR 5 0.6, YEAR 6 0.2 AND THEREAFTER 0. THE PROJECT WILL COME TO AN END IN 5 YEARS WHEN THE TRAP BECOMES TECHNOLOGICALLY OBSOLETE. THE FIRM'S TAX BRACKET IS 35%, AND THE REQUIRED RATE OF RETURN ON THE PROJECT IS 12%. WHAT IS THE PROJECT NPV? WHAT IS THE IRR? WHAT IS PAYBACK IN YEARS?

Answer 1

1]	[$ in millions]	0	1	2	3	4	5	6
	Sales in millions of units		0.5000	0.6000	1.0000	1.0000	0.6000	0.2000
	Sales revenue		$          2.0000	$          2.4000	$           4.0000	$        4.0000	$        2.4000	$        0.8000
	-Production cost		$          0.7500	$          0.9000	$           1.5000	$        1.5000	$        0.9000	$        0.3000
	-Depreciation		$          1.0000	$          1.0000	$           1.0000	$        1.0000	$        1.0000	$        1.0000
	=NOI		$          0.2500	$          0.5000	$           1.5000	$        1.5000	$        0.5000	$      -0.5000
	-Tax at 35%		$          0.0875	$          0.1750	$           0.5250	$        0.5250	$        0.1750	$      -0.1750
	=NOPAT		$          0.1625	$          0.3250	$           0.9750	$        0.9750	$        0.3250	$      -0.3250
	+Depreciation		$          1.0000	$          1.0000	$           1.0000	$        1.0000	$        1.0000	$        1.0000
	=OCF		$          1.1625	$          1.3250	$           1.9750	$        1.9750	$        1.3250	$        0.6750
	-Capital expenditure	$          6.0000							Total
	-Change in NWC	$          0.2000	$          0.0400	$          0.1600	$                    -	$      -0.1600	$      -0.1600	$      -0.0800	$                 -
	+After tax salvage value = 0.5*(1-35%)							$        0.3250
	=FCF	$        -6.2000	$          1.1225	$          1.1650	$           1.9750	$        2.1350	$        1.4850	$        1.0800	$        2.7625
	PVIF at 12% [PVIF = 1/1.12^t]	1	0.89286	0.79719	0.71178	0.63552	0.56743	0.50663
	PV at 12%	$        -6.2000	$          1.0022	$          0.9287	$           1.4058	$        1.3568	$        0.8426	$        0.5472	$      -0.1166
	NPV	$        -0.1166
2]	IRR is that discount rate for which NPV is 0. It has to be found out by trial and error.
	Discounting at 11%:
	PVIF at 11%	1	0.90090	0.81162	0.73119	0.65873	0.59345	0.53464
	PV at 11%	$        -6.2000	$          1.0113	$          0.9455	$           1.4441	$        1.4064	$        0.8813	$        0.5774	$        0.0660
	IRR lies between 11% and 12%.
	By simple interpolation IRR = 11%+1%*0.0660/(0.0660+0.1166) =			11.36%
3]	Cumulative cash flows	$        -6.2000	$        -5.0775	$        -3.9125	$         -1.9375	$        0.1975	$        1.6825	$        2.7625
	Payback period = 3+1.9375/2.1350 =	3.91	Years
4]	Recommendation:
	As the NPV is negative, the project should not be undertaken.
	Note:
	The details regarding sales are given for 6 years. But, in the last portion it is said the trap will become obsoleted in 5 years.
	The period of the project is taken as 6 years in line with the sales figures. The salvage value of the machine is also at EOY 6.