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 $549,000. 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 $1.60 per trap and believes that the traps can be sold for $6 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	0.8	1.0	1.0	0.5	0.3	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.)

Answer 1

Scenario 1: Net working Capital of each date is equal to 10% of next year forecast sale

Year	0	1	2	3	4	5	6	Thereafter
Sales (No. Millions of Traps)	0	0.6	0.8	1	1	0.5	0.3	0
Sales Revenue (No.of traps*$6) (In Million $)	$           -	$      3.60	$      4.80	$      6.00	$      6.00	$      3.00	$      1.80
Cost of Goods Sold (No.of traps*$1.6) (In Million $)	$           -	$      0.96	$      1.28	$      1.60	$      1.60	$      0.80	$      0.48
EBITDA (Revenue - COGS)	$           -	$      2.64	$      3.52	$      4.40	$      4.40	$      2.20	$      1.32
Initial Investment (In Million $) CapEx	$       6.30
Depreciation		$      1.05	$      1.05	$      1.05	$      1.05	$      1.05	$      1.05
Book Value of Equipment	$       6.30	$      5.25	$      4.20	$      3.15	$      2.10	$      1.05	$          -
Salvage Value							$   0.549
After Tax Salvage Value							$   0.357
CapEx (Net Capital Expenditure)	$       6.30	$          -	$          -	$          -	$          -	$          -	$    (0.36)	The after tax salvage value is a loss/expenditure if its value if negative else it is an profit/income. Hence it is recorded with opposite sign in the CapEx column
Net Working Capital (NWC)	$       0.36	$      0.48	$      0.60	$      0.60	$      0.30	$      0.18	$          -
Increase in NWC (NWCt-NWCt-1)	$       0.36	$      0.12	$      0.12	$          -	$    (0.30)	$    (0.12)	$    (0.18)
Tax Rate (T)	35%	35%	35%	35%	35%	35%	35%
EBIT (Revenue-COGS-Depreciation)	$           -	$      1.59	$      2.47	$      3.35	$      3.35	$      1.15	$      0.27
NOPLAT (EBIT*(1-T))	$           -	$      1.03	$      1.61	$      2.18	$      2.18	$      0.75	$      0.18
FCF (NOPLAT+Depreciation-CAPEX-Increase in NWC)	$     (6.66)	$      1.96	$      2.54	$      3.23	$      3.53	$      1.92	$      1.76
Req Rate of Return (r)	10%
PV of each FCF @ 10% discount rate	-6.66	1.785	2.095455	2.424869	2.40933	1.190617	0.994801
NPV of the project (In Million $)	$ 4.2401	<- Sum of all the PV's

NPV of the project in the scenario 1 = $ 4.2401 Million

Scenario 2: Net working Capital of each date is equal to half of that of the scenario 1

Year	0	1	2	3	4	5	6	Thereafter
Sales (No. Millions of Traps)	0	0.6	0.8	1	1	0.5	0.3	0
Sales Revenue (No.of traps*$6) (In Million $)	$           -	$      3.60	$      4.80	$      6.00	$      6.00	$      3.00	$      1.80
Cost of Goods Sold (No.of traps*$1.6) (In Million $)	$           -	$      0.96	$      1.28	$      1.60	$      1.60	$      0.80	$      0.48
EBITDA (Revenue - COGS)	$           -	$      2.64	$      3.52	$      4.40	$      4.40	$      2.20	$      1.32
Initial Investment (In Million $) CapEx	$       6.30
Depreciation		$      1.05	$      1.05	$      1.05	$      1.05	$      1.05	$      1.05
Book Value of Equipment	$       6.30	$      5.25	$      4.20	$      3.15	$      2.10	$      1.05	$          -
Salvage Value							$   0.549
After Tax Salvage Value							$   0.357
CapEx (Net Capital Expenditure)	$       6.30	$          -	$          -	$          -	$          -	$          -	$    (0.36)	The after tax salvage value is a loss/expenditure if its value if negative else it is an profit/income. Hence it is recorded with opposite sign in the CapEx column
Net Working Capital (NWC)	$       0.18	$      0.24	$      0.30	$      0.30	$      0.15	$      0.09	$          -
Increase in NWC (NWCt-NWCt-1)	$       0.18	$      0.06	$      0.06	$          -	$    (0.15)	$    (0.06)	$    (0.09)
Tax Rate (T)	35%	35%	35%	35%	35%	35%	35%
EBIT (Revenue-COGS-Depreciation)	$           -	$      1.59	$      2.47	$      3.35	$      3.35	$      1.15	$      0.27
NOPLAT (EBIT*(1-T))	$           -	$      1.03	$      1.61	$      2.18	$      2.18	$      0.75	$      0.18
FCF (NOPLAT+Depreciation-CAPEX-Increase in NWC)	$     (6.48)	$      2.02	$      2.60	$      3.23	$      3.38	$      1.86	$      1.67
Req Rate of Return (r)	10%
PV of each FCF @ 10% discount rate	-6.48	1.839545	2.145041	2.424869	2.306878	1.153361	0.943998
NPV of the project (In Million $)	$ 4.3337	<- Sum of all the PV's

NPV of the project in the scenario 2 = $ 4.3337 Million

Thus the increase in the project NPV = 4.337 - 4.2401 = $ 0.0936 Million