Question

Your firm is considering producing a new variety of widget. You have already test marketed

the widgets at a cost of $90,000. You estimate sales will be $500,000 in the first year, $800,000

in the second year, $500,000 in the third year, and zero after three years.

To produce the new widgets will require an investment in working capital at year 0 of $50,000.

Net working capital will be 20% of sales in years 1 and 2. Labor, materials, and selling

expenses will be 60% of sales. An additional $80,000 in promotional expenses will be incurred

in the first year of production.

You already own sufficient widget-producing equipment to produce the new variety of widget.

The equipment was purchased for $1 million, has a book value of $600,000, and is being

depreciated at the rate of $200,000 per year. You don't anticipate any use for the surplus

capacity of this equipment other than this new variety of widget.

To produce the new widgets, you will, however, need additional packaging equipment. The

equipment costs $100,000. It will be depreciated straight-line to zero over two years, beginning

in the first year of production. The equipment will have no value after three years.

Production will also require the use of warehouse space. If this space is not used for the new

widgets, it can be rented for $40,000 per year.

The tax rate is 40% and the cost of capital is 12%

Keeping everything constant from the first problem and only focusing on the incremental changes what is the NPV of this change?

Answer 1

		Present Value(PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=discount rate =12%=0.12
		N=Year   of Cash Flow
		Annual Depreciation of packaging Equipment	$50,000	(100000/2)
		Depreciation tax shield for two years	$20,000	(50000*40%)
		Cost of test marketing ($90,000) is a sunk cost and not relevant for this analysis
		Old Machine book value and depreciation are not relevant
		CASH FLOW ANALYSIS OF THE PROJECT
	N	Year	0	1	2	3
	a	Cash Flow for packaging Equipment	-$100,000
	b	Initial cash flow for working capital	-$50,000
	C=a+b	Total initial cash flow	-$150,000
	d	Annual Sales		$500,000	$800,000	$500,000
	e=60%*d	Annual Labor material and selling expenses		-$300,000	-$480,000	-$300,000
	f	Additional Promotional expense		-$80,000
	g=d+e+f	Before tax operating profit		$120,000	$320,000	$200,000
	h=-g*40%	Tax Expenses		-$48,000	-$128,000	-$80,000
	i=g+h	After tax operating profit		$72,000	$192,000	$120,000
	j	Add depreciation Tax Shield		$20,000	$20,000
	K=i+j	Annual Operating Cash Flow		$92,000	$212,000	$120,000
	L	Add: After tax Opportunity cost of Using Warehouse(40000*(1-0.4)		$24,000	$24,000	$24,000
	m	Working Capital Need		$100,000	$160,000
	W	Working Capital Cash Flow in Year1,2 and3		-$50,000	-$60,000	$160,000
	CF=C+K+L+W	Net Cash Flow	($150,000)	$66,000	$176,000	$304,000	SUM
	PV=CF/(1.12^N)	Present Value of Net Cash Flow	($150,000)	$58,929	$140,306	$216,381	$265,616
	NPV=Sum of PV	Net Present Value(NPV)	$265,616