Question

1. The WeDream Company has spent $10 million, a big sunk cost, in research and development, and has successfully invented a new electronic device. It is thinking of building a plant to produce this new device. The plant and equipment will cost $5 million. It will last for ten years and will have no salvage value at the end of that time.The land the plant will be built on could be rented out for $300,000 per year before taxes for the ten years while the plant is in production. The costs of running the plant are expected to be $2.5 million per year. The total working capital required to allow inventories to be financed during the first year of production is $150,000. From the second year to the eighth year when the plan is in production, the total working capital needs will be 10% higher each year. In the ninth year, the total working capital needs will drop by 50%, and in the tenth year, the plant will stop production, and the working capital requirement will drop to zero. When the plant ceases production all the working capital can be recovered. The revenues from selling the devices are expected to be $6.75 million per year. All cash flows occur at the end of the year. The company uses straight line depreciation. Its corporate tax rate is 35 percent and the opportunity cost of capital for this project is 10 percent.

   Should the WeDream Company build the plant?

Answer 1

		Present Value(PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=discount rate=Cost of Capital=10%=0.10
		N=Year   of Cash Flow
		$10 million spent is sunk cost and not relevant for this decision
		Before tax Rent of Land	$300,000
		After tax Rent of land =300000*(1-0.35)	$195,000
		Opportunity cost of using the land	$195,000
	A	Cost of Plant and Equipment	$5,000,000
	B	Salvage Value	$0
	C=(A-B)/10	Annual depreciation	$500,000
		N=Year   of Cash Flow
	N	Year	0	1	2	3	4	5	6	7	8	9	10
		Initial investment:
	A	Investment in production facilities	-$5,000,000
	b	Annual Revenue		$6,750,000	$6,750,000	$6,750,000	$6,750,000	$6,750,000	$6,750,000	$6,750,000	$6,750,000	$6,750,000	$6,750,000
	c	Annual Cost (Before Depreciation)		-$2,500,000	-$2,500,000	-$2,500,000	-$2,500,000	-$2,500,000	-$2,500,000	-$2,500,000	-$2,500,000	-$2,500,000	-$2,500,000
	d	Depreciation Expenses		-$500,000	-$500,000	-$500,000	-$500,000	-$500,000	-$500,000	-$500,000	-$500,000	-$500,000	-$500,000
	e=b+c+d	Before tax Operating Income		$3,750,000	$3,750,000	$3,750,000	$3,750,000	$3,750,000	$3,750,000	$3,750,000	$3,750,000	$3,750,000	$3,750,000
	f=e*(1-0.35)	After Tax Operating Income		$2,437,500	$2,437,500	$2,437,500	$2,437,500	$2,437,500	$2,437,500	$2,437,500	$2,437,500	$2,437,500	$2,437,500
	g	Add : Depreciation (non cash expense)		$500,000	$500,000	$500,000	$500,000	$500,000	$500,000	$500,000	$500,000	$500,000	$500,000
	H=f+g	Annual Operating Cash Flow		$2,937,500	$2,937,500	$2,937,500	$2,937,500	$2,937,500	$2,937,500	$2,937,500	$2,937,500	$2,937,500	$2,937,500
	I	Opportunity cost of use of land		-$195,000	-$195,000	-$195,000	-$195,000	-$195,000	-$195,000	-$195,000	-$195,000	-$195,000	-$195,000
	j	Working Capital need		$150,000	$165,000	$181,500	$199,650	$219,615	$241,577	$265,734	$292,308	$146,154	$0
	K	Working Capital Cash Flow		-$150,000	-$15,000	-$16,500	-$18,150	-$19,965	-$21,962	-$24,158	-$26,573	$146,154	$146,154
	CF=A+H+I+K	Net Cash Flow	-$5,000,000	$2,592,500	$2,727,500	$2,726,000	$2,724,350	$2,722,535	$2,720,539	$2,718,342	$2,715,927	$2,888,654	$2,888,654	SUM
	PV=CF/(1.1^N)	Present Valure	-$5,000,000	$2,356,818	$2,254,132	$2,048,084	$1,860,768	$1,690,480	$1,535,673	$1,394,939	$1,267,000	$1,225,071	$1,113,701	$11,746,667
	NPV=Sum of PV	Net Present Value(NPV)	$11,746,667
		WeDream Company should build the plant
		NPV is Positive