Question

You are financial analyst for a company that is considering supplementing their business of workout equipment production and sales with a new product line of supplements. This is a brand new type of venture that comes with considerable risk. You have been given the following details:

• The project timeline is infinite (meaning the plan is to have the product line forever), but you are going to model the first 5 years specifically. Following that, you may assume NCFs will increase by a terminal growth rate of 1.5% annually forever after, which you will use to calculate the terminal value of the project.

• You have been told to expect sales of 300,000$ during the first year followed by 350,000$ during the second, 400,000$ in the third 450,000 in the fourth, 500,000$ in the fifth and final year. During the first three years, you are to assume cost of goods sold to be 45% of sales, while that number decreases to 35% during the final two years.

• The project initially requires the purchase of three new machines. Machine A costs 500,000$, B costs 400,000$, C costs 100,000$. All three machines can be depreciated as 3 year MACRS property classes. An increase in NWC of 200,000$ will be required up front as well, and NWC of 2/3rd of revenues will be required throughout the five years. Since the project is infinite, you do not recover any at the end of 5 years.

• While machines A and B are expected to last for long time, Machine C has a usable lifespan of 3 years before needing to be replaced. At that time, you expect to be able to sell it for 25,000$. You will immediately be required to purchase another identical machine, which cost 100,000$ and can be depreciated as a 3 year property class as well.

• The firm has a tax rate of 21% that will be applied to this project. You may ignore tax carryover losses, if applicable.

• The WACC is 9.8%.

What is the NPV of the project?

Answer 1

		Initial Cash Out Flow
		Machine A	$500,000
		Machine B	$400,000
		Machine C	$100,000
		Increase in NWC(Net Working Capital)	$200,000
		Total initial cash outflow	$1,200,000
		Analysis of operating cash flow :
	N	Year	1	2	3	4	5
	A	Sales Revenue	$300,000	$350,000	$400,000	$450,000	$500,000
	B=0.45*A from Year1 to 3 & =0.35*A for year 4 &5	Cost of goods sold	$135,000	$157,500	$180,000	$157,500	$175,000
	C=A-B	Before tax operating cash flow	$165,000	$192,500	$220,000	$292,500	$325,000
	D=C*(1-0.21)	After Tax Operating Cash flow	$130,350	$152,075	$173,800	$231,075	$256,750
		Depreciation Tax Shield
	E	MACRS 3 yearDepreciation Rate	33.33%	44.45%	14.81%	7.41%
	F=500000*E	Depreciation of Machine A	$            166,650	$    222,250	$      74,050	$         37,050
	G=400000*E	Depreciation of Machine B	$            133,320	$    177,800	$      59,240	$         29,640
	H=1000008E	Depreciation of Machine C	$              33,330	$      44,450	$      14,810
	I	Depreciation of replacement machine C				$         33,330	$        44,450
	J=F+G+H+I	Total Depreciation expenses	$            333,300	$    444,500	$    148,100	$       100,020	$        44,450
	K=J*0.21	Depreciation Tax Shield	$              69,993	$      93,345	$      31,101	$         21,004	$          9,335
	L=D+K	Net Operating Cash flow considering depreciation	$200,343	$245,420	$204,901	$252,079	$266,085
		Cash flow due to replacement of machine C:
	M=(100000-33330-44450-14810)	Book Value at end of 3 years			$        7,410
	O	Salvage Value at the end of 3 years			$25,000
	P=O-M	Gain on salvage			$17,590
	Q=P*0.21	Tax on gain			$3,694
	R=O-Q	Net Cash inflow due to salvage of machine C			$21,306
	S	Cash flow due to purchase of replacement			($100,000)
	T=(2/3)*A	Net Working capital required	$200,000	$233,333	$266,667	$300,000	$333,333
	U	Cash flow due to change in Net working capital	$0	($33,333)	($33,333)	($33,333)	($33,333)
	V=L+R+S+U	TOTAL CASH FLOW	$200,343	$212,087	$92,874	$218,746	$232,751	SUM
	PV=V/(1.098^N)	Present Value of Cash Flow	$            182,462	$    175,917	$      70,159	$       150,498	$     145,841	$ 724,878
	W	Sum of PV of first 5 years cash flow	$            724,878
	X=W*1.015	Total Cash Flow in Year 6=232751*1.015	$            735,751
	Y=X/(0.098-0.015)	Value of Future cash flows in perpetuity in year5	$        8,864,467
	Z=Y/(1.098^5)	Present Value of Future cash flows from year 6 to infinity	$        5,554,449
	PVT=W+Z	PV of total Cash inflows in future	$        6,279,326
	NPV=PVT-Initial cash outflow	Net Present Value(NPV) of the Project	$        5,079,326	(6279326-1200000)