Question

The Olney Company purchased a machine 3 years ago at a cost of $150,000. It had an expected life of 10 years at the time of purchase and an expected salvage value of $5,000.    The existing machine costs $54,000 year to run and generates $1,000,000 a year in revenue with a gross profit margin of 20%.   The old machine can be sold today for $55,000 and the expectation is that it can be sold for $7,500 in 7 years.

A new machine with a 7 year life can be purchased for $225,000. Cash operating expenses will be $65,000 per year. The new machine will boost revenue to $1,075,000 in the first three years of operation and then revenue of the new machine will increase to $1,090,000 per annum for the balance of machine’s life. The machine has a gross profit margin of 23% due to fewer defects. At the end of its useful life, the machine will have no value. The firm's tax rate is 34 percent. Straight-line depreciation is used for all assets. The firm’s WACC is 12 percent. The firm has an ACP of 63 days and pays its bills after 25 days.

Calculate project’s NPV and IRR.

The firm reduces its ACP to 55 days and starts to pay its bills after 30 days. What will be the project’s NPV ?

Answer 1

		We need to find incremental cash flow for the new machine compared to the old machine
	STEP 1	Initial Investment:
		Cost of new machine	$225,000
		Before tax cash flow of old machine	$55,000
		Depreciation for 3 years((150000-5000)/10)*3	$            43,500
		Current book value=(150000-43500)	$          106,500
		Tax saving for loss on sale	$            17,510	(106500-55000)*0.34
	ICF	Cash flow for initial investment(Year0) today	($152,490)	(225000-55000-17510)
	STEP2	Incremental annual cash flow;
		Year	0	1	2	3	4	5	6	7
	A	Revenue from new machine		$1,075,000	$1,075,000	$1,075,000	$1,090,000	$1,090,000	$1,090,000	$1,090,000
	B=0.23*A	Gross Profit from new machine(23%)		$247,250	$247,250	$247,250	$250,700	$250,700	$250,700	$250,700
	C	Cash operating expenses		$65,000	$65,000	$65,000	$65,000	$65,000	$65,000	$65,000
	D=B-C	Cash inflow from new machine		$182,250	$182,250	$182,250	$185,700	$185,700	$185,700	$185,700
	E	Revenue from old machine		$1,000,000	$1,000,000	$1,000,000	$1,000,000	$1,000,000	$1,000,000	$1,000,000
	F=0.2*E	Gross Profit from oldmachine(20%)		$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000
	G	Cash operating expenses		$54,000	$54,000	$54,000	$54,000	$54,000	$54,000	$54,000
	H=F-G	Cash inflow from old machine		$146,000	$146,000	$146,000	$146,000	$146,000	$146,000	$146,000
	I=D-H	Before tax annual savings		$36,250	$36,250	$36,250	$39,700	$39,700	$39,700	$39,700
	J=I*(1-0.34)	After tax annual savings		$23,925	$23,925	$23,925	$26,202	$26,202	$26,202	$26,202
	STEP 3	Deprteciation tax shield:
	K=225000/7	Depreciation of new machine		$        32,143	$         32,143	$      32,143	$      32,143	$       32,143	$        32,143	$       32,143
	L=0.34*K	Depreciation tax shield		$        10,929	$         10,929	$      10,929	$      10,929	$       10,929	$        10,929	$       10,929
	M	Depreciation of old machine(106500-7500)/7		$        14,143	$         14,143	$      14,143	$      14,143	$       14,143	$        14,143	$       14,143
	P=M*0.34	Loss of depreciiation tax shield on old machine		$           4,809	$           4,809	$         4,809	$        4,809	$         4,809	$          4,809	$          4,809
	Q=L-P	Net Cash flow from depreciation tax shield		$           6,120	$           6,120	$         6,120	$        6,120	$         6,120	$          6,120	$          6,120
	STEP 4	Terminal Cash Flow:
	R	Terminal cash flow from new machine								$0
	S	Terminal cash flow from old machine								$7,500
	T=R-S	Net Terminal Cash flow								($7,500)
	STEP 5	Cash flow due to working capital:
	U=(63/365)*(A-E)	Accounts receivable increase for new machine		$12,945	$12,945	$12,945	$15,534	$15,534	$15,534	$15,534
	V=(25/365)*(A-B)	Average accounts payable for new machine		$56,695	$56,695	$56,695	$57,486	$57,486	$57,486	$57,486
	W=(25/365)*(E-F)	Average Accounts payable for old machine		$54,795	$54,795	$54,795	$54,795	$54,795	$54,795	$54,795
	X=V-W	Increase in working capital due to new machine		$1,901	$1,901	$1,901	$2,692	$2,692	$2,692	$2,692
	Y=U-X	Net increase in working capital		$11,045	$11,045	$11,045	$12,842	$12,842	$12,842	$12,842
	Z	Cash flow due to working capital	($11,045)			($1,798)				$12,842
		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Discount Rate=WACC=12%=0.12
		N=Year of Cash Flow
	N	Year	0	1	2	3	4	5	6	7
	CF=ICF+J+Q+T+Z	Total Cash Flow	($163,535)	$30,045	$30,045	$28,247	$32,322	$32,322	$32,322	$37,664	SUM
	PV=CF/(1.12^N)	Present Value of Cash Flow	$       (163,535)	$        26,826	$         23,952	$      20,106	$      20,541	$       18,340	$        16,375	$       17,037	$ (20,357)
	NPV	Net Present Value=Sum of PV of cash flows	$          (20,357)
	IRR	Internal Rate of Return(Using excel IRR functionover Cash flows)	8.10%