Question

The Wagner Company currently uses an injection-molding machine that was purchased 2 years ago. This machine is being depreciated on a straight-line basis, and it has 6 years of remaining life. Its current book value is $2,100, and it can be sold for $2,500 at this time. Thus, the annual depreciation expense is $2,100/6=$350 per year. If the old machine is not replaced, it can be sold for $500 at the end of its useful life. Wagner is offered a replacement machine that has a cost of $8,000, an estimated useful life of 6 years, and an estimated salvage value of $800. This machine falls into the MACRS 5-year class, so the applicable depreciation rates are 20%, 32%, 19%, 12%, 11%, and 6%. The replacement machine would permit an output expansion, so sales would rise by $1,000 per year; even so, the new machine’s much greater efficiency would reduce operating expenses by $1,500 per year. The new machine would require that inventories be increased by $2,000, but accounts payable would simultaneously increase by $500. Wagner’s marginal federal-plus-state tax rate is 40%, and its WACC is 15%. Should it replace the old machine?

Please do not do the calculations in excel, I am trying to follow all of the steps through for setting up the NPV equation.

Answer 1

		DEPRECIATION OF OLD MACHINE
		Year from today	1	2	3	4	5	6
	D1	Annual Depreciation expense	$350	$350	$350	$350	$350	$350
		Salvage Value						$500
		DEPRECIATION OF NEW MACHINE
		Year(from today)	1	2	3	4	5	6
	A	Depreciation Rate	20%	32%	19%	12%	11%	6%
	D2=A*$8000	Depreciation amount	$1,600	$2,560	$1,520	$960	$880	$480
		Present value of Cash Flow=(Cash Flow)/((1+i)^N)
		i=discount Rate =WACC =15%=0.15
		N=Year of Cash Flow
	N	Year From Today	1	2	3	4	5	6
	D=D2-D1	Incremental Depreciation	$1,250	$2,210	$1,170	$610	$530	$130
	E=D*40%	Depreciation tax shield	$500	$884	$468	$244	$212	$52
	B	Before tax saving in operating cost	$1,500	$1,500	$1,500	$1,500	$1,500	$1,500
	C	Increase in Sales	$1,000	$1,000	$1,000	$1,000	$1,000	$1,000
	F=B+C	Before tax increase in operating Cash flow	$2,500	$2,500	$2,500	$2,500	$2,500	$2,500
	G=F*(1-0.4)	After tax increase in operating cash flow	$1,500	$1,500	$1,500	$1,500	$1,500	$1,500
		TerminalCash Flows;
		Before tax incremental Salvage Value(800-500)						$300
	H	After tax Incremental Salvage value =300*(1-0.4)						$180
	J	Release of additional working capital(2000-500)						$1,500
	K=H+J	Total TerminalCash Flow						$1,680
	L=E+G+K	Total Cash Inflow	$2,000	$2,384	$1,968	$1,744	$1,712	$3,232	SUM
	M=L/(1.15^N)	Present Value of Cash Inflow	$1,739	$1,803	$1,294	$997	$851	$1,397	$8,081
	PV	Sumof Present Value of Cash inflows	$8,081
		Initial Outlay:
		Cost of new machine	$8,000
		Salvage Value of old machine	($2,500)
		Increase in working capital	$1,500	(2000-500)
	I	Initial Outlay:	$7,000
	NPV=PV-I	Net Present value	$1,081	(8081-7000)
		The Machine Should be replace
		NPV is Positive