Question

Lease or Buy Wolfson Corporation has decided to purchase a new machine that costs $4.2 million. The machine will be depreciated on a straight-line basis and will be worthless after four years. The corporate tax rate is 35 percent. The Sur Bank has offered Wolfson a four-year loan for $4.2 million. The repayment schedule is four yearly principal repayments of $1.05.million and an interest charge of 9 percent on the outstanding balance of the loan at the beginning of each year. Both principal repayments and interest are due at the end of each year. Cal Leasing Corporation offers to lease the same machine to Wolfson. Lease payments of $1.2 million per year are due at the beginning of each of the four years of the lease. a. Should Wolfson lease the machine or buy it with bank financing? b. What is the annual lease payment that will make Wolfson indifferent to whether it leases the machine or purchases it?

Answer 1

		BORROW AND BUY OPTION
		REPAYMENT SCHEDULE OF LOAN ($4.2 million)
		Year		1	2	3	4
	A	Beginning Balance		$4,200,000	$3,150,000	$2,100,000	$1,050,000
	B=A*9%	Interest		$378,000	$283,500	$189,000	$94,500
	C	Principal=$4.2 million/4		$1,050,000	$1,050,000	$1,050,000	$1,050,000
	D=A-C	Ending Balance		$3,150,000	$2,100,000	$1,050,000	$0
	E=B*(1-0.35)	After Tax interest cost		$245,700	$184,275	$122,850	$61,425
		Depreciation Tax Shield:
		Annual Depreciation =$4.2 million/4	$1,050,000
		Annual Depreciation Tax Shield=1050000*35%	$367,500
		Present Value of Cash Flow =(Cash Flow)/((1+i)^N)
		N=Year of Cash Flow
		i=discount rate=after tax interest paid=9*(1-0.35)	5.85%	0.0585
	N	Year	0	1	2	3	4
		Annual Cash Inflows:
	.(1)	Annual Depreciation tax Shield		$367,500	$367,500	$367,500	$367,500
	,(2)	After tax Interest Cost for amount borrowed		-$245,700	-$184,275	-$122,850	-$61,425
	.(3)	Cash outflow for repayment of principal		-$1,050,000	-$1,050,000	-$1,050,000	-$1,050,000
	CF=(1)+(2)+(3)	PROJECT NET CASH FLOW	$0	-$928,200	-$866,775	-$805,350	-$743,925	SUM
	PV=CF/(1.0585^N)	PRESENT VALUE OF NET CASH FLOW	$0	-$876,901	-$773,615	-$679,066	-$592,606	-$2,922,188
	PW=Sumof PV	Net Present Value(PW) of Costs	-$2,922,188
		LEASE OPTION
	N	Year	0	1	2	3	4
	CF	Lease Payment	($1,200,000)	($1,200,000)	($1,200,000)	($1,200,000)		SUM
	PV=CF/(1.0585^N)	PRESENT VALUE OF NET CASH FLOW	-$1,200,000	-$1,133,680	-$1,071,025	-$1,011,833	$0	-$4,416,537
	PW=Sumof PV	Net Present Value(PW) of Costs	-$4,416,537
	a	BUY IT WITH BANK FINANCING
		Becasuse Present Worth of Costs is less
	b	Annual lease payment that will make it indifferent to the two options:
	PV	Required Present Worth	-$2,922,188
	Rate	Discount Rate	5.85%
	Nper	Number of payments	4
	Type	Beginning of year lease payments	1
	PMT	Annual lease payment that will make it indifferent to the two options:	($793,976.13)	(Using PMT function of excel with Rate =5.85%,Nper=4, Pv=2922188,Type=1)
		Annual lease payment that will make it indifferent to the two options:	$793,976.13
									Clipboard 5 Font Alignment Number Styles Cells Editing H52 =PMT(H49,H50,-H48,,1) L M 4 CF H I J 0 1 2 ($1,200,000) ($1,200,000) ($1,200,000) -$1,200,000 $1,133,680 - $1,071,025 -$4,416,537 K 3 ($1,200,000) $1,011,833 Year Lease Payment PRESENT VALUE OF NET CASH FLOW Net Present Value(PW) of Costs SUM $0 PV=CF/(1.05854N) PW=Sumof PV $4,416,537 BUY IT WITH BANK FINANCING Becasuse Present Worth of Costs is less Annual lease payment that will make it indifferent to the two options: -$2,922,188 5.85% PV Rate Nper Type Required Present Worth Discount Rate Number of payments Beginning of year lease payments Annual lease payment that will make it indifferent to the two options: Annual lease navment that will make it indifferent PMT ($793,976.13)! (Using PMT function of excel with Rate =5.85%, Nper=4, Pv=2922188, Type=1)