Question

Suppose Proctor​ & Gamble​ (P&G) is considering purchasing $ 10 million in new manufacturing equipment. If it purchases the​ equipment, it will depreciate it for tax purposes on a​ straight-line basis over five​ years, after which the equipment will be worthless. It will also be responsible for maintenance expenses of $ 1.00 million per​ year paid in each of the years 1 through 5. It can also lease the equipment under a true tax lease for ​$2.6 million per year for the five​ years, in which case the lessor will provide necessary maintenance. Assume​ P&G's tax rate is 30 % and its borrowing cost is 7.0 %

a. What is the NPV associated with leasing the equipment versus financing it with the​ lease-equivalent loan?

b. What is the​ break-even lease rate long—that ​is, what lease amount could​ P&G pay each year and be indifferent between leasing and financing a​ purchase?

Answer 1

a). NPV of leasing vs financing with lease-equivalent loan = 2,145,497.73

Formula	Year (n)	0	1	2	3	4	5
	Buy
	Capital expenditure (CE)	-10000000
	Maintenance expense (ME)		-1000000	-1000000	-1000000	-1000000	-1000000
(1-Tax rate)*ME	After-tax maintenance expense (AME)		-700000	-700000	-700000	-700000	-700000
-(CE*Tax rate)/5	Depreciation tax shield (DTS)		600000	600000	600000	600000	600000
CE + DTS	Free Cash Flow (FCF)	-10000000	-100000	-100000	-100000	-100000	-100000
	Lease
	Lease payment (LP)	-2600000	-2600000	-2600000	-2600000	-2600000	0
LP*Tax rate	Tax saving (TS)	780000	780000	780000	780000	780000	0
LP + TS	Free Cash Flow (FCF)	-1820000	-1820000	-1820000	-1820000	-1820000	0
FCF (Lease) - FCF (Buy)	FCF (Lease - Buy)	8180000	-1720000	-1720000	-1720000	-1720000	100000
Borowing rate*(1-Tax rate)	Discounting rate (rd)	4.90%	4.90%	4.90%	4.90%	4.90%	4.90%
1/(1+rd)^n	Discount factor @ rd	1.000	0.953	0.909	0.866	0.826	0.787
FCF(Lease - Buy)*Discount factor	PV of FCF	8180000	-1639657	-1563067	-1490054	-1420452	78726.79
Sum of all PVs	NPV	2145497.73

b). Using the above table, with Solver (or trial and error), we find that there is no positive break-even rate.