Question

10. Your firm plans to purchase or lease $275,000 worth of excavation equipment. If purchased, the equipment will be depreciated straight-line over five years, after which it is worthless. If leased, the firm will make annual lease payments at the beginning of each of the next five years (first payment today). The lease also requires a security deposit of $20,000 today. The security deposit will be returned at the end of the lease if the asset is returned in acceptable condition (reflecting only normal wear-and-tear). Your cost of borrowing is 7.5%, your marginal tax rate is 21%, and the lease qualifies as a true tax lease. What is the maximum pre- tax lease payment for which you would prefer the lease to the alternative of borrowing money to buy the equipment?

11. Your firm needs a $725,000 machine. If purchased, the machine will be depreciated straight-line over seven years and is expected to have a residual value of $25,000 at the end of the seventh year. Your (pre-tax) cost of borrowing is 6.5% and tax rate is 21%. If this is a non-tax lease, with beginning of year payments, what is the maximum lease payment for which you would prefer the lease to the alternative of borrowing money to buy the machine?

Answer 1

In order to compare the two types of investment, we need to find out the cash flows of both the types:

i) Purchasing the equipment: We get a tax benefit because of the depreciation

							remarks
Year	0	1	2	3	4	5
Purchase of machine	-275000
Depreciation		55000	55000	55000	55000	55000	equals 20% of cost of the machine
Tax saving		11550	11550	11550	11550	11550	equals 21% of depreciation
Total cash flow	-275000	11550	11550	11550	11550	11550
Discount rate	1	0.930233	0.865333	0.804961	0.748801	0.696559	Discount rate of 7.5%
DCF	-275000	10744.19	9994.592	9297.295	8648.646	8045.252	Equals Cash flow * Discount rate
NPV	-228270

Secondly, the cash flow because of the easing would be as follows:

Year	0	1	2	3	4	5
Deposit	-20000					20000
Lease amount		-X	-X	-X	-X	-X
Discount rate	1	0.930233	0.865333	0.804961	0.748801	0.696559
DCF	-20000	-0.93X	-0.87X	-0.8X	-0.75X	13931.17 - 0.7 X

The NPV here would be -6068.83 - 4.046 X

Equating the two NPVs we get -228270 = -6068.83 - 4.046 X

X = 54920

Hence, the maximum pre-tax lease which we would agree to pay would be 54920 before considering the option of purchasing the equipment.