Question

Lewis Securities Inc. has decided to acquire a new market data and quotation system for its Richmond home office. The system receives current market prices and other information from several online data services and then either displays the information on a screen or stores it for later retrieval by the firm’s brokers. The system also permits customers to call up current quotes on terminals in the lobby.

The equipment costs $1,000,000 and, if it were purchased, Lewis could obtain a term loan for the full purchase price at a 10% interest rate. Although the equipment has a 6-year useful life, it is classified as a special-purpose computer and therefore falls into the MACRS 3-year class. If the system were purchased, a 4-year maintenance contract could be obtained at a cost of $20,000 per year, payable at the beginning of each year. The equipment would be sold after 4 years, and the best estimate of its residual value is $200,000. However, because real-time display system technology is changing rapidly, the actual residual value is uncertain.

As an alternative to the borrow-and-buy plan, the equipment manufacturer informed Lewis that Consolidated Leasing would be willing to write a 4-year guideline lease on the equipment, including maintenance, for payments of $260,000 at the beginning of each year. Lewis’s marginal federal-plus-state tax rate is 40%. You have been asked to analyze the lease-versus-purchase decision and, in the process, to answer the following question

1. What is the present value of owning the equipment? (Hint: Set up a time line that shows the net cash flows over the period to , and then find the PV of these net cash flows, or the PV cost of owning.)  

2. What is Lewis’s present value of leasing the equipment? (Hint: Again, construct a time line.)

Answer 1

1.NPV of owing the equipment is calculated as follows,

NPV = Present Value of cash inflows- Present value of cash outflows

Year	1	2	3	4
Depreciation	333,300.00	444,500.00	148,100.00	74,100.00
A. Tax Savings on depreciation	133,320.00	177,800.00	59,240.00	29,640.00
Maintenance cost	20,000.00	20,000.00	20,000.00	20,000.00
Tax on Maintenance cost	8,000.00	8,000.00	8,000.00	8,000.00
B. After tax Maintenance cost	12,000.00	12,000.00	12,000.00	12,000.00
Loan amount	1,000,000.00	784,529.20	547,511.31	286,791.64
Loan repayment	315,470.80	315,470.80	315,470.80	315,470.80
Loan interest repayment	100,000.00	78,452.92	54,751.13	28,679.16
C. Loan Principal repayment	215,470.80	237,017.88	260,719.67	286,791.64
Tax on Loan interest repayment	40,000.00	31,381.17	21,900.45	11,471.67
D. After tax Loan interest repayment	60,000.00	47,071.75	32,850.68	17,207.50
E. After tax Salvage value	-	-	-	120,000.00
Net cashflow (A-B-C-D+E)	(154,150.80)	(118,289.64)	(246,330.35)	(166,359.14)
PV factor @ 6%	0.943	0.890	0.840	0.792
PV of Net cashflow	(145,425.29)	(105,277.35)	(206,823.71)	(131,772.02)
NPV @ 6%	(589,298.37)

Depreciation is calculated as follows,

Year	Opening Book value	Depreciation rate	Depreciation	Closing Book value
1	1,000,000.00	33.33	333,300.00	666,700.00
2	666,700.00	44.45	444,500.00	222,200.00
3	222,200.00	14.81	148,100.00	74,100.00
4	74,100.00	7.41	74,100.00	-

Annual loan payment is calculated as follows,

Annual loan payment =P*r*((1+r)ⁿ/((1+r)ⁿ-1))

Where,

P means Principal

r means interest rate per year

n means no. of years

Annual loan payment =P*r*((1+r)ⁿ/((1+r)ⁿ-1))

Annual loan payment =10,00,000*0.10*((1+0.10)⁴/((1+0.10)⁴-1))

Annual loan payment =$3,15,470.80

Annual tax savings from maintenance is calculated as follows,

Annual tax savings from maintenance = Annual maintenance expense*Corporate tax rate

Annual tax savings from maintenance =20,000*0.40

Annual tax savings from maintenance =$8,000

After tax Salvage value is calculated as follows,

Particulars	Amount
Cost of Equipment	1,000,000
Total accumulated depreciation	1,000,000
Book value	-
Sale value	200,000
Gain on sale	200,000
Tax on Gain @ 40%	80,000
After tax Salvage value	120,000

Cost of capital is calculated as follows,

Cost of capital =Kd*(1-tax rate)

Cost of capital =10*(1-0.40)

Cost of capital = 6%

2. NPV cost of leasing the equipment is calculated as follows,

NPV = Present Value of cash inflows- Present value of cash outflows

Year	Lease payment	After tax lease payment	PV factor @ 6%	PV of After tax lease payment
1	260000	156000	0.943	147,169.81
2	260000	156000	0.890	138,839.44
3	260000	156000	0.840	130,980.61
4	260000	156000	0.792	123,566.61
NPV of lease	540,556.48

In the lease-versus-purchase decision, it is better to go ahead with lease as it is cheaper