Question

You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner (leasing is a very common practice with expensive, high-tech equipment). The scanner costs $5,400,000, and it would be depreciated straight-line to zero over four years. Because of radiation contamination, it actually will be completely valueless in four years. You can lease it for $1,570,000 per year for four years. Assume that the tax rate is 24 percent. Suppose the entire $5,400,000 purchase price of the scanner is borrowed. The rate on the loan is 7 percent, and the loan will be repaid in equal annual installments. Calculate the amount of annual loan repayment. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Complete the schedules given below and calculate the NAL. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16. A negative answer should be indicated by a minus sign.)

Answer 1

Calculation of Equal annual Payments
Loan Amount (P) =			5400000
Loan period=			4 Years
Interest rate = 7% or			0.07
Equal annual Payment =   P*r (1+r)^n
	_______________
	(1+r)^n - 1
	* (1+0.07)^4
	__________________
	(1+0.07)^4    -     1
	5400000 * 0.07	1.31079601
	__________________
	0.31079601
Equal Annual payments =		$15,94,231.83
Amount of annual loan repayment is $1,594,231.83.
Calculation of NPV of Leasing
After tax cost of debt = 7 * (1-0.24) =		5.32
Annual lease =			-1570000
Tax benefit @ 24%=			376800
Net Lease			-1193200
Cumulative P.V.F. @ 5.32% for 4 Years =			3.519750206
Present value of lease for 4 Years =			-4199765.946
Calculation of NPV for buying
Purchase cost			-5400000
Tax benefit of depreciation		324000
(5400000/4*24%)=
Cumulative P.V.F. @ 5.32% for 4 Years =		3.519750206
Present value of tax benefit=			1140399.067
NPV of buying			-4259600.933
Calculation of NAL of leasing
NAL = NPV of leasing - NPV of leasing
-4199765.946	- (-4259600.93)
59834.98736
NAL is $59.834.99. So leasing option should be chosen.