Question

Big Sky Mining Company must install $1.5 million of new machinery in its Nevada mine. It can obtain a bank loan for 100% of the purchase price, or it can lease the machinery. Assume that the following facts apply.

(1) The machinery falls into the MACRS 3-year class.

(2) Under either the lease or the purchase, Big Sky must pay for insurance, property taxes, and maintenance.

(3) The firm’s tax rate is 25%.

(4) The loan would have an interest rate of 15%. It would be nonamortizing, with only interest paid at the end of each year for four years and the principal repaid at Year 4.

(5) The lease terms call for $400,000 payments at the end of each of the next 4 years.

(6) Big Sky Mining has no use for the machine beyond the expiration of the lease, and the machine has an estimated residual value of $250,000 at the end of the 4th year.

a. What is the cost of owning?

b. What is the cost of leasing?

c. What is the NAL of the lease?

d. Provide an analysis to prove that the NPV of the lease to the lessor is the same (except for (+) (-) sign) as that of the lessee.

Answer 1

	Discount rate = 15%*(1-25%) =	11.25%
a]	COST OF OWNING:	0	1	2	3	4
	Receipt of loan	$      15,00,000
	Payment for the machine	$    -15,00,000
	After tax interest [-1500000*15%*(1-25%)]		$     -1,68,750	$    -1,68,750	$     -1,68,750	$       -1,68,750
	Repayment of principal					$    -15,00,000
	MACRS Depreciation		$       4,99,950	$      6,66,750	$       2,22,150	$        1,11,150
	Tax shield on depreciation at 25%		$       1,24,988	$      1,66,688	$          55,538	$            27,788
	After tax residual value = 250000*(1-25%) =					$        1,87,500
	Annual cash flows of buying	$                     -	$         -43,763	$          -2,063	$     -1,13,213	$    -14,53,463
	PVIF at 11.25%	1	0.89888	0.80798	0.72627	0.65283
	PV at 11.25%	$                     -	$         -39,337	$          -1,666	$         -82,223	$       -9,48,864
	Cost of owning [PV]	$    -10,72,090
b]	COST OF LEASING:
	After tax lease rent = 400000*(1-25%) =	$        3,00,000
	Cost of leasing [PV] = 300000*(1.1125^4-1)/(0.1125*1.1125^4) =	$       -9,25,787
c]	NAL = .-925787-(-1072090) =	$        1,46,303
d]	From the lessors point of view, his NPV would be:
	PV of owning	$    -10,72,090
	PV of after tax lease rent receivable	$        9,25,787
	NPV for the lessor	$       -1,46,303
	As can be seen the NAL and the NPV for the lessor
	have the same dollar amount with opposite signs [+/1]