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. (The depreciation rates for Year 1 through Year 4 are equal to 0.3333, 0.4445, 0.1481, and 0.0741.)
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 12%. It would be non amortizing, 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 $200,000 at the end of the 4th year.

1. What is the cost of owning? Enter your answer as a positive value. Do not round intermediate calculations. Write out your answer completely. For example, 5 million should be entered as 5,000,000. Round your answer to the nearest dollar.

   $   ?????

2. What is the cost of leasing? Enter your answer as a positive value. Do not round intermediate calculations. Write out your answer completely. For example, 5 million should be entered as 5,000,000. Round your answer to the nearest dollar.

   $   ?????

3. What is the NAL of the lease? Do not round intermediate calculations. Write out your answer completely. For example, 5 million should be entered as 5,000,000. Round your answer to the nearest dollar.

   $ ????

Answer 1

Solution:

MACRS Depreciation Schedule:

Year	1	2	3	4
Depreciation rate	0.3333	0.4445	0.1481	0.0741
Depreciation Expense	$ 499,950	$666,750	$222,150	$111,150
Tax Shield	$124,987.5	$166,687.5	$55,537.5	$27787.5

We construct a table of incremental cashflows from the two alternatives. We use the discount rate as 12% x (1-25%) = 9%

Cost of Ownership	Year	0	1	2	3	4
Loan Proceeds		$1,500,000
Purchase Cost		($1,500,000)
After Tax Interest Payments			(135,000)	(135,000)	(135,000)	(135,000)
Principal Payment						(1,500,000)
Tax savings from depreciation			$ 124,987.5	$ 166,687.5	$ 55,537.5	$ 27787.5
Salvage Value						$200,000
Tax on salvage value						($50,000)
Net cash flow from ownership			($10,012.5)	$ 31,687.5	(79,462.5)	(1,457,212.5)
PV cost of ownership	$1,076,201
Cost of leasing
Annual lease payments			($400,000)	($400,000)	($400,000)	($400,000)
Tax Shield			$100,000	$100,000	$100,000	$100,000
After tax lease payments			($300,000)	($300,000)	($300,000)	($300,000)
PV cost of leasing	$ 971,916
PV of Ownership cost at 9%	$ 1,076,201
Less: PV Of leasing at 9%	$ 971,916
Net Advantage to leasing (NAL)	$104,285