Question

Big Sky Mining Company must install $1.5 million of new machinery in its Nevada moine. 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, Bug 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 nonamortirizing, with only interest paid at the end of each year for four years and the principal repaidat Year 4.

(5) The lease terms call for $400,000 payments at the end 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?

Answer 1

Best way to answer these kind of questions is to create after tax cashflows and discount to present value

a) If machine is owned, cashflows are as below:

Interest outgo = 15%*$1.5Mn= -$225k every year
Adjusting for tax rate of 25%, = -225*0.75= 168.75k pa

For MACRS- 3 year class, depreciation rates are 33.33, 44.45 14.81, 7.41% respectively for Year 1 to 4 . Hence, cashflow due to tax advantage of depreciation are as below:

		Depreciation amount
Original cost		1500000	tax advantage @ 25%
Y1	33.33	499950	124988
Y2	44.45	666750	166688
Y3	14.81	222150	55538
Y4	7.41	111150	27788

Now, when completely depreciated machine is sold at $250k, after tax proceeds = (1-0.25)*(250-0) = $187.5k

Putting all the cashflows together now and discounting at 15% (int rate), cost of ownership comes out as below:

Year	Bank Loan	Interest outgo	Depreciation tax advantage	Salvage Value	Total	Int Rate	Discount factor	PV
1		-168750	124987.5		-43762.5	15%	0.87	-38054
2		-168750	166687.5		-2062.5	15%	0.76	-1560
3		-168750	55537.5		-113213	15%	0.66	-74439
4	-1500000	-168750	27787.5	187500	-1453463	15%	0.57	-831022
Total								-945075

b) for lease, calculation is quite simpler as there are only 4 lease payments to be discounted to present, However, same should be adjusted for tax advantage . Calculations as below:

Year	Lease payments	tax benefit adjusted @ 25%	Discount factor	PV
1	-400000	-300000	0.87	-260870
2	-400000	-300000	0.76	-226843
3	-400000	-300000	0.66	-197255
4	-400000	-300000	0.57	-171526
Total				-856494

c) NAL of lease = 945075-856494 = $88,581