Question

QUESTION 3: Carmin Marbles Works (CMW) needs to expand its facilities. To do so, the company must acquire a polishing machine costing $100,000. The machine can be leased or purchased. The firm is in the 30% tax bracket and its before-tax cost of borrowing is 11% per annum. The terms of the lease and purchase plans are as follows: Lease: The leasing arrangement requires beginning-of-year payments of $30,000 over 4 years. Under this option, maintenance and insurance costs will be paid by the lessor. CMW intend to exercise its option to purchase the machine for $10,000 at the termination of the lease contract. Purchase: If the company purchases the machine, the installed cost of $100,000 will be financed with a 4-year bank loan, interest calculated on a yearly reducing balance, requiring equal end-of-year payments. The machine will be depreciated under MACRS using a three- year recovery period as follows: Yrl Yr2 Yr3 Yr4 Depreciation rates 33% 45% 15% 7% Carmin will pay $5,000 per year for the service contract that covers all maintenance costs, payment to be made at the end of the year. Annual insurance premium is estimated to be $1,500 paid in advance. The company plans to keep the machine at the end of the leasing contract. to Which alternative lease or purchase - would you recommend? [Total: 20 marks]

Answer 1

a]	LEASING:
	Discount rate = 11%*(1-30%) =	7.70%
	Annual after tax lease rent = 30000*(1-30%) =	$            21,000
	PV of lease rent = -21000*(1.077^4-1)*1.077/(0.077*1.077^4) =	$           -75,413
	[Formula for PV of annuity due is used]
	PV of purchase option = -10000/1.077^4 =	$             -7,433
	NPV of leasing	$           -82,846
b]	PURCHASE:
	Loan amortization:
	Loan installments = 100000*0.11*1.11^4/(1.11^4-1) =	$            32,233
	Loan amortization schedule:	0	1	2	3	4
	Beinning balance of loan		$    1,00,000	$     78,767	$      55,198	$     29,037
	Interest at 11%		$        11,000	$        8,664	$        6,072	$        3,194
	Total		$    1,11,000	$     87,431	$      61,270	$     32,231
	Less: Installment		$        32,233	$     32,233	$      32,233	$     32,231
	Ending balance of loan		$        78,767	$     55,198	$      29,037	$                0
	Cash flows for purchasing:
	Principal repayment [Installment-Interest]		$      -21,233	$    -23,569	$    -26,161	$    -29,037
	After tax interest [Interest*(1-30%)]		$         -7,700	$      -6,065	$       -4,250	$      -2,236
	Depreciation		$        33,000	$     45,000	$      15,000	$        7,000
	Tax shield on depreciation at 30%		$          9,900	$     13,500	$        4,500	$        2,100
	After tax maintenance cost [5000*70%]		$         -3,500	$      -3,500	$       -3,500	$      -3,500
	Insurance premium-after tax [1500*70%[	$             -1,050	$         -1,050	$      -1,050	$       -1,050
	Loan receipt	$      1,00,000
	Purchase of asset	$    -1,00,000
	After cash flows of purchase	$             -1,050	$      -23,583	$    -20,684	$    -30,461	$    -32,673
	PVIF at 7.7%	1	0.92851	0.86212	0.80048	0.74325
	PV at 7.7%	$             -1,050	$      -21,897	$    -17,832	$    -24,384	$    -24,284
	NPV of purchasing	$           -89,447
c]	Net advantage of leasing = -82846-(-89447) =	$               6,601
	As the NAL of leasing is positive, leasing is