Question

4. Guzman Trucking Company needs to acquire a new machine to expand its operations. The machine can be leased or purchased. The firm is in the 40% tax bracket and its after-tax cost of debt is 5.4%. The terms of the lease and purchase are as follows:

Lease: The leasing arrangement requires beginning of year payments of $16,900 over five years.   The lessor assumes all maintenance costs.

Purchase: If Guzman purchases the machine, the cost of $80,000, will be financed with a five-year, 9% non-amortizing loan. Maintenance costs are $3,000 per year and the machine will have a residual value of $5,000. The machine falls into the MACRS-5 category: 20%, 32%, 19.2%, 11.52%, 11.52% and 5.76%.

Which alternative—lease or purchase—do you recommend? Why?

Answer 1

We will calculate a net benefit of leasing option to choose between lease or purchase alternative.
Net advantage of leasing = NPV of leasing - NPV of buying
Calculation of net present value (NPV) of leasing a new machine
Year	0	1	2	3	4	5
Lease payments	-$16,900	-$16,900	-$16,900	-$16,900	-$16,900	$0
Tax benefit @ 40%	$6,760	$6,760	$6,760	$6,760	$6,760	$0
Net Cash flow	-$10,140	-$10,140	-$10,140	-$10,140	-$10,140	$0
x Discount factor @ 5.4%	1	0.948766603	0.900158068	0.854039912	0.810285	0.768771
Present Values	-$10,140	-$9,620	-$9,128	-$8,660	-$8,216	$0
NPV of leasing	-$45,764
Calculation of net present value (NPV) of buying a new machine
Year	0	1	2	3	4	5
Purchase price	-$80,000
Residual value (after tax)						$4,843
Maintenance cost		-$3,000	-$3,000	-$3,000	-$3,000	-$3,000
Tax benefit @ 40% of Maintenance cost		$1,200	$1,200	$1,200	$1,200	$1,200
Depreciation tax shield		$6,400	$10,240	$6,144	$3,686	$3,686
Net Cash flow	-$80,000	$4,600	$8,440	$4,344	$1,886	$6,730
x Discount factor @ 5.4%	1.00000	0.94877	0.90016	0.85404	0.81028	0.76877
Present Values	-$80,000	$4,364	$7,597	$3,710	$1,529	$5,174
NPV of buying a new machine	-$57,626
Net advantage of leasing = NPV of Leasing - NPV of buying
Net advantage of leasing = -$45,764 - (-$57626)
Net advantage of leasing = $11,862
I would recommend lease alternative as this option gives a net benefit of $11,862.
Working
Calculation of depreciation tax shield on new machine using MACRS-5 category rates
Year	Depreciable Value	Depreciation rates	Depreciation	Depreciation Tax shield @ 40%
1	$80,000.00	20%	$16,000.00	$6,400.00
2	$80,000.00	32%	$25,600.00	$10,240.00
3	$80,000.00	19.20%	$15,360.00	$6,144.00
4	$80,000.00	11.52%	$9,216.00	$3,686.40
5	$80,000.00	11.52%	$9,216.00	$3,686.40
6	$80,000.00	5.76%	$4,608.00	$1,843.20
Calculation of after tax residual value of machine
Sale value	$5,000.00
Less : Book value [$80000 - $75392]	$4,608.00
Gain on sale	$392.00
Tax @ 40% of Gain	$156.80
After tax residual value [Sale value - tax]	$4,843.20