Question

You are evaluating how much Ace Limo should charge a client who will lease a car for 7 years. It will cost Acme $85,000 to buy the car and the car can be depreciated on a five-year MACRS schedule. Acme Limo’s pretax administrative costs including Maintenance, Insurance and Selling Cost are $10,000 per year and they occur at the beginning of each year. The after tax cost of capital is 10% and the tax rate is 21%. Lease payments are made in advance, that is, at the start of each year. The inflation rate is zero.

How much is the present value of after tax administrative costs?

What is the present value of Depreciation tax Shield?

What is the after tax break-even operating lease rate for the car?

What is the before tax break even operating lease rate for the car?

Depreciation Table for 5-year asset

Year      %
1     20.00%
2     32.00%
3     19.20%
4     11.52%
5     11.52%
6     5.76%

Answer 1

1) Statement showing present value of after tax administrative costs

Year	Maintenance, Insurance and Selling Cost	Tax savings @ 21%	After tax Maintenance, Insurance and Selling Cost	PVIF @ 10%	PV
0	10000	2100	7900.00	1.0000	7900
1	10000	2100	7900.00	0.9091	7182
2	10000	2100	7900.00	0.8264	6529
3	10000	2100	7900.00	0.7513	5935
4	10000	2100	7900.00	0.6830	5396
5	10000	2100	7900.00	0.6209	4905
6	10000	2100	7900.00	0.5645	4459
7
Present value of after tax administrative costs	42307

Thus Present value of after tax administrative costs = $ 42307

2) Statement showing present value of Depreciation

Year	Depreciation rates	Depreciation = Cost x Depreciation rates	Depreciation tax Shield @ 21%	PVIF @ 10%	PV
1	20%	17000	3570	0.9091	3245
2	32%	27200	5712	0.8264	4721
3	19%	16320	3427	0.7513	2575
4	12%	9792	2056	0.6830	1404
5	12%	9792	2056	0.6209	1277
6	6%	4896	1028	0.5645	580
7
Present value of Depreciation tax Shield	13803

Thus Present value of Depreciation tax Shield = 13803 $

3) after tax break-even operating lease rate for the car can be fond as follows

Cost of car = (after tax operating lease x PVIFA(6,10%) +1) + Present value of after tax administrative costs - present value of Depreciation tax Shield

=85000 = [after tax operating lease x (4.3553 + 1) ] + 42307 -13803

=85000 = [after tax operating lease x 5.3553 ] + 28504

56496 = after tax operating lease x 5.3553

after tax operating lease = 10549.55 $

i.e 10550 $

4) Before tax operating lease = After tax operating lease/(1-tax rate)

= 10550/(1-0.21)

=10550/0.79

=13354 $