Question

You work as a financial analyst at WPWilly, Inc. You are evaluating how much Acme 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.
a. How much is the present value of after tax administrative costs? (sample answer:$2500.50)
b. What is the present value of Depreciation tax Shield?  (sample answer:$2500.50)
c. What is the after tax break-even operating lease rate for the car?  (sample answer: $2500.50)
d. What is the before tax break even operating lease rate for the car?  (sample answer: $2500.50)

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

Answer 1:

Administrative costs per year incurred at the beginning of each year = $10,000

After tax cost of capital is = 10% and

Tax rate is = 21%

After tax administrative costs per year = 10000 * (1 - 21%) = $7,900

Present value of after tax administrative costs = PV(rate, nper, pmt, fv, type) = PV(10%, 7, -7900, 0, 1)

=$42306.56

Present value of after tax administrative costs = $42,306.56

Answer 2:

Present value of Depreciation tax Shield = $13,802.70

Working:

Answer C:

Present value of cost of limo, administrative cost net of tax and present value of depreciation tax shield =

= 85000 + 42,306.56 - 13802.70

= $113,503.86

PV of $1 annuity due for 7 years at 10% = ((1 - 1/(1+10%)^7)/10%) * (1 + 10%) = 5.355260699

After tax break-even operating lease rate for the car = 113503.86 / 5.355260699 = $21,194.83

After tax break-even operating lease rate for the car = $21,194.83

Answer D:

Before tax break even operating lease rate for the car = After tax break-even operating lease rate for the car / (1 - Tax rate)

= 21194.83 / (1 - 21%)

= $26,828.90