The chapter opener described an arrangement in which the city of Cincinnati gave

Question

The chapter opener described an arrangement in which the city of Cincinnati gave up the right to collect parking fees over a 30-year period in exchange for a lump sum of $92 million plus a 30-year annuity of $3 million. Suppose that if the city had not entered into that arrangement, it would have collected parking fees the following year of $6 million (net of operating costs), and those fees would have grown at a steady 3% for the next 30 years. At an interest rate of 4%, what is the present value of the parking revenue that the city could have collected? Using the same 4% to value the payments that the city was set to receive in their privatization deal, do you think that the city made the correct decision? Why or why not?

Explanation / Answer

parking revenue can be treated as a grwoing annuity whith growth rate g and interest rate r

present value = initial payment * [ 1 - ((1+g)/(1+r))^n]/r-g

= 6000000 * [1- (1.03/1.04)^30]/0.04-0.03

= 150,977,800.8

present value of deal

= 95,000,000

No, finiancially the city does not made a good deal as the deal value is less than the income genrated from praking fees

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