Present value of growing annuity versus ordinary annuity


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?

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Finance Basics: Present value of growing annuity versus ordinary annuity
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