The New York Taxi Cab Company has just purchased a new fleet of models for the year

Question:

The New York Taxi Cab Company has just purchased a new fleet of models for the year 2000. Each brand-new cab cost $20,000. From past experience, the company estimates after-tax cash returns for each cab as
An = $65,800 - 30,250(1 + 0.15)n-1
Sn = $20,000(1 - 0.15)n
where An stands for net after-tax cash flows from the cab's operation during period n and Sn stands for the after-tax of the cab at the end of period n. The management views the replacement process as a constant and infinite chain.
(a) If the firm's is 10% and it expects no major technological and functional change in future models, what is the optimal period (constant replacement cycle) to replace its cabs? (Ignore inflation.)
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