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)

and

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 salvage value 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 MARR 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.)

b) What is the internal rate of return for a cab if it is retired at the end of its economic service life? What is the internal rate of return for a sequence of identical cabs if each cab in the sequence is replaced at the optimal time?