Question

A firm must decide whether to provide their salespeople with firm-owned cars or to pay a mileage allowance for their own cars. New cars would cost about $28,000 each and could be resold 4 years later for about $11,000 each. Annual operating costs would be $1200 per year plus $0.24 per mile. If the salespeople drove their own cars, the firm would pay $0.50 per mile. How many miles must each salesperson drive each year for it to be economically practical for the firm to provide the cars? Assume a 10% annual interest rate.

Answer 1

Annual Worth (AW) of costs, if firms provide the cars, is computed as follows.

Let number of miles driven per year be M.

AW ($) = 28,000 x A/P(10%, 4) + (1,200 + 0.24M) - 11,000 x P/F(10%, 4) x P/A(10%, 4)

= 28,000 x 0.3155 + 1,200 + 0.24M - 11,000 x 0.6830 x 0.3155

= 8,834 + 1,200 + 0.24M - 2,370.35

= 7,663.65 + 0.24M

If they drive their own car, AW of costs = $0.50 x M

For equivalence,

7,663.65 + 0.24M = 0.50M

0.26M = 7,663.65

M = 7,663.65 / 0.26 = 29,475.58 miles per year per salesperson