Question

5. You are considering to invest $11,000 in a vehicle which is expected to last 3 years with a salvage value of $4,800. The annual operating and maintenance costs for the vehicle for year 1, 2, and 3 are expected to be $1801, $1848, and $1876 respectively. If the expected miles driven on the vehicle during year 1, 2, and 3 are 14,500, 13,000, and 11,500 respectively, and the interest rate is 7% what should be your reimbursement rate per mile so that you can break even

Answer 1

Step-by-step explanation:

The said Reimbursement rate per mile : $ 0.35

At break-even,

Initial Investment = Present value of cash inflows

Initial investment : $ 11,000

Let the reimbursement rate per mile be r.

The Present value of the cash inflows at 7% discount rate

`= (14,500 r - 1,801) * 0.9346 + (13,000 r - 1,848) * 0.8734 + (11,500 r - 1,876) * 0.8163 + 4,800 * 0.8163 \\\\= 13,551.7 r - 1,683.21 + 11,354 r - 1,614.04 + 9,387.45 r - 1,531.38 + 3,918.24 \\\\= 34,293.15 r - 4,828.63 + 3,918.24\\\\ = 34,293.15 r - 910.35`

At the break even,

The Initial Investment = Present value of cash inflows

`34,293.15 r - 910.35 = 11,000`

or

`r = $ 0.3473 per mile`

Therefore, the reimbursement rate per mile so that you can break even is $0.3473