Question

2. Kennesaw State University will furnish an automobile to certain employees or permit them to use their personal cars and will pay 55 cents per mile. It is assumed that a car would cost $23,350 and have a life of 8 years, with a trade-in value of $4400. There would be estimated costs of $105 per month for incidentals (including insurance); 5 cents per mile for oil, tires, and repairs; and 4 cents per mile for fuel. What is the number of miles per year of travel required to justify the purchase of an automobile by an employee for use on the job? Use sinking-fund analysis with interest at 11 percent.

Answer 1

Ans:

Cost of Car: $23,350.

Salvage Value after 8 Years: $4,400

Present value at 11% interest rate: 1/(1.11)⁸

   ^: 0.4339

Present value of salvage value: 4,400*0.4339= $1,909.

Net Outflow: 23,350-1,909= $21,441

------ Annual Maintenance costs: 105*12= $1,260

Annuity Factor Value for 8 Years at 11%= 1/(1.11)+1/(1.11)²..............+1/(1.11)⁸

⁼ 5.1461 (Please note that you can also take annuity factor value from annuity table)

Present value of annual maintenance cost for 8 Years= 1,260*5.1461= $6,484

Present value of Net outflow of Car cost and maintenance cost: $27,925 (21,441+6,484).

----- Now to justify the purchase of car minimum savings per annum from car should be: Total Cost/Annuity factor for 8 years.

: 27,925/5.1461= $5,426.45 (used annuity factor to consider 11% rate of return on money invested in purchase)

----- Running Cost per mile= 9 cents (For oil, repairs and fuel)

----- Cost per mile for personal cars= 55 cents

savings per mile in case of purchase of car: 55-9= 46 cents = $0.46

-------Total number of miles per year required to justify the purchase are: 5,426.45/0.46= 11,796.63 Miles.