Question

After deciding to get a new car, you can either lease the car or purchase it with a four-year loan. The car you wish to buy costs $35,500. The dealer has a special leasing arrangement where you pay $100 today and $500 per month for the next four years. If you purchase the car, you will pay it off in monthly payments over the next four years at an APR of 7 percent, compounded monthly. You believe that you will be able to sell the car for $23,500 in four years.
   
What is the cost today of purchasing the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
  
Cost of purchasing           $  
  
What is the cost today of leasing the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
  
Cost of leasing           $  

What break-even resale price in four years would make you indifferent between buying and leasing? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
  
Break-even resale price           $

Answer 1

Solution 1:

Cost of buying car today = Buying cost - Present value sale value after 4 years

Monthly rate of interest = 7/12 = 0.5833333%

Present value of resale price = $23,500 * PV Factor at 0.583333% for 48th period

= $23,500 * 0.756399 = $17,775.37

Cost of buying = $35,500 - $17,775.37 = $17,724.63

Solution 2:

Cost of leasing the Car = $100 + $500*cumuative PV factor at 0.583333% for 48 periods

= $100 + $500 * 41.76020 = $20980.10

Solution 3:

Let breakeven sale price in 4 year is X to make indifferent between buying and leasing

Therefore

Cost of buying = Cost of leasing today

$35,500 - (X * PV factor at 0.5833333% for48th period) = $20,980.10

$35,500 - 0.756399X = $20980.10

0.756399X = $14,519.90

X = $19,196.09