Question

Problem 4-60 Calculating Annuity Values

After deciding to get a new car, you can either lease the car or purchase it with a two-year loan. The car you wish to buy costs $36,500. The dealer has a special leasing arrangement where you pay $102 today and $502 per month for the next two years. If you purchase the car, you will pay it off in monthly payments over the next two years at an APR of 6 percent, compounded monthly. You believe that you will be able to sell the car for $24,500 in two 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 two 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

In order to answer this question, we should find out the present & value of both options and compare them since we are purchasing the car the lowest pv is the best option the p.r of leasing is the pr of lease payments, ples Initial payment of $102 the interest rate we use for leasing options is same as the Interest rate of loan. (4) cost of purchasing the car :-) I The pr of purchasing the car is I the Current price of car minus the per of oresole price. por. of resale price = $24500 (100g) 24 = $21,736

NOTE here all the payments monthly Compounded ost o rate= 6% = 0.05% are w at no a 19 - / Por of the deciston to purchase Car is. $36500 - 21,436.05 - $14, 763.95 (6) Cost of leasing sgt brasa bir p.v. of annuity = { 1 - 1+ 1 do sulap- periodic payment til 6 552 ..! & trowal out rate per period now go to penal to ne number of periods here are 6% = 0.05% to va na lara ayso r e p - $502 92 ip.v= soal - (1.005) 24 7 smoz 0.005: J = $11,326-56 to . Cost of leasing = 11,326.56 + 100 site 6 $ 11,487.56 . 12

NOTE: It is cheaper to ease car than Buying it since the pr of the cash flows is lower. (c) Break even resale price: - To find the break even resale price we need to find the resale price that makes the por of the bothe options same I u. The por of the decision to buy is $36,500 - pv of resale price = $11, 128:56 p.v of resale price = 25,07).uy The break even resale price is the Future value of this value, so Future value= p.r[lton - 25,071.44 [1.oosgdy .. Break even resale price = $28,259.52