Problem 4-60 Calculating Annuity Values After deciding to get a new car, you can

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 $31,500. The dealer has a special leasing arrangement where you pay $92 today and $492 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 5 percent, compounded monthly. You believe that you will be able to sell the car for $19,500 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           $

Explanation / Answer

When you purchase the car, you will make monthly payments and at tend of you 2 years, you will receive 19,500 on sale.

Net PV of cost of purchasing = 31,500 – 19,500/(1 + 0.05/12)^24 = $13,852.00

PV of cost of leasing = 92 + (492/(0.05/12)) * (1 – 1/(1 + 0.05/12)^24) = $11,306.60

To make indifferent between the options, the PV of both costs must be same and required resale price be S.

31,500 – S/(1 + 0.05/12)^24 = 11,306.60

S/(1 + 0.05/12)^24 = 31,500 - 11,306.60 = 20,193.40

S = 20,193.40*(1 + 0.05/12)^24 = 22,312.52

Break-even resale price = $22,312.52

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