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After deciding to acquire a new car, you realize you can either lease the car or purchase it with a three-year loan. The car you want costs $32,500. The dealer has a leasing arrangement where you pay $94 today and $494 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at an APR of 6 percent. You believe that you will be able to sell the car for $20,500 in three years.a. What is the present value of purchasing the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16)b. What is the present value of leasing the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16)c. What break-even resale price in three 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)

Respuesta :

Answer:

a. $15,369.28

b. $16,332.28

c. $19,347.60

Explanation:

a. What is the present value of purchasing the car?

PV of resale = SP ÷ (1 + r)^n ................................................. (1)

Where SP = Resales proceed = $20,500

r = discount rate = 6% annually = 0.06 annually = (0.06 ÷ 12) monthly = 0.005 monthly

n = number of periods = 3 years = 3 × 12 = 36 months

Substituting into equation (1), we have:

PV of resale = $20,500 ÷ (1 + 0.005)^36 = $17,130.7208354753

Net PV = Purchase price - PV of resale

            = $32,500 - $17,130.7208354753

Net PV = $15,369.28

Therefore,  the present value of purchasing the car $15,369.28.

b. What is the present value of leasing the car?

PV of future period payment can be calculated using the following formula:

PV of monthly payment = M × 1 - (1 + r)^-n ÷ r .......................................... (2)

Where,

M = monthly payment = $494

r = discount rate = 6% annually = 0.06 annually = (0.06 ÷ 12) monthly = 0.005 monthly

n = number of periods = 3 years = 3 × 12 = 36 months

Substituting into equation (2), we have:

PV of monthly payment = $494 × {[1 - (1 + 0.005)^-36] ÷ 0.005}

PV of monthly payment =  $16,238.2820221969  

PV of leasing the car = Today's payment + PV of monthly payment

                                   = $94 + $16,238.2820221969

PV of leasing the car = $16,332.28

Therefore, PV of leasing the car is $16,332.28.

c. What break-even resale price in three years would make you indifferent between buying and leasing?                    

This will be calculated by equating the PV of leasing the car to the difference between the purchase price and the PV of resale as follows:

PV of leasing car = Purchase price - PV of resale

$16,332.28 = $32,500 - PV of resale

Solving for PV of resale, we have:

PV of resale = $16,167.72.

The future value (FV) of resale price in 3 years can be calculated as follows:

FV of resale = PV of resale × (1 + r)^n

FV of resale = $16,167.72 × (1 + 0.005)^36 = $19,347.60

Therefore, the break even resale price in 3 years is $19,347.60.

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