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.
