In: Finance
Car Lease
use the information to answer the following questions.
You have decided to acquire a new car that costs $30,000. You are considering whether to lease it for three years or to purchase it and financing the purchase with a three year installment loan. The lease requires no down payment and lasts for three years. Lease payments are $400 monthly starting immediately, whereas the installment loan will require monthly payments starting a month from now at an annual percentage rate (APR) of 8%. The discount rate (APR) is also 8%.
1) If you expect the resale value of the car to be $20,000 three years from now, should you buy or lease it?
2) What is the break-even resale price of the care three years from now, such that you would be indifferent between buying and leasing it?
3. Car lease, Q1-1.
What is the value of the lease payment?
Hint:
(A) 12764.72 (B) 12849.82 (C) 13489.90 (D) 12953.80
4. Car lease, Q1-2
What is the present value of the resale value of $20,000 in three years?
(A) 17549.09 (B) 15745.09 (C) 15769.04 (D) 14759.08
5. Car lease: Q1-3
Following the car installment plan, the car would be brought now at $30000, and sold in three years at 20,000.
Estimate the loss in value as measured by the difference in their present values. This is the net cost of purchasing and reselling the car.
Compare the cost with leasing, should you buy or lease?
(A) Lease (B) buy
6. Care lease, Q2
What is the break-even resale price of the care three years from now, such that you would be indifferent between buying and leasing it?
(A) 18357 (B) 22987 (C) 19385 (D) 21785
Q1-1]
Value of the lease payment is calculated using PV function :
rate = 8% / 12 (converting annual rate into monthly rate)
nper = 3 * 12 (3 years with 12 monthly payments each year)
pmt = -400 (Monthly payment. This is entered with a negative sign because it is a cash outflow)
fv = 0 (There is no cash inflow at the end of lease period)
type = 1 (first payment is made immediately. It is an annuity due)
PV is calculated to be $12,849.82.
Q1-2]
Present value = future value / (1 + periodic interest rate)number of periods
Here, the periodic rate is the monthly rate, which is 8%/12
number of periods = number of years * 12 = 3 * 12 = 36.
Present value = $20,000 / (1 + (8%/12))36
Present value = $15,745.09.
Q1-3]
Loss in value = purchase price - present value of the resale value
Loss in value = $30,000 - $15,745.09
Loss in value = $14,254.91.
Q1-4]
For you to be indifferent, the loss in value should equal the present value of lease payments.
Let us say the resale price is X. Then :
$30,000 - (X / (1 + (8%/12))36) = $12,849.82
X = ($30,000 - $12,849.82) * (1 + (8%/12))36
X = $21,785