Question

# You are planning to acquire a new car with a negotiated purchase price of \$50,000. You...

You are planning to acquire a new car with a negotiated purchase price of \$50,000. You prefer to turn your cars over after 4 years. You have two financing choices: lease or borrow & buy. You can obtain a four-year loan at 6% annual rate (which means 0.5% monthly rate) for the entire purchase price of the car. A four-year lease (equal monthly lease payments start immediately) requires a down payment of \$4,000. The market value of the car is expected to depreciate 48% in four years. What is the break-even lease payment? Assume taxes are irrelevant to this problem.

 PV of buying = Initial investment (Down payment)+PV of loan installments-PV of salvage value= 4000+46000-50000*(1-48%)/1.005^48 = \$   29,535.44 Note: PV of loan installments would equal the loan as the discount rate would be the borrowing rate. \$29535 should be the PV of the break even lease payments. Hence, lease paymets (beginning of the year) using the formula for finding PV of annuity due = = 29535.44*0.005*1.005^48/((1.005*(1.005^48-1)) = \$         690.19

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