You are planning to acquire a new car with a negotiated purc

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.

Solution

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