Question

Joe is interested in driving a new SUV for three years. There are two options—purchasing or leasing. A local car dealer quoted him a leasing deal of $2000 down and $299 a month for 36 months. Alternative he can purchase the vehicle at $22,000 and sell the SUV in 36 months at 60% of the purchase price. Joe would like to get your help in deciding which option is best. Assume that the interest rate is 6% (APR compounded monthly).

Answer 1

We can compare the present value of both leasing as well as purchasing option and based on this we can

decide which option is better.

Calculation of present value of leasing option.

Using present value of annuity option , we can calculate the present value of lease payments.

Present value of annuity = P * {[1 - (1+r)^-n]/r}

Present value of annuity = present value of lease payments = ?

P = monthly lease payments = $299

r = rate of interest per month = 6%/12 = 0.005

n = no.of months lease payments = 36

Present value of annuity = 299 * {[1 - (1+0.005)^-36]/0.005}

Present value of annuity = 299 * {0.16436/0.005} = 9828.43

Present value of leasing option = down payment + present value of lease payments = $2000 + $9828.43 = $11,828.43

Calculation of present value of purchasing option.

Present value of salvage value = Salvage value * discount factor at the end of 3rd year = ($22000*60%) * (1/1.06^3) = $11,082.97

Present value of purchasing option = Purchase cost - Present value of salvage value = $22000 - $11082.97 = $10,917.03

The purchase option is best for Joe as this option has lower present value (outflow) compared to leasing option .