Question

Linda needs a new car and is deciding whether to buy or lease the car. She estimates that if she buys the car, it will cost her $17,000 today (t = 0) and that she would sell the car four years from now for $7,000 (at t = 4). If she were to lease the car she would make a fixed lease payment at the end of each of the next 48 months (4 years). Assume that the operating costs are the same regardless of whether she buys or leases the car. Assume that if she leases, there are no up-front costs and that there is no option to buy the car after four years. Linda estimates that she should use a 6% nominal interest rate to discount the cash flows. What is the breakeven lease payment? (That is, at what monthly lease payment would she be indifferent between buying and leasing the car?)

a. $271.59
b. $277.39
c. $275.60
d. $279.83
e. $269.85

Answer 1

The breakeven lease payment is found by comparing the present value of buying cost to leasing payments. After calculating the present value of the future resale value when buying and setting it equal to the present value of lease payments, we find that the breakeven monthly payment is approximately $271.59.

Step-by-step explanation:

To find the breakeven lease payment Linda would be indifferent to between buying and leasing the car, we need to compare the present value (PV) of buying the car to the present value of the leasing payments.

First, we consider buying the car. Linda pays $17,000 upfront (t = 0) and receives $7,000 after 4 years (t = 4). Using the present value formula for a future sum:

PV = F / (1 + r)n

Where:

• F is the future sum of money to be received,
• r is the interest rate per period,
• n is the number of periods.

For $7,000 at the end of 4 years, at a nominal interest rate of 6% converted monthly (0.5% per month),
PV = $7,000 / (1 + 0.005)48 = $5,582.47 approximately.

The net cost of buying is the initial cost minus the present value of the future selling price:
Net cost of buying = $17,000 - $5,582.47 = $11,417.53

Now, let's calculate the lease option using the annuity present value formula:

PV = Pmt * [1 - (1+r)-n] / r

Where:

• Pmt is the monthly payment,
• r and n are defined as above.

We want to find the monthly payment that makes the present value of leasing equal to the net cost of buying:

$11,417.53 = Pmt * [1 - (1+0.005)-48] / 0.005

After solving for Pmt, we find that the breakeven monthly payment is approximately $271.59, making the correct answer option (a).