Scenario: You Are Purchasing A New Lexus Car, Cost $88,850

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Scenario: You are purchasing a new Lexus car. The cost is $88,850. You will make a 10% down payment. Your local bank’s interest rate is 4%. You can borrow the balance either from your local bank using a four-year loan or from the dealership’s finance company.

If you purchase from your dealership’s finance company, the APR will be 10% with your 10% down and monthly payments over three years. However, the dealership will give you a rebate of 5% of the car price after the three-year term is complete. You want the best deal possible, so you consider the following questions: What type of car have you selected, and what will it cost? What is the interest rate from your local bank for a car loan for four years? What will your payment be to your local bank, assuming your 10% down payment? (Be sure to use the formula and show your work). How much will that car have cost in four years? What will your payment be to the dealership finance company assuming your 10% down payment? (Be sure to use the formula and show your work). How much will that car have cost in 3 years? Which is the better deal and why? (here is the formula from the chapter, based on 1 year: FV1=PV0 (1+r)

Paper For Above instruction

Purchasing a vehicle is a significant financial decision that requires careful analysis of costs and financing options. In this scenario, the focus is on evaluating the total costs associated with buying a new Lexus automobile priced at $88,850, considering different financing strategies—bank loan versus dealership financing—and understanding the long-term implications of each choice.

Car Details and Down Payment

The vehicle selected is a Lexus costing $88,850. With a 10% down payment, the initial amount paid out-of-pocket amounts to $8,885. Consequently, the financed amount from either the bank or the dealership is $79,965 ($88,850 - $8,885). These figures serve as the basis for calculating monthly payments, total costs, and the comparative benefits of each financing option.

Interest Rate from the Local Bank

The local bank offers a financing rate of 4% annual interest for a four-year loan. This interest rate reflects prevailing lending conditions and is lower than the dealership’s APR, indicating potentially lower total costs if the bank financing is chosen.

Monthly Payment Calculation for Bank Loan

To compute the monthly payment to the bank, we utilize the amortization formula:

PMT = [P x r] / [1 - (1 + r)^-n]

Where:

• P = Principal (amount borrowed) = $79,965
• r = monthly interest rate = 4% / 12 = 0.003333
• n = total number of payments = 4 years x 12 months = 48 months

Plugging in the numbers:

PMT = [$79,965 x 0.003333] / [1 - (1 + 0.003333)^-48]

Calculating numerator: $79,965 x 0.003333 ≈ $266.55

Calculating denominator: 1 - (1 + 0.003333)^-48 ≈ 1 - (1.003333)^-48 ≈ 1 - 0.8607 ≈ 0.1393

Monthly payment: $266.55 / 0.1393 ≈ $1,913.91

Thus, the monthly payment to the bank is approximately $1,913.91.

Total Cost of the Car Over Four Years with Bank Financing

The total amount paid over four years is:

Monthly payment x total number of payments: $1,913.91 x 48 ≈ $91,827.36

Adding the initial down payment of $8,885, the overall cost of the car in four years becomes:

$91,827.36 + $8,885 ≈ $100,712.36

This total represents the expenditure associated with bank financing, excluding any additional costs or fees.

Dealership Financing and Rebate Calculation

When financing through the dealership, the APR is 10% with monthly payments over three years. The amount financed remains $79,965, with a 10% down payment of $8,885. The monthly payment is calculated as follows:

PMT = [P x r] / [1 - (1 + r)^-n]

• P = $79,965
• r = 10% / 12 = 0.008333
• n = 3 years x 12 months = 36 months

Calculations:

PMT = [$79,965 x 0.008333] / [1 - (1 + 0.008333)^-36]

Numerator: $79,965 x 0.008333 ≈ $666.37

Denominator: 1 - (1.008333)^-36 ≈ 1 - 0.7229 ≈ 0.2771

Monthly payment: $666.37 / 0.2771 ≈ $2,405.61

The total paid over three years is: $2,405.61 x 36 ≈ $86,602.00

After the three-year term, a rebate of 5% of the original car price is issued, totaling:

5% x $88,850 = $4,442.50

Subtracting this rebate from the total paid:

$86,602.00 - $4,442.50 ≈ $82,159.50

The net cost of the car in this scenario is approximately $82,159.50.

Cost in 3 Years

In three years, the total cost for the dealership financed car, after accounting for the rebate, is approximately $82,159.50. This reflects the effective expenditure considering the rebate and the total payments made within the period.

Comparison and Conclusion

Comparing the two options, the dealership’s financing approach results in a lower total expenditure of approximately $82,159.50 over three years, whereas the bank loan totals around $100,712.36 over four years. Despite the shorter-term payments, the dealership’s rebate significantly reduces the overall cost, making it the more economical choice.

Therefore, the dealership financing option provides better value due to the rebate and the shorter payment period, despite the higher APR. The lower total cost outweighs the benefits of a lower interest rate from the bank, considering the rebate incentives. This comparison emphasizes the importance of evaluating long-term costs, rebates, and interest rates in vehicle financing decisions.

References

• Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
• Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
• Higgins, R. C. (2012). Analysis for Financial Management. McGraw-Hill Education.
• Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2019). Fundamentals of Corporate Finance. McGraw-Hill Education.
• Brigham, E. F., & Houston, J. F. (2019). Fundamentals of Financial Management. Cengage Learning.
• Investopedia. (2023). Car Loan Calculations. https://www.investopedia.com
• U.S. Department of Energy. (2020). Fuel Economy and Vehicle Cost Savings. https://www.fueleconomy.gov
• Consumer Reports. (2023). Car Buying Guide. https://www.consumerreports.org
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