Question

Automobiles are often leased, and there are several terms unique to auto leases. Suppose you are considering leasing a car. The price you and the dealer agree on for the car is $31,200. This is the base capitalized cost. Other costs that may be added to the capitalized cost price include the acquisition (bank) fee, insurance, or extended warranty. Assume these costs are $1,100. Capitalized cost reductions include any down payment, credit for a trade-in, or dealer rebate. Assume you make a down payment of $2,000 and there is no trade-in or rebate. If you drive 12,000 miles per year, the lease-end residual value for this car will be $22,000 after three years.

The lease or “money” factor, which is the interest rate on the loan, is the APR of the loan divided by 2,400. The money factor of 2,400 is the product of three numbers: 2, 12, and 100. The 100 is used to convert the APR, expressed as a percentage, to a decimal number. The 12 converts this rate to a monthly rate. Finally, the monthly rate is applied to the sum of the net capitalization cost plus the residual. If we divide this sum by 2, the result is the average anticipated book value. Thus, the end result of the calculation using the money factor is to multiply a monthly rate by the average book value to get a monthly payment. The lease factor the dealer quotes you is .00263.

The monthly lease payment consists of three parts: Depreciation fee, finance fee, and sales tax. The depreciation fee is the net capitalized cost minus the residual value divided by the term of the lease. The finance fee is the net capitalization cost plus the residual times the money factor, and the monthly sales tax is the monthly lease payment times the tax rate. A. What APR is the dealer quoting you? B. What is your monthly lease payment for a 36-month lease if the sales tax is 7 percent?

Answer 1

Answer: Total Net Capitalized Cost = Base Capitalised Cost + Other Cost/Expenses - Cost Reductions

Therefore, Total Net Capitalized Cost = 31,200 + 1,100 - 2000 = 30,300 $

Depreciation Fee = (Net Capitalized Cost - Residual Value) / Term of the lease

Therefore, Monthly Depreciation Fee = (30,300 - 22,000) / 36 Months = 230.56 $ (Note that it is assumed that depreciation is calculated on net capitalized cost excluding down payment, otherwise someone may also interpret and calculatre depreciation on capitalized cost without reducing down payment)

A) It is mentioned that Lease/Money Factor = APR/2400, The Lease Factor Mentioned in the question is 0.00263

Therefore, 0.00263 = APR/2400

APR = 0.00263 * 2400 = 6.312%

B) Monthly Finance Fee = (Net Capitalized Cost + Residual Value) * Lease Factor

Therefore, Monthly Finance Fee = (30,300 + 22,000) * 0.00263 = 137.55 $

Total Monthly Lease Payment Before Tax = Monthly Depreciation Fee + Monthly Finance Fee

Therefore, Total Monthly Lease Payment Before Tax = 230.56 $ + 137.55 $ = 368.10 $

Sales Tax = 368.10 $ * 7% = 25.77 $

Therefore, Total Monthly Lease Payment After Tax = 368.10 + 25.77 = 393.87 $