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Vehicle lease payment by the federal disclosure form: depreciation, rent charge, money factor and constant-yield rate (Federal Reserve sample leasing form)

ToolLease versus Buy
SourceBoard of Governors of the Federal Reserve System (2013). Keys to Vehicle Leasing. Consumer guide with the sample leasing form, Washington, DC. Sample Leasing Form, page 1 (Federal Consumer Leasing Act Disclosures).
LevelUndergraduate

Problem

The sample disclosure of the Federal Reserve's consumer guide leases a vehicle with an agreed value of $21,500 and $800 of other capitalized amounts for 48 months. The lessee puts $3,500 down as a capitalized cost reduction; the residual value is $12,350 and the rent charge $5,295; the monthly sales or use tax is $12.25, the security deposit $350, title and registration fees $135 and the disposition fee $400. Find the base and total monthly payments, the amount due at signing and the total of payments, and express the rent charge as a money factor and as a yearly rate.

Inputs to Enter

  • Analysis: Vehicle lease (Regulation M worksheet) and lease or loan; choosing it loads this case
  • Agreed value 21,500, other capitalized amounts 800, capitalized cost reduction 3,500, residual value 12,350, 48 months
  • Rent charge entered 5,295; monthly tax amount 12.25; security deposit 350; fees at signing 135; disposition fee 400
  • Lease or loan part (not from the guide, illustrative): down payment 3,500, loan APR 8.5 % for 60 months, value at lease end = residual value, discount rate 3 %
Open the Lease versus Buy tool

Answers

  • Gross capitalized cost 22,300.00; adjusted capitalized cost = 22,300 − 3,500 = 18,800.00; depreciation and any amortized amounts = 18,800 − 12,350 = 6,450.00 (form: the same)
  • Total of base monthly payments = 6,450 + 5,295 = 11,745.00; base monthly payment = 11,745 / 48 = 244.69; total monthly payment = 244.69 + 12.25 = 256.94 (form: 244.69, 256.94)
  • Amount due at signing = 3,500 + 256.94 + 350 + 135 = 4,241.94; total of monthly payments 48 × 256.94 = 12,333.12; total of payments = 4,241.94 + 12,333.12 + 400 − 256.94 − 350 = 16,368.12 (form: 4,241.94, 12,333.12, 16,368.12)
  • Money factor equivalent to the rent charge = 5,295 / ((18,800 + 12,350) × 48) = 0.0035413; by the trade rule × 2400 it is 8.499 % a year (a factor of 8.5 / 2400 gives a rent charge of 5,295.50)
  • Constant-yield (actuarial) rate of the 48 base payments in advance: 8.497 % a year; the same payments in arrears would earn 8.367 %
  • Lease or loan with the illustrative loan: present value of the cost of buying 13,120.15 against 15,666.59 for the lease at 3 %; buying costs less by 2,546.44, and the two are equal at an end value of 9,479.33

Notes

Choose the vehicle analysis in the Analysis dropdown and press Submit. The form's figures are read from the image of the sample form (archived copy; the Federal Reserve site refuses scripted requests). The form prints no rate: the guide says the money factor is not a lease rate, and the × 2400 conversion is a trade convention the tool derives, shown beside the constant-yield rate. The page's opening case (business equipment, after tax) and the lease-or-loan inputs are illustrative. The other analyses load Example 1 of the DoD Contract Pricing Reference Guides, volume 2, chapter 9 (28,438 to lease against 27,302 to buy; the tool gives 28,437.21 and 27,301.61 with unrounded factors) and the guide's 36-month lease (implicit rate 10.085 %).