Vehicle Financing Term Analysis

Compare Option A and Option B vehicle financing by total cash outlay, net present cost, liquidity position, and outstanding amortized loan balance.

Financing Inputs

Sales tax is capitalized into the financed amount. Taxed incentives/rebates reduce the taxable selling price. Trade-in value and ancillary fees are excluded.

Calculating

Option A

Vehicle price ($) Taxed incentives/rebates ($) Down payment ($) Sales tax rate (%) Loan term (months) APR (%)

Option B

Vehicle price ($) Taxed incentives/rebates ($) Down payment ($) Sales tax rate (%) Loan term (months) APR (%)

Liquidity And Discount-Rate Assumptions

The real discount rate adjusts the nominal risk-free rate for inflation. It is used for present-value and purchasing-power analysis.

Initial liquidity ($) Risk-free annual rate (%) Inflation annual rate (%) Marginal tax rate (%)

Configuration File

Save the current inputs to a JSON file or restore a previously saved configuration.

Decision Summary

The lower net present cost is treated as the preferred economic alternative. Liquidity curves show timing and opportunity-cost tradeoffs.

Comparison Table

Metric	Option A	Option B	Difference

Charts

The line chart runs through the longer loan term so early payoff effects are visible.

Cost Comparison

Total cash outlay, net present cost, opportunity return, and inflation erosion.

Liquidity And Loan Balance Over Time

Nominal liquidity, opportunity-return liquidity, real purchasing-power liquidity, and outstanding amortized loan balance.

Sensitivity Assumptions

Configure one-variable sensitivity ranges for the term decision. Rate movements are entered in basis points.

Risk-free rate change (bp) Inflation rate change (bp) APR spread change (bp)

Sensitivity Table

Each scenario changes one assumption while holding the rest constant.

Scenario	Option A NPC	Option B NPC	Option B Less Option A	Preferred Alternative

Calculation Breakdown

Formulas

Taxable selling price: $ S = \max(V - R, 0) $
Sales tax: $ T = S \cdot \tau $
Amount financed: $ L = \max(S + T - D, 0) $
Periodic loan rate: $ j = \frac{APR}{12} $
Monthly debt service: $ PMT = \frac{L \cdot j}{1 - (1 + j)^{-n}} $
Total cash outlay: $ C = D + n \cdot PMT $
After-tax risk-free annual rate: $ i_{AT,annual} = i_{annual}(1 - tax) $
After-tax risk-free monthly rate: $ i = \frac{i_{AT,annual}}{12} $
Inflation monthly rate: $ \pi_m = \frac{\pi_{annual}}{12} $
Real monthly discount rate: $ q = \frac{1 + i}{1 + \pi_m} - 1 $
Net present cost: $ NPC = D + \sum_{m=1}^{n}\frac{PMT}{(1 + q)^m} $
Nominal liquidity: $ A^{0}_m = A^{0}_{m-1} - PMT_m $
Opportunity-return liquidity: $ A^{rf}_m = A^{rf}_{m-1}(1 + i) - PMT_m $
Real purchasing-power liquidity: $ A^{real}_m = \frac{A^{rf}_m}{(1 + \pi_m)^m} $
Outstanding loan balance: $ B_m = B_{m-1}(1 + j) - PMT_m $
After-tax risk-free opportunity return: $ A^{rf}_{N} - A^{0}_{N} $
Inflation erosion: $ A^{rf}_{N} - A^{real}_{N} $
Nominal-to-PV reduction: $ C - NPC_{rf} $
Inflation impact on PV: $ NPC_{real} - NPC_{rf} $

Notation

$ V $: Vehicle price before incentives/rebates.
$ R $: Taxed incentives/rebates.
$ S $: Taxable selling price after incentives/rebates.
$ \tau $: Sales tax rate per dollar of taxable selling price.
$ T $: Capitalized sales tax amount.
$ D $: Down payment.
$ L $: Amount financed.
$ APR $: Annual percentage rate on the loan.
$ j $: Monthly loan rate.
$ n $: Loan term in months.
$ m $: Month index in a cash-flow or amortization schedule.
$ PMT $: Scheduled level monthly debt service.
$ PMT_m $: Debt-service cash flow paid in month $ m $; zero after payoff.
$ C $: Total cash outlay.
$ i_{annual} $: Annual nominal pre-tax risk-free rate.
$ tax $: Marginal tax rate applied to taxable risk-free interest.
$ i_{AT,annual} $: Annual nominal after-tax risk-free rate.
$ i $: Monthly nominal after-tax risk-free rate.
$ \pi_{annual} $: Annual inflation rate.
$ \pi_m $: Monthly inflation rate.
$ q $: Monthly real discount rate.
$ NPC $: Net present cost using the real monthly discount rate.
$ NPC_{rf} $: Net present cost discounted at the nominal risk-free monthly rate.
$ NPC_{real} $: Net present cost discounted at the real monthly discount rate.
$ A^{0}_m $: Nominal liquidity position at month $ m $ with no investment return.
$ A^{rf}_m $: Liquidity position at month $ m $ compounded at the nominal risk-free rate.
$ A^{real}_m $: Purchasing-power liquidity position at month $ m $, expressed in current dollars.
$ B_m $: Outstanding loan balance at month $ m $.
$ N $: Comparison horizon, equal to the longer loan term.

Computed Values

Glossary

APR: Annual percentage rate for the loan. The calculator converts it to a monthly rate for amortization.
Amortization: The process of paying a loan down over time with fixed payments split between interest and principal.
Taxed Incentives/Rebates: Manufacturer or dealer incentives treated as taxable price reductions before sales tax is calculated.
Down Payment: Initial capital contribution paid at closing. It reduces the financed amount but remains part of total cash outlay.
Financed Principal: The amount borrowed after reducing the selling price for taxed incentives/rebates, adding sales tax, and subtracting the down payment.
Monthly Debt Service: The fixed monthly payment required to amortize the loan over its stated term.
Finance Charge: The total interest expense incurred on the financed amount over the loan term.
Total Cash Outlay: Down payment plus all scheduled monthly debt-service payments over the financing term.
Net Present Cost: The present value of the down payment and scheduled future debt-service payments.
Risk-Free Rate: The nominal return assumption for a low-default-risk investment, used as an opportunity-cost benchmark.
Inflation Rate: The assumed rate of general price-level increase, used to estimate purchasing-power erosion.
Real Liquidity Position: Projected liquidity adjusted for inflation and expressed in current-dollar purchasing power.
PV Inflation Impact: The change in net present cost attributable to using an inflation-adjusted discount rate.