Every number has a formula. Here they are.

Principles

• All amounts are in euro, VAT included, from a private buyer’s point of view.
• All scenarios in a comparison share the same assumptions (horizon, mileage, prices, rates): the comparison is fair by construction.
• Every default value is a declared, editable assumption.
• We always separate cash (what leaves your account) from economic cost (what it really costs you, accounting for time and residual value).
• Default prices and taxes refer to the Italian market: enter your own values for other countries.

Time and cash flows

The simulation is monthly, from t = 0 (signing/purchase) to the horizon H. Every euro is a signed flow: positive when it leaves you, negative when it comes back (selling the car).

Prices rise once a year: in year y (0, 1, 2…) an item costs price × (1 + g)y, where g is the annual increase chosen for that cost family.

Energy and real-world consumption

We use real-world consumption, not type-approval figures. With e = share of km driven electrically (1 for electric cars, 0 for combustion and full hybrids, user-defined for plug-ins) and h = share of home charging:

fuel/km            = (1 − e) × real consumption (l/100 km) / 100
grid kWh/km        = e × real consumption (kWh/100 km) / 100 / (1 − charging losses)
electricity price  = h × home price + (1 − h) × public price
energy cost/km     = fuel/km × fuel price + kWh/km × electricity price

If you only know the official WLTP figure, an indicative reference to estimate the real one (in line with EU on-board fuel consumption monitoring data, OBFCM):

Running costs

maintenance/month = (fixed per year / 12 + wear per 1,000 km × km in the month / 1,000) × maintenance inflation
tyres/month       = cost of a set / tyre life in km × km in the month
road tax          = 0 in exempt years, then the annual amount

Tyres are accrued as they wear, not when the set is replaced: a horizon that ends halfway through a set does not distort the comparison. In a lease, items included in the payment are not counted separately.

Depreciation

Market value is a share of the new list price, as a function of age a (months) and mileage:

a ≤ 12:  share = 1 − year-1 loss × a / 12
a > 12:  share = (1 − year-1 loss) × (1 − annual loss)(a − 12) / 12
km factor = 1 − penalty per 10,000 km × (km driven − expected km) / 10,000   (bounded between 0.5 and 1.2)
value = list price × max(minimum share, share × km factor)

Alternatively the engine accepts a table of residual values (age → share) with linear interpolation: this is where real market data plugs in.

Ownership models

Cash

Price paid + costs at month 0; at the end the car is worth its market value.

Loan

French (annuity) amortisation with an optional balloon. With monthly rate i = nominal rate / 12, principal C, balloon B and n instalments:

instalment = (C − B × (1 + i)−n) × i / (1 − (1 + i)−n)

The APR is estimated as the internal rate of return of the loan flows (principal net of upfront fees against instalments, collection fees and balloon), annualised. If the loan runs longer than the horizon, the outstanding debt is paid off on sale.

Long-term lease

Upfront payment and monthly payments in advance; at the end of the contract, excess km × excess km charge, plus estimated return charges. If the horizon exceeds the term, the contract is renewed on the same terms (new upfront payment). There is no residual value: the car is not yours.

Cash and economics

With r = alternative annual return and rm = (1 + r)1/12 − 1:

net cash cost     = Σ flows  (payments − value of the car at the end)
economic cost     = Σ flowt × (1 + rm)H − t
opportunity cost  = economic cost − net cash cost

The economic cost is the value of all flows at the end of the period: every euro spent earlier could have earned r until the horizon. That is why paying cash has a hidden cost, and a loan with a nominal rate below r can cost less even though more money leaves your account.

The economic breakdown reconciles exactly with the total:

economic cost = depreciation (price + costs − final value)
              + loan interest and fees
              + lease
              + energy + maintenance + insurance + road tax + other costs
              + opportunity cost

Indicators

Limits and sources

• Vehicle profiles are illustrative: segment archetypes with rounded values, not real models.
• We do not (yet) model business taxation, deductibility, VAT recovery, local incentives or early termination penalties.
• Estimates are not financial advice: always check the actual terms of offers and contracts.