Why This MattersUnderstand the question a formula answers before deciding whether to follow the symbols.
Understand what each calculation measures, which numbers it uses, and what it cannot tell you. Full formulas and worked examples are retained.
Add the included assets, then subtract the included debt. Keep the same date and ownership rules throughout.
Balance-sheet identity. Specify valuation date, ownership and attributable obligations. If business equity is already net of business debt, do not subtract the same debt again.
Subtract an upfront purchase from cash before the first month starts. A later receipt cannot fund an opening payment.
Opening liquidity after a cash acquisition; L(pre) is cash before that use. The model flags an unfunded opening payment even if later income would make the ending balance positive.
Start with the previous cash balance, add income, and subtract each stated use once. A negative balance needs funding the example has not provided.
Monthly cash identity for t = 1 through the declared horizon. Every payment appears once. A negative result is an unmet cash need, not permission to overdraw or an assumed loan.
Opening cash $2,000 + take-home earned income $3,000 + net asset income $100 − essentials $2,400 − other consumption $300 − investment transfer $200 − one-off use $500 = closing cash $1,700.
The $200 investment transfer reduces available cash here. It is not necessarily a $200 loss of net worth: another owned asset may increase. State whether you are measuring cash or total wealth.
Compare net cash from assets with essential bills. This is one ratio, not a complete test of financial independence.
Asset-income coverage. Negative asset cash produces negative coverage. Zero essentials makes this ratio undefined. Coverage is not a full financial-independence test.
Estimate how long cash covers a constant monthly essential shortfall. This version leaves out other spending and investment transfers; use the full cash plan for those.
Constant-flow runway in months. For a no-earned-income case set Y to zero. This simple estimate excludes Q and I; a full planned-spending forecast uses M03. If the denominator is nonpositive, report no projected monthly deficit under these assumptions, not infinite security.
With $6,000 available cash, no earned income, $2,500 essential outflows and $500 monthly net asset income, the constant essential-only deficit is $2,000 per month. Runway is $6,000 / $2,000 = 3 months.
If outflows arrive before receipts, a bill may become unfunded earlier. Other consumption, investing, price changes and one-off events require a full cash path.
Follow the debt from its starting balance through interest, any included financed fee, and the payment. The payment cannot exceed the amount owed.
One-debt schedule: opening balance, monthly contractual rate, financed fee and end-of-month payment. The actual payment is capped at the amount due. Daily interest, penalties, new draws and minimum-payment rules are outside this simplified schedule.
Adjust a net money return for price changes over the same period to compare buying power.
Same-period return rates. The nominal input must already reflect the stated fee and tax assumptions. Do not subtract inflation from a rate in another period. This conversion is not a return forecast.
After an asset loses value, subtract the unchanged debt. The remaining ownership value can fall by a larger percentage than the asset.
Holding debt fixed for the illustration, a $100,000 asset financed with $60,000 debt begins with $40,000 equity. A 20% asset decline leaves $20,000 equity: a 50% decline in equity before interest, costs and amortization.
Opening asset value $100,000 minus fixed debt $60,000 leaves equity $40,000. After a 20% asset decline, value is $80,000 and equity is $20,000.
The asset falls 20%; the equity falls 50%. This example holds debt fixed and omits costs. It explains amplification, not the likelihood of a price change.
Add the squared shares for the income sources or groups you named. This describes concentration; it is not a chance of losing income.
For nonnegative source incomes, divide each by total income and sum the squared shares. Two equal sources have H = 0.5; one combined group has H = 1. With no income, the index is undefined.
Check every included month and scenario against your chosen cash cushion. Also report any balance below zero separately.
A chosen reserve-policy constraint. Separately record whether L(t,s) falls below zero. Any breach is retained even if ending cash later recovers. The declared horizon and scenario set are part of the result.
Keep only actions that pass every stated required check. An unresolved check means more information is needed, not that the action is inherently wrong.
This defines the known feasible set under the chosen floor, horizon and scenarios. An unknown required check prevents membership until resolved. It is not evidence that the action is inherently wrong.
Compare each stated dimension separately. One option dominates only if it is no worse on all of them and better on at least one.
Compare quantities with the same units and meanings, and state which direction is preferred. Compare scenario by scenario where relevant. This partial ordering need not produce one winner; a time-versus-cash tradeoff can remain unresolved until the person states a preference.
Option A leaves $600 monthly cash and requires 45 work hours; option B leaves $400 and requires 35. If more available cash and fewer work hours are both preferred, neither dominates the other.
A comparison must preserve the same time period, cash boundary and required checks. A cash advantage does not override a failed ethical condition. The option workshop leaves the preference to the reader.
Follow cash after each payment and receipt in the cycle. Same-day income is counted first in this example; actual bank processing may differ.
Daily timing follows every event in a declared cycle. Minimum event balance can reveal a gap hidden by a positive ending balance. The calendar credits income before payments on the same day; settlement timing still requires verification.
For each month, add interest and subtract the allocated payment. Compare the two orders using the same payment budget and stated rounding rules.
The debt tool compares two orders with the same fixed monthly budget. APR is divided by 12, interest rounds to cents, minimums are applied first and unused budget rolls to remaining debts. It excludes daily interest, changing rates, fees and lender-specific rules.
Grow the current investment balance using the chosen monthly factor, then add the month-end contribution. Fees and inflation use the separately stated rules.
The compound tool uses an assumed effective annual return and multiplicative annual fee. Net annual factor is (1 + return) × (1 - fee); its twelfth root supplies the monthly factor. Contributions arrive at month end. Inflation deflates nominal results; tax is excluded.
An assumed 6% annual return with a 0.5% proportional annual fee gives factor 1.06 × 0.995 = 1.0547, or 5.47% net nominal return under this convention.
With assumed 3% inflation for the same period, real return is 1.0547 / 1.03 − 1 = approximately 2.398%. Rates are assumptions. Actual fee timing, tax and market paths may differ.
Find the lowest cash amount, including the starting balance and every modeled month end. A later recovery does not hide an earlier shortfall.
The lowest opening or month-end available cash in a disclosed scenario. H is a finite horizon in months. This minimum detects an earlier shortage even when the final cash balance is positive. It does not inspect payment timing within a month.
A path with opening cash $1,000, month 1 cash −$200 and month 2 cash $700 has a minimum of −$200. The $700 ending balance does not fund the missing $200 in month 1.
Change the ordering of receipts or the horizon and the minimum can change. Use the daily calendar when the relevant constraint is a payment date.
Calculate the additional cash needed at the start to keep this fixed cash path above the chosen minimum. The calculation does not identify a source for that money.
Under fixed cash flows, an additional amount available at the opening shifts every balance by that amount. F is the household’s chosen cash floor. The formula gives the least nonnegative opening addition that would meet that floor along this particular path, without identifying or assuming funding.
If the lowest modeled cash is $900 and the chosen floor is $3,000, the arithmetic top-up is $2,100. Add $2,100 to every opening and month-end balance; the minimum becomes $3,000.
This identity assumes the addition has no repayment, fee, tax, eligibility or behavior effect. A loan usually changes future cash flows, so its proceeds cannot be treated as a free top-up. Rebuild the path with its actual terms.
Find the equal end-of-period payment that clears a fixed-rate loan over a chosen number of periods before monthly cent rounding. Zero interest uses a separate rule.
An unrounded level end-of-period payment P that amortizes opening principal D over n periods at a fixed periodic rate i. There are no fees, extra draws or missed payments. The debt tool instead accepts supplied minimums and an extra-payment budget, rounds interest each month, and caps the final payment.
Starting with D(t+1) = D(t)(1+i) − P, repeated substitution gives D(n) = D(0)(1+i)^n − P[(1+i)^n − 1]/i. Set D(n)=0 and solve for P.
For $1,200 over 12 months at zero interest, P=$100. At a positive rate, the payment must also cover interest. Rounding changes the final settlement; the closed form is a mathematical reference, not a lender payoff quote.