A payment probability after signing is not the probability of cash today

A commercial team may estimate a 75% chance that a deposit arrives this month if a contract is signed in time. That is not a 75% chance of receiving the deposit when signing itself remains uncertain. The missing condition can materially overstate expected receipts.

OpenStax's treatment of conditional probability explains that the probability of two events occurring together equals the probability of the first multiplied by the probability of the second given the first. A scenario tree makes that relationship visible by placing the condition on each later branch.

Use complete business statements rather than isolated percentages. Contract signed by the agreed cutoff is one event. Deposit collected by month end, given that timely signing, is another. Changing the cutoff changes the event and may change the appropriate probability.

Consider an invented opportunity with a $100,000 deposit. Assume a 60% chance of signing by the cutoff. Conditional on timely signing, assume a 75% chance that the full deposit is received by month end and a 25% chance that it arrives later. If signing misses the cutoff, assume no deposit can arrive this month.

The complete timely-cash path has probability 60% multiplied by 75%, or 45%. Timely signing followed by later payment has probability 60% multiplied by 25%, or 15%. The remaining 40% belongs to the no-timely-signing path. Those three mutually exclusive path probabilities sum to 100%.

Expected deposit cash this month is therefore $45,000 under these assumptions. Using the conditional 75% directly would produce $75,000 and overstate the modeled expectation by $30,000. Neither expected amount is a guarantee of a partial receipt: the example's actual month-end deposit is either $100,000 or zero.

Branches leaving the same node should represent mutually exclusive alternatives that cover the possibilities within that node. If the signing branch includes both approved and still-under-review contracts, the categories may overlap. A total of 100% does not repair an ambiguous event definition.

A probability tree can have different numbers of branches at different nodes. An unsigned opportunity may have no collection branch this month, while a signed contract may have full payment, partial payment and no payment outcomes. Represent those actual alternatives instead of forcing every stage into an identical yes-or-no format.

Attach the appropriate amount and date to each complete path. A partial-deposit branch needs its own cash amount; it should not inherit the full $100,000 merely because some cash arrives. Keep refundable deposits and later repayment obligations identifiable when they affect the decision.

The multiplication rule does not require signing and collection to be independent when the second probability is correctly conditional. That distinction matters because a late signature can leave less time for procurement approval, invoice processing and payment before the period closes.

Estimate collection timing from contracts that reached a comparable signing stage with comparable time remaining. A general customer payment rate may not describe deposits awaiting a purchase order or contracts signed on the last business day. Preserve the evidence supporting the conditional estimate.

When several opportunities share a customer, procurement committee or commercial dependency, their outcomes may also be connected. Summing expected receipts remains an arithmetic summary, but estimating the chance of a total cash shortage requires a joint model or explicit combined scenarios. Independent branches across unrelated-looking rows can miss that connection.

Once the contract is signed in time, the current forecast no longer includes the possibility that timely signing fails. Under the unchanged example assumptions, the remaining probability of payment this month is 75%. The earlier 45% described the situation before signing was known.

Do not multiply by the old 60% signing probability again after moving the opportunity into a signed-contract population. Conversely, do not preserve a 75% payment estimate if the actual signing date is later than the condition used to estimate it. Update the evidence and remaining timeline together.

Keep the original forecast for performance review. The revised estimate can properly differ because new information arrived. Overwriting the earlier tree would prevent the team from examining whether signing expectations, collection assumptions or both caused the original miss.

Record which observation resolved a branch, such as an executed agreement or a confirmed bank receipt. A salesperson moving an opportunity to a more optimistic stage is new judgment; it is not automatically the same evidence as the modeled event occurring.

Identify the steps between signature and cleared cash: required purchase order, deposit invoice, customer approval and bank receipt. A branch probability should summarize those supported uncertainties, not replace the operational record that explains them. Confirm the relevant dates with the people responsible.

Where the business can take an action, distinguish the action from a random event. Sending a correct deposit invoice is a controllable task. The customer's subsequent processing time is an uncertain outcome. A model that treats an unassigned internal task as a favorable probability can disguise a preventable delay.

Show how the funding decision changes if cash does not arrive. The response may depend on a specific notification date or approved facility. Record the required lead time so management can act before the model's month-end outcome is fully known.

A useful review includes the event definitions, branch assumptions, path probabilities and actual cash amounts. Check probabilities at each split and again across complete paths. Reconcile expected cash to the weighted path amounts without replacing the individual outcomes.

For a material receipt, management should be able to see exactly which conditions must occur before the money is available. That makes the tree more useful than a single confidence percentage: it shows what is known, what remains conditional and which operating step can still change the cash timing.