Cash-flow timeline

A timeline is the control surface for financial mathematics. Mark t = 0 as the declared valuation date, not automatically “today.” Mark later boundaries at equal intervals and place each cash flow on its actual boundary. A single sum at t = 3 is not three annual payments, and a payment at the beginning of each year is not an end-of-year stream.

For a three-year target, a minimal timeline reads:

t=0             t=1             t=2             t=3
valuation date                                      $60,000 target

The three gaps—not the four labels—supply n = 3. If the rate is monthly, the same horizon must be rewritten as 36 monthly intervals before it can be used.

Signs and viewpoints

Signs describe a declared viewpoint. A borrower may show loan proceeds as a positive inflow and repayments as negative outflows. A lender sees the reverse. The value of the stream can be reconciled under either convention if the viewpoint is consistent. An unlabeled negative number is not self-explanatory.

Accounting and finance uses

An accounting learner uses the timeline to preserve measurement date and cash- flow timing before consulting the applicable guidance. A finance learner uses it to separate an investment, distribution, borrowing, or repayment from the date at which value is compared. Neither use makes the selected cash flows or rate appropriate merely because the diagram is tidy.

Stop when dates are missing, intervals are unequal but the method assumes equal periods, payment timing is ambiguous, or annual and subannual units do not match. Fix the fact pattern before calculating.