TVM, cash flow & loans
Assumptions
- TVM rates are per period and must use the same unit as NPER. Cash paid out is negative, cash received is positive, and payments occur at period end unless Beginning is selected.
- Cash-flow item 0 occurs today; later items are one equal period apart. NPV includes item 0. IRR returns one bracketed root, while projects with multiple sign changes can have multiple or no economically useful IRRs. RATE can likewise have more than one mathematically valid solution; TVM reports one numerical root from its iterative search.
- Loans use a fixed nominal annual rate divided by 12 and whole monthly periods. CPM fixes the payment; CAM fixes principal repayment.
Limitations
- Convert quoted annual rates to the required periodic rate before using TVM or cash-flow tools.
- Loan schedules exclude fees, insurance, taxes, prepayments, variable rates, and lender-specific per-row rounding, so they are not payoff statements.
Worked example
TVM: PV = -10,000, rate = 5% per period, NPER = 10, PMT = 0 gives FV = 16,288.95. Cash flows [-1,000, 600, 600] at 10% give NPV = 41.32.