Cash Flow Diagrams

Overview

Engineering reference data for Cash Flow Diagrams in economics.

Key Formulas

Present Value

$PV = \frac{FV}{(1+r)^n}$

Discount a future value to present.

Net Present Value

$NPV = \sum_{t=0}^{n} \frac{C_t}{(1+r)^t}$

Sum of discounted cash flows.

Compound Interest

$FV = PV(1+r)^n$

Future value with compound interest.

Variables

Transaction Examples

Loan Transaction

A loan transaction is characterized by an initial positive cash flow (receiving the funds) followed by a series of negative cash flows (repayments).

$$PV = \sum_{t=1}^{n} \frac{-C_t}{(1 + r)^t} + C_0$$

Where $C_0$ is the initial loan amount (positive) and $C_t$ are the repayment amounts (positive values), hence the negative sign in the sum for outflows.

Investment Transaction

An investment transaction begins with an initial negative cash flow (the outlay) followed by a series of positive cash flows (returns).

$$PV = -C_0 + \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t}$$

Cash Flow Direction Comparison

References

• Original Source