Internal Rate Of Return Irr

Overview

Engineering reference data for Internal Rate Of Return Irr 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

Solving for IRR

The Internal Rate of Return (IRR) is found by solving the equation where the Net Present Worth (NPW) equals zero:

$$\sum_{t=0}^{n} \frac{F_t}{(1 + \text{IRR})^t} = 0$$

where $F_t$ is the cash flow at time $t$ (positive for inflows, negative for outflows). This equation typically requires iterative numerical methods, such as:

• Trial and Error: Test different rates until the NPW approaches zero.
• Interpolation: Use two rates where NPW changes sign to estimate IRR.
• Newton-Raphson Method: A more efficient iterative approach for convergence.

Minimum Attractive Rate of Return (MARR)

MARR is the minimum acceptable rate of return for an investment, serving as a benchmark for project viability.

Decision Criteria

• If $\text{IRR} \geq \text{MARR}$, the project is financially acceptable.
• If $\text{IRR} < \text{MARR}$, the project is rejected.

MARR is influenced by factors like cost of capital, risk assessment, and available investment opportunities.

References

• Original Source