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Internal Rate of Return (IRR) Calculator
Calculate the profitability of potential investments with multiple cash flows
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Internal Rate of Return
NPV at IRR
Investment Decision
Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows from a project equal to zero. It’s used to evaluate the attractiveness of a project or investment.
In the formula, CFt represents the cash flow at time t, and IRR is the rate being solved for. The calculation is typically done through trial and error or using financial calculators/software.
Example Calculation
For an investment with an initial outlay of $10,000 and cash inflows of $3,000, $4,000, and $5,000 over three years:
-$10,000 + $3,000/(1+IRR) + $4,000/(1+IRR)2 + $5,000/(1+IRR)3 = 0
Solving this equation gives an IRR of approximately 8.21%.
IRR vs. Other Investment Metrics
While IRR is a popular metric for evaluating investments, it has limitations and should be used alongside other metrics:
- Net Present Value (NPV): Measures the absolute dollar value of an investment, while IRR measures the percentage return.
- Payback Period: Measures how quickly an investment recovers its initial cost, ignoring the time value of money.
- Profitability Index: Ratio of present value of future cash flows to initial investment, similar to IRR but easier to calculate.
Understanding Internal Rate of Return
Internal Rate of Return (IRR)
The discount rate that makes the net present value (NPV) of all cash flows from a project equal to zero. It represents the expected annualized rate of return for an investment.
IRR Calculation
IRR is calculated by finding the rate that sets the NPV equation to zero. This typically requires iterative methods or financial calculators, as there’s no algebraic solution for IRR with multiple cash flows.
IRR Decision Rule
Accept projects with IRR greater than the required rate of return (hurdle rate). When comparing mutually exclusive projects, the one with the higher IRR is generally preferred, though NPV may be a better metric for ranking.
IRR Limitations
IRR assumes reinvestment at the IRR rate, which may not be realistic. It can also give multiple values for non-conventional cash flows and may lead to incorrect decisions when comparing projects of different sizes or durations.
Modified IRR (MIRR)
A modification of IRR that addresses reinvestment rate assumptions by assuming positive cash flows are reinvested at the firm’s cost of capital and negative cash flows are financed at the firm’s financing cost.
Practical Applications
IRR is widely used in capital budgeting to evaluate the profitability of investments, compare projects, and make decisions about whether to proceed with a particular investment or project.