Corporate Finance & Capital Budgeting Lab

Internal Rate of Return (IRR) & MIRR Calculator

Calculate Internal Rate of Return (IRR), Modified IRR (MIRR), Net Present Value (NPV), and Profitability Index across hurdle rates in a free corporate finance lab.

Capital Budgeting Engine Cash Flow Schedule Capex vs Terminal Value Matrix Theoretical Framework FAQ

Industry Presets

Load benchmark capital deployment models.

Step 1: Outlay, Annual Cash Flows, Terminal Exit & Hurdle Rates

Project Cash Flow Parameters

💰 Investment Outlay & Intermediate Operating Cash Flows

Gross capital expenditure invested at project inception ($t=0$).
Terminal exit or asset liquidation value realized at the end of Year 5.

📈 Cost of Capital & Reinvestment Hurdle

%
Corporate hurdle rate or weighted average cost of capital used to compute NPV and discount outflows.
%
Realistic rate at which positive intermediate annual cash flows can be reinvested in the business.

💡 MIRR vs. IRR Core Insight:

Standard IRR assumes all intermediate cash inflows are reinvested at the project's internal rate of return (e.g. 24.8%). MIRR replaces this flawed assumption with your actual reinvestment hurdle (e.g. 8.0%), yielding a grounded institutional metric.

Step 2: Valuation, Yield & Capital Efficiency Metrics

Investment Yield & Value Creation Summary

ACCELERATE (Value Accretive)
Internal Rate of Return (IRR)
24.82%
NPV = $0 root discount rate
Modified IRR (MIRR)
17.65%
Reinvested @ 8.0% hurdle
Net Present Value (NPV)
$5.92M
Discounted @ 10.0% WACC
Profitability Index (PI)
1.59x
PV of Inflows / Outlay
HURDLE SPREAD (IRR - WACC): +14.82%

Economic value spread generated above the firm's financing and equity cost of capital.

REINVESTMENT BIAS DRAG (IRR - MIRR): 7.17%

Magnitude by which conventional IRR exaggerates returns due to the reinvestment rate fallacy.

Annual Cash Flow & Present Value Schedule

Detailed breakdown of nominal cash flows, discount factors, discounted present values, and cumulative net cash recovery across the 5-year investment horizon.

Period / Milestone Nominal Cash Flow ($) Discount Factor (WACC) Present Value (PV $) Cum. Nominal ($) Cum. Present Value ($)

NPV Profile Curve (Discount Rate Sensitivity)

Examine how Net Present Value declines as the discount rate rises. The exact discount rate where Net Present Value crosses zero is the project's Internal Rate of Return (IRR).

Discount Rate (Hurdle %) Project Net Present Value (NPV $) Decision Status

6×5 Sensitivity Matrix: Initial Outlay vs. Terminal Value

Stress-test investment returns against capital expenditure cost overruns (±30%) and exit multiple / terminal valuation volatility (±30%). Each cell displays the resulting IRR and Net Present Value.

Corporate Finance Formulation: IRR, MIRR & Capital Budgeting

1. The Internal Rate of Return (IRR)

The Internal Rate of Return is the discount rate $r$ that equates the present value of future cash inflows to the initial capital outlay:

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

Because IRR cannot be solved analytically for polynomials of degree $n \ge 5$, corporate treasuries and this calculator use the Newton-Raphson numerical method to solve for the root where $\text{NPV}(r) = 0$.

2. The Reinvestment Rate Fallacy & MIRR

Standard IRR inherently assumes that all interim cash inflows can be reinvested for the remainder of the project at the IRR rate. If a project earns a 35% IRR, standard IRR assumes cash can be perpetually redeployed at 35%—an assumption rarely true in practice.

The Modified Internal Rate of Return (MIRR) corrects this by compounding positive inflows at a realistic cost of capital or reinvestment rate ($r_{\text{reinvest}}$) and discounting negative outflows at a financing rate ($r_{\text{finance}}$):

$$\text{MIRR} = \left( \frac{\text{Terminal Value of Inflows @ } r_{\text{reinvest}}}{|\text{PV of Outflows @ } r_{\text{finance}}|} \right)^{\frac{1}{n}} - 1$$

3. The Profitability Index (PI)

When capital is constrained across multiple attractive investments, projects are ranked by their capital efficiency using the Profitability Index:

$$\text{PI} = \frac{\text{Present Value of Future Cash Inflows}}{\text{Initial Outlay}} = 1 + \frac{\text{NPV}}{\text{Initial Outlay}}$$

A PI > 1.0 indicates value accretion. When budgeting under capital rationing, ranking by PI maximizes total shareholder value.

4. Mutually Exclusive Projects: NPV vs. IRR Conflicts

When choosing between two mutually exclusive projects, IRR can be misleading due to:

  • Scale Differences: A 100% IRR on a $10,000 project creates only $10,000 in value, whereas a 20% IRR on a $10,000,000 project creates millions in value.
  • Timing Differences: Early heavy cash flows yield a higher IRR than back-loaded cash flows even when the back-loaded project has a superior NPV.
  • Decision Rule: When NPV and IRR conflict on mutually exclusive projects, always choose the project with the higher Net Present Value (NPV).

Frequently Asked Questions

The Internal Rate of Return (IRR) is the annualized effective discount rate that sets the Net Present Value (NPV) of all cash inflows and outflows of an investment project to exactly zero.

Standard IRR assumes that intermediate cash flows generated by the project are reinvested at the same high rate as the IRR itself, which is often unrealistically optimistic. The Modified Internal Rate of Return (MIRR) resolves this by compounding positive intermediate cash flows at an explicit reinvestment rate (such as WACC or Treasury yield) and discounting negative cash flows at a financing rate.

Under the standard capital budgeting decision rule, an independent project should be accepted if its IRR exceeds the company's cost of capital (WACC or hurdle rate). If IRR is greater than WACC, the project creates positive Net Present Value (NPV > 0) and increases shareholder value.

Yes. If a project has unconventional cash flows where the sign of the cash flows changes more than once (e.g. initial outflow, positive mid-term cash flows, followed by a major cleanup or decommissioning expense), Descartes' Rule of Signs shows that there can be multiple internal rates of return. In such cases, MIRR or NPV should be used instead.

Yes. You can download the complete annual nominal cash flow schedule, discount factors, cumulative present values, NPV profile, and 6×5 sensitivity matrix as a UTF-8 CSV spreadsheet with formula defense.

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