Capital Investment Decisions
Internal Rate of Return
IRR is the discount rate at which NPV becomes zero. It is the project's break-even return.
Concept First
Learn It Step By Step
Start with the business meaning, then move into the formula.
What is Discount Rate?
The required return used to bring future cash back to today. A higher discount rate lowers present value. Example: if investors require 12% return for the risk of a project, 12% is used to discount future cash flows.
What is Years?
The number of years between today and the cash flow. The farther away the cash flow, the more it is discounted. Example: cash received at the end of Year 3 is discounted for three years, not one year.
What is Initial Investment?
Project cash-flow inputs must be kept consistent across years before applying the investment decision rule. Example: machinery cost, installation cost, and initial working capital paid today to start a project.
How should I read the answer?
Accept the project if IRR exceeds the cost of capital. IRR is intuitive because it is expressed as a percentage.
Formula Lab
Understand the Formula
Read the formula like a business sentence before calculating it.
Formula
Find r such that Sum of Cash Flow_t / (1 + r)^t - Initial Investment = 0
Solved Case Study
Read the Numbers Like an Analyst
Work through one business case slowly: understand the situation, calculate the ratios, then interpret what the numbers are really saying.
Case context
TechVision's IRR is approximately 58.7 percent versus 12 percent cost of capital, a strong accept signal.
1. Understand what IRR solves
IRR is the discount rate that makes NPV equal zero.
2. Compare IRR with cost of capital
TechVision's IRR is about 58.7% and cost of capital is 12%.
The project return is far above the hurdle rate.
3. Interpret carefully
A high IRR is attractive, but always check NPV, scale of investment, timing, and whether cash flows change sign more than once.
Interpretation
What This Means In Practice
Read the result as a business signal, not as a standalone number.
Capital decisions are cash-flow decisions
Accept the project if IRR exceeds the cost of capital. IRR is intuitive because it is expressed as a percentage. The question is not only whether the project is attractive on paper. Ask when cash goes out, when cash comes back, what risk it carries, and whether returns beat the cost of capital.
Decision lens
IRR is widely accepted and easy to communicate, but multiple IRRs can occur when cash flows change sign more than once. Use the method as one part of a decision: strategic fit, NPV, IRR, payback risk, funding capacity, and sensitivity to forecast errors all matter.
Key Takeaway
IRR is widely accepted and easy to communicate, but multiple IRRs can occur when cash flows change sign more than once.
Practice Checkpoint
Check Your Understanding
Work through the quiz in smaller sets. Your answers stay visible while this page is open, so you can review before moving on.
Question 1 of 20
Level 1IRR is the discount rate at which:
Question 2 of 20
Level 1When should MIRR be considered?
Question 3 of 20
Level 1Which underlying item must you understand before calculating or interpreting the result?
Question 4 of 20
Level 1Which statement is the best conceptual reading of this measure?
Question 5 of 20
Level 1While analysing the result, which connected business driver should you also check because it can explain movement in the result?
15 questions remaining in this lesson.
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Connected Concepts
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