15 Session 6: IRR · The Internal Rate of Return Problem
| Unit | 2 — Measurement and Theory |
| Book Chapter | 4 (sections 4.2–4.4) |
| Track | Common core (both tracks) |
15.1 Learning Objectives
By the end of this session, students will be able to:
- Define IRR precisely and state its mathematical relationship to NPV.
- Identify the two structural biases of IRR (reinvestment assumption + sign-pattern dependence).
- Distinguish money-weighted from time-weighted returns and explain when each is appropriate.
- Compute IRR for a simple cash flow pattern and identify when multiple IRRs exist.
- Explain why a constant-rate metric cannot correctly summarize performance when discount rates are stochastic.
- Prepare for Session 7’s PME discussion by understanding why IRR’s failures motivated PME’s development.
15.2 Pre-Class Assignment
- Read: Book Chapter 4, sections 4.2–4.4 (~10 pages)
- Optional: Phalippou (2008), “The Hazards of Using IRR to Measure Performance: The Case of Private Equity,” Journal of Performance Measurement
15.3 In-Class Outline (75 minutes)
| Time | Segment | Format |
|---|---|---|
| 0:00–0:05 | Why measurement matters: returns based on bad valuations are bad returns | Lecture |
| 0:05–0:20 | What IRR is, mathematically and conceptually | Lecture + math |
| 0:20–0:35 | Money-weighted vs. time-weighted returns | Lecture + worked example |
| 0:35–0:50 | Two IRR biases: reinvestment + sign-pattern | Lecture + worked examples |
| 0:50–1:05 | Multiple IRRs and the descending-discount problem | Lecture + numerical examples |
| 1:05–1:15 | The constant-rate fallacy: IRR under stochastic discount rates | Lecture |
15.4 Discussion Questions
- The GP-LP relationship has IRR baked into the carried interest formula. If GE-LAV becomes adopted methodology, does the carry formula need to change? How?
- Public mutual funds use TWR. Why has PE never moved to TWR despite known IRR flaws?
- Two PE funds have identical IRRs of 18% but very different cash flow timing patterns. How would you distinguish them from each other in selecting which to commit capital to?
15.5 Worked Numerical Example: When IRR Misleads
Setup: Two PE funds, both reporting IRR = 18%.
Fund A (front-loaded distributions): - \(t=0\): \(-\$100M\) - \(t=2\): \(+\$80M\) - \(t=4\): \(+\$40M\) - \(t=6\): \(+\$20M\) - IRR: 18% (capital out quickly)
Fund B (back-loaded distributions): - \(t=0\): \(-\$100M\) - \(t=2\): \(+\$0M\) - \(t=4\): \(+\$0M\) - \(t=8\): \(+\$200M\) - IRR: 18% (capital out only at end)
The reinvestment problem:
If LP can reinvest at 7% public market rate:
- Fund A realized return: $80M from year 2 grows at 7% to \((80 \cdot 1.07^6) + (40 \cdot 1.07^4) + 20 = \$120M + \$52M + \$20M = \$192M\) at year 8 — total return 92% over 8 years = 8.4% annualized
- Fund B realized return: $200M at year 8 — total return 100% = 9.05% annualized
Interpretation: Same reported IRR (18%), but Fund B’s realized return to the LP is higher because the IRR overstatement is larger for Fund A.
Lesson: Reported IRR can rank funds in the wrong order when reinvestment assumption matters.
15.6 What to Expect Next Session
Session 7 dives into PME (Public Market Equivalent) and its variants. We’ll cover: - The Kaplan-Schoar PME and what it computes - Long-Nickels PME (with implicit reinvestment in the benchmark) - Direct Alpha (Gredil-Griffiths-Stucke) - LA-IRR and LA-PME — the GE-LAV-corrected versions - Which method to use in which context
Reading: Book Chapter 4, sections 4.5–4.10 (~12 pages).