Analyst Dojo
Lesson 2 of 5 6–9% of the exam

IRR and multiple of invested capital (MOIC)

The internal rate of return (IRR) is the discount rate that sets the present value of all cash flows to zero, so it rewards good timing. The multiple of invested capital (MOIC) divides realized plus unrealized value by invested capital. It is easy to read but ignores how long the money took.

6 min cram, 26 min full read. Based on the 2027 CFA® Program Level I curriculum, Alternative Investments, Learning Module 2. Also part of the 2026 curriculum, so it applies to the November 2026 exam too.

Tailor this to you: take the self-assessment

Before this: Why alternative investment performance is hard to judge, Returns of Financial Assets

On the exam

  • Describe the performance appraisal of alternative investments
  • Calculate and interpret alternative investment returns both before and after fees

Calculate and interpret MOIC and describe IRR's role. Expect a MOIC calculation (watch what counts as invested capital), a cash flow IRR on your calculator, and a concept item on which measure ignores timing.

How deeply to learn each part
Know the idea
Understand it in general. It frames other topics, but you will not calculate with it.
Use it
Understand it well enough to solve a question with it. Recognize when it applies.
Memorize
Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

Cram mode: the one-screen version of this lesson. Switch to Full for the explanations, worked examples and interactives.

Which return measure do private equity and real estate use?

Private equity and real estate funds draw capital over several years and pay it out at irregular dates, so a single period return does not describe them. Two measures are standard. The internal rate of return (IRR) uses every cash flow and its date. The multiple of invested capital (MOIC) is a quick shortcut that ignores dates.

IRR and MOIC compared
Return measures for long-lived alternativescash goes in and out at irregular times
  • Internal rate of return (IRR) Memorize the preferred measure
    • Considers timing of cash flows Memorize rewards or penalizes the manager for timing decisions
    • Harder to calculate Memorize needs a financial calculator
    • Needs assumptions Memorize a financing rate for outflows and a reinvestment rate for inflows
  • Multiple of invested capital (MOIC) Memorize a shortcut also called the money multiple
    • Easy to calculate and explain Memorize "we got 2× our money"
    • Ignores timing Memorize 2× in 2 years is not 2× in 15 years

How do you calculate the IRR of a deal?

The IRR is the discount rate that sets the present value of all the cash flows to zero. It is the same idea as the money-weighted return from the rates and returns module, and the same as the capital budgeting IRR in Corporate Issuers.

Internal rate of return Use it
∑t=0nCFt(1+IRR)t=0\sum_{t=0}^{n} \frac{CF_t}{(1 + IRR)^t} = 0

The manager decides when to call capital and when to return it. The timing of cash flows is therefore part of the manager’s skill, and IRR is the yardstick that rewards or penalizes it.

IRR assumes outflows are financed at some rate (often a weighted average cost of capital) and inflows are reinvested at some rate, which may or may not be earned in practice. Those assumptions affect the answer.

How do you calculate MOIC?

MOIC, also called the money multiple, divides everything the investment is worth by the money put in. The realized value is cash already received from exits and distributions. The unrealized value is the estimated worth of what is still held.

Multiple of invested capital Memorize
MOIC=Realized value+Unrealized valueInvested capital\text{MOIC} = \dfrac{\text{Realized value} + \text{Unrealized value}}{\text{Invested capital}}

The denominator is invested capital : the paid-in capital less management fees and fund expenses, so only the money that actually went into investments.

Invested capital Memorize
Invested capital=Paid-in capital−Fees and expenses\text{Invested capital} = \text{Paid-in capital} - \text{Fees and expenses}
Rearrange itMOIC: solve for any input
The question asks for
A fund has invested USD 450 million. It has received USD 270 million from exits, and its remaining holdings are valued at USD 585 million. The MOIC is closest to:

(270 + 585) ÷ 450 = 1.9×

MOIC (multiple, ×)1.9

On your calculator
  1. 270+585=÷450=1.9
  1. 270ENTER585+450÷1.9

ENTER enter (on the HP, puts the number on the stack)

MOIC is easy to calculate and easy to say: investors like to hear that they received two or three times their money. But it says nothing about how long that took.

Why does the time frame matter?

A multiple on its own can hide a very different yearly return. If a single investment returns a multiple MM after TT years with nothing paid out in between, the equivalent yearly return is M1/T−1M^{1/T} - 1.

A multiple as a yearly rate Use it
r=MOIC1/T−1r = \text{MOIC}^{1/T} - 1
Rearrange itA multiple as a yearly rate: solve for any input
The question asks for
A fund returns 2× its single investment in one lump sum after 5 years. The equivalent yearly return is closest to:

2^(1 ÷ 5) − 1 = 14.87%

Equivalent yearly return, r14.87%

On your calculator
  1. 2y^x(1÷5)=−1=0.1487

y^x power

  1. 2ENTER51/xy^x1−0.1487

ENTER enter (on the HP, puts the number on the stack) · 1/x reciprocal · y^x power

InteractiveIRR vs MOIC: same money, different years

Try this 0 of 3

  • Delay the exit by a year and compare both measures
  • Push the IRR above 16% without changing any amount
  • Mark the last inflow as a valuation, not a sale
IRR13.52%
MOIC1.80×
Invested50.00
Realized90.00

Selected cash flow

ReceivedPaid in012345678−40−10+15+75

Drag an arrow along the axis, or select it and use Earlier and Later. Years are along the bottom; amounts are USD millions.

The worked example: 1.80× the money back, 13.52% a year.

Show working

IRR: solve −40.00 − 10.00 ÷ (1 + IRR) + 15.00 ÷ (1 + IRR)^4 + 75.00 ÷ (1 + IRR)^5 = 0 → IRR = 13.52%

IRR on your calculator
  1. CF2NDCLR WORKopen the cash flow worksheet and clear it
  2. 40+|-ENTER↓CF0 = −40
  3. 10+|-ENTER↓C01 = −10
  4. ↓0ENTER↓2ENTERC02 = 0, F02 = 2 (years in a row)
  5. ↓15ENTER↓C03 = 15
  6. ↓75ENTER↓C04 = 75
  7. IRRCPT13.52

CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · +|- change sign · ENTER enter (on the HP, puts the number on the stack) · IRR internal rate of return · CPT compute

  1. fCLEAR REGclear the cash flow registers
  2. 40CHSgCF0t = 0
  3. 10CHSgCFj−10
  4. 0gCFj2gNj0, 2 years in a row
  5. 15gCFj15
  6. 75gCFj75
  7. fIRR13.52

f gold shift key · CLEAR REG clear all registers · CHS change sign · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · Nj times cash flow j repeats · IRR internal rate of return

MOIC = (realized + unrealized value) ÷ invested capital = (15 + 75) ÷ (40 + 10) = 90.00 ÷ 50.00 = 1.80×

MOIC on your calculator
  1. 15+75=÷(40+10)=1.8000
  1. 15ENTER75+40ENTER10+÷1.8000

ENTER enter (on the HP, puts the number on the stack)

MOIC has no time in it: the same 1.80× over a longer life means a lower annual return. For comparison, 2.0× in 5 years is 2^(1/5) − 1 = 14.9% a year; in 10 years it is 7.2% a year.

MOIC counts the money; IRR also counts the years.

The same logic shows up inside one deal. If the sale proceeds of 75 in the first example arrive in year 6 instead of year 5, the cash flows are −40, −10, 0, 0, +15, 0 and +75. MOIC stays at 1.80×, but the IRR falls from 13.52% to 11.40%. MOIC counts the money; IRR also counts the years.

Exam tip When a question gives a multiple and a holding period, convert before comparing. When it gives uneven cash flows, use the cash flow worksheet.

Go deeper Limits of IRR

IRR depends on the reinvestment and financing assumptions described above, and a set of cash flows that changes sign more than once can have more than one IRR. These issues are covered with capital budgeting in Corporate Issuers. For this module, remember the contrast: IRR counts timing but is harder to calculate and needs assumptions; MOIC is simple but blind to time.

Go deeper Why the middle of a fund's life is hard to read

After a private equity fund has called all its commitments, interim accounting values matter less for a while because no cash moves on them. Values may then sit near cost with only small adjustments until an impairment or a sale. The unrealized part of MOIC therefore rests on Level 3 estimates, so treat an interim MOIC with caution.

Memorize this

MemorizeIRR versus MOIC

IRRMOIC
Timing of cash flowscountedignored
Effortcalculator or solverone division
Assumptionsfinancing and reinvestment ratesnone
Usepreferred measureshortcut for private equity and real estate

Memory hook MOIC counts the money; IRR also counts the years.

Know it cold MOIC=realized+unrealizedinvested capital\text{MOIC}=\dfrac{\text{realized}+\text{unrealized}}{\text{invested capital}}, with invested capital = paid-in capital − fees and expenses.

MemorizeA multiple needs a time frame

Memory hook Same 2.0×: five years is about 15% a year, ten years is about 7% a year. Double the time and the yearly rate roughly halves.

Know it cold Single outflow and single inflow: r=MOIC1/T−1r=\text{MOIC}^{1/T}-1.

IRR and MOIC compared
Return measures for long-lived alternativescash goes in and out at irregular times
  • Internal rate of return (IRR) Memorize the preferred measure
    • Considers timing of cash flows Memorize rewards or penalizes the manager for timing decisions
    • Harder to calculate Memorize needs a financial calculator
    • Needs assumptions Memorize a financing rate for outflows and a reinvestment rate for inflows
  • Multiple of invested capital (MOIC) Memorize a shortcut also called the money multiple
    • Easy to calculate and explain Memorize "we got 2× our money"
    • Ignores timing Memorize 2× in 2 years is not 2× in 15 years
Internal rate of return Use it
∑t=0nCFt(1+IRR)t=0\sum_{t=0}^{n} \frac{CF_t}{(1 + IRR)^t} = 0
Quick example

Cash flows of −100, +30, +40 and +90 at years 0 to 3. The rate that sets the present value to zero is 22.56%.

On your calculator
  1. CF2NDCLR WORK
  2. 100+|-ENTER↓
  3. 30ENTER↓↓
  4. 40ENTER↓↓
  5. 90ENTER
  6. IRRCPT 22.56

CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · +|- change sign · ENTER enter (on the HP, puts the number on the stack) · IRR internal rate of return · CPT compute

  1. fCLEAR REG
  2. 100CHSgCF0
  3. 30gCFj
  4. 40gCFj
  5. 90gCFj
  6. fIRR 22.56

f gold shift key · CLEAR REG clear all registers · CHS change sign · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · IRR internal rate of return

Multiple of invested capital Memorize
MOIC=Realized value+Unrealized valueInvested capital\text{MOIC} = \dfrac{\text{Realized value} + \text{Unrealized value}}{\text{Invested capital}}
Quick example

Invested capital 36, realized value 20, remaining holdings valued at 61. (20 + 61) ÷ 36 = 2.25×.

On your calculator
  1. 20+61=÷36= 2.25
  1. 20ENTER61+36÷ 2.25

ENTER enter (on the HP, puts the number on the stack)

Invested capital Memorize
Invested capital=Paid-in capital−Fees and expenses\text{Invested capital} = \text{Paid-in capital} - \text{Fees and expenses}
Quick example

Investors have paid in 320 and fees and expenses took 24. Invested capital is 320 − 24 = 296.

On your calculator
  1. 320−24= 296
  1. 320ENTER24− 296

ENTER enter (on the HP, puts the number on the stack)

A multiple as a yearly rate Use it
r=MOIC1/T−1r = \text{MOIC}^{1/T} - 1
Quick example

A single investment returns 3.0× its cost after 8 years. 3^(1/8) − 1 = 14.72% a year.

On your calculator
  1. 3y^x(1÷8)=−1= 0.1472

y^x power

  1. 3ENTER81/xy^x1− 0.1472

ENTER enter (on the HP, puts the number on the stack) · 1/x reciprocal · y^x power

How it is asked

  1. MOIC with a follow-on investment

    A fund invests 3.6 and later 0.9 more, then exits for 9.9. MOIC?

    9.9 ÷ (3.6 + 0.9) = 2.20×. Traps: 2.75× (ignores the follow-on) and 11.00× (divides by the follow-on only).

  2. Which measure ignores timing

    Which measure ignores the timing of cash flows: IRR, MOIC or the money-weighted return?

    MOIC. IRR and the money-weighted return are the same idea and both use timing.

  3. Same multiple, different holding period

    Two funds both return 2.5×, one over 3 years, one over 7. Compared with the 7-year fund, the 3-year fund's IRR is...

    Higher. The same multiple earned faster means a higher yearly rate.

  4. What counts as invested capital

    Paid-in 350, fees and expenses 35, realized 190, unrealized 405. MOIC?

    (190 + 405) ÷ (350 − 35) = 1.89×. Traps: 1.70× (divides by paid-in) and 0.60× (leaves out unrealized).

Exam traps

  • Leaving unrealized value out of the MOIC numerator. Remaining holdings count.
  • Saying MOIC accounts for timing. It does not; IRR does.
  • Dividing by committed capital, or by paid-in capital, rather than invested capital (paid-in less fees and expenses).
  • Forgetting a follow-on investment in the denominator.

Checkpoint

6 exam-style questions. About 90 seconds each.

  1. 1A fund invests INR 2.5 billion and later another INR 0.5 billion in a company, and exits for INR 7.2 billion. The MOIC is closest to:

  2. 2Which of the following performance measures ignores the timing of cash flows?

  3. 3Two funds both return 1.8× invested capital, one over 4 years and one over 9 years. Compared with the 9-year fund, the 4-year fund's IRR is most likely:

  4. 4Investors in a private equity fund have paid in USD 400 million. Fees and expenses took USD 40 million. The fund has distributed USD 300 million and its remaining holdings are valued at USD 480 million. The MOIC is closest to:

  5. 5A fund's cash flows, in USD millions, are −100 at year 0, −20 at year 1, 0 at year 2, +60 at year 3 and +110 at year 4. The IRR is closest to:

  6. 6Which statement about IRR as a measure for long-lived alternative investments is most accurate?

Key takeaways

  • IRR is the money-weighted return: the discount rate that sets the present value of all cash flows to zero. It rewards timing.
  • MOIC = (realized + unrealized) ÷ invested capital. It has no time dimension.
  • Invested capital is paid-in capital less fees and expenses.
  • Always ask how long a multiple took: the same multiple earned sooner means a higher IRR.
Internal rate of return Use it
∑t=0nCFt(1+IRR)t=0\sum_{t=0}^{n} \frac{CF_t}{(1 + IRR)^t} = 0
Quick example

Cash flows of −100, +30, +40 and +90 at years 0 to 3. The rate that sets the present value to zero is 22.56%.

On your calculator
  1. CF2NDCLR WORK
  2. 100+|-ENTER↓
  3. 30ENTER↓↓
  4. 40ENTER↓↓
  5. 90ENTER
  6. IRRCPT 22.56

CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · +|- change sign · ENTER enter (on the HP, puts the number on the stack) · IRR internal rate of return · CPT compute

  1. fCLEAR REG
  2. 100CHSgCF0
  3. 30gCFj
  4. 40gCFj
  5. 90gCFj
  6. fIRR 22.56

f gold shift key · CLEAR REG clear all registers · CHS change sign · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · IRR internal rate of return

Multiple of invested capital Memorize
MOIC=Realized value+Unrealized valueInvested capital\text{MOIC} = \dfrac{\text{Realized value} + \text{Unrealized value}}{\text{Invested capital}}
Quick example

Invested capital 36, realized value 20, remaining holdings valued at 61. (20 + 61) ÷ 36 = 2.25×.

On your calculator
  1. 20+61=÷36= 2.25
  1. 20ENTER61+36÷ 2.25

ENTER enter (on the HP, puts the number on the stack)

Invested capital Memorize
Invested capital=Paid-in capital−Fees and expenses\text{Invested capital} = \text{Paid-in capital} - \text{Fees and expenses}
Quick example

Investors have paid in 320 and fees and expenses took 24. Invested capital is 320 − 24 = 296.

On your calculator
  1. 320−24= 296
  1. 320ENTER24− 296

ENTER enter (on the HP, puts the number on the stack)

A multiple as a yearly rate Use it
r=MOIC1/T−1r = \text{MOIC}^{1/T} - 1
Quick example

A single investment returns 3.0× its cost after 8 years. 3^(1/8) − 1 = 14.72% a year.

On your calculator
  1. 3y^x(1÷8)=−1= 0.1472

y^x power

  1. 3ENTER81/xy^x1− 0.1472

ENTER enter (on the HP, puts the number on the stack) · 1/x reciprocal · y^x power

All Alternative Investments formulas, every lesson

Practice exam-style questions on Alternative Investment Performance and Returns

Questions about this lesson?

Where this comes back

Questions candidates ask

How do you calculate MOIC?

Add the value already realized and the value of the remaining holdings, then divide by invested capital, which is paid-in capital less fees and expenses. With 90 realized, nothing left and 50 invested, the MOIC is 90 ÷ 50 = 1.80×.

What is the difference between IRR and MOIC?

IRR is the discount rate that sets the present value of all cash flows to zero, so it uses their timing. MOIC divides total value by invested capital and ignores timing, so a 2× result in 3 years and in 15 years look the same.

Why do private equity funds use IRR?

The manager decides when capital is called and when proceeds are returned, so timing is part of the result. IRR rewards or penalizes those timing decisions, which MOIC cannot do.

Spotted an error? Tell us and we will fix it.

  1. Why alternative investment performance is hard to judge
  2. IRR and multiple of invested capital (MOIC)
  3. Leverage, redemptions, lockups and gates
  4. Calculating returns after fees: management, incentive, hurdle and high-water mark
  5. Fund of funds fees, survivorship bias and backfill bias

Ask Sensei Listen instead

Questions on IRR and multiple of invested capital (MOIC)

Learn with Sensei, out loud The voice tutor, in early access

Sensei teaches the lesson aloud and stops when you interrupt: "wait, why is the geometric mean lower?" It answers with the lesson's own example, then quizzes you by voice. Every account can try Sensei on one module, with one voice question.

USD 149 a month founding price (regular USD 199), kept for as long as you stay subscribed. Everything in Plus included.

In active development and improving every day. Send feedback · Plans and pricing

Analyst Dojo Plus

Your free review list holds 10 items.

Plus keeps everything you save, for USD 19 a month. To make room on the free plan, remove something from your review list.

See Plus

Lessons, checkpoints and the lesson questions in practice stay free. Compare plans