Modified Internal Rate of Return
Also written MIRR · Modified Internal Rate of Return (MIRR)
A variant of IRR that discounts a fund's capital calls and compounds its distributions at the investor's opportunity cost, instead of assuming every cash flow earns the IRR itself.
In plain language
An ordinary IRR quietly assumes something that is rarely true: that every rupee the fund hands back can be reinvested at the fund's own IRR, and that every rupee called costs the investor that same rate. If a fund shows 22%, the arithmetic behaves as if the investor could redeploy each distribution at 22% too.
The workbook's objection is simply that this "does not fit in real life situation". A 22% IRR may be neither the investor's cost of capital nor the opportunity cost of other investments in the market.
The Modified Internal Rate of Return fixes that one assumption. It takes a rate the investor can actually live with — the opportunity cost of funds — and uses it to bring all the capital calls back to the start and to carry all the distributions forward to the end. The return that links those two figures is the MIRR, which the workbook calls "more realistic" than the plain FIRR.
How it works
The workbook builds it in three moves on its own cash flows (Rs crore):
| Year | Y0 | Y1 | Y2 | Y3 | Y4 | Y5 | Y6 | Y7 |
|---|---|---|---|---|---|---|---|---|
| Capital calls | -20 | -30 | ||||||
| Distributions | 0 | 0 | 20 | 30 | 40 | 50 |
The plain FIRR on these flows is 22%.
- Discount the calls to Y0 at the opportunity cost (10%). The Y1 call of 30 becomes 30 × 0.91 = 27.3; with the Y0 call of 20, the total is 47.3.
- Compound the distributions to Y7 at the same 10%. 20 × 1.33 = 26.6, 30 × 1.21 = 36.3, 40 × 1.1 = 44 and 50 stays 50 — a total of 156.9.
- Take the IRR of the two totals — 47.3 out at Y0 and 156.9 in at Y7. That is the MIRR: 18.7%.
In the workbook's summary table of performance measures, IRR (FIRR) and MIRR are the two absolute-return rate measures; TVPI is the absolute-return total measure; Direct Alpha and KS-PME are the market-adjusted counterparts.
The formula
PV of calls = sum of each capital call / (1 + c)^t (discounted to Y0)
FV of dists = sum of each distribution x (1 + c)^(n - t) (compounded to year n)
MIRR = (FV of distributions / PV of capital calls)^(1/n) - 1
c = opportunity cost of funds, n = number of years to the final year
A worked example
Illustrative figures. Kaveri Growth Fund calls Rs 40 crore at the start (Y0) and Rs 60 crore a year later (Y1), then distributes Rs 30 crore, Rs 50 crore, Rs 70 crore and Rs 90 crore at the ends of Y3, Y4, Y5 and Y6.
Its plain IRR works out to about 23.0%.
Mr Iyer, a family-office investor, decides his realistic opportunity cost is 12%:
PV of calls = 40 + 60 / 1.12 = Rs 93.57 crore
FV of dists = 30 x 1.12^3 + 50 x 1.12^2 + 70 x 1.12 + 90
= 42.15 + 62.72 + 78.40 + 90.00 = Rs 273.27 crore
MIRR = (273.27 / 93.57)^(1/6) - 1 = about 19.6%
A more conservative trustee who uses 8% gets PV of calls Rs 95.56 crore, FV of distributions Rs 261.71 crore and an MIRR of about 18.3%.
Same fund, same cash flows, one IRR — but two MIRRs, because each investor states a different opportunity cost. Both are below the 23% headline, which is the workbook's point: the reinvestment assumption was flattering the IRR.
Why NISM asks about it
Chapter 6 (Risk and Return — Investor and Fund Perspective) introduces the MIRR at 6.6.2, immediately after the FIRR at 6.6.1, and places it in the summary table at the end of 6.6.8. Expect a conceptual question — what the MIRR changes about the IRR (the rate used to discount calls and compound distributions) — and a question on the table: which metrics are rate-of-return measures and which are total-return measures, and which are absolute versus market-adjusted.
Common exam traps
- MIRR does not change the cash flows; it changes the rate applied to them. The calls and distributions are exactly the same as for the IRR.
- In the workbook's example one rate (10%) is used for both discounting the calls and compounding the distributions. Do not invent two different rates unless a question gives them.
- Calls are discounted back to Y0; distributions are compounded forward to the final year. Reversing the directions is the usual computational slip.
- MIRR is an absolute-return measure, not a market-adjusted one. The market-adjusted pair is Direct Alpha (rate) and KS-PME (total return).
- When the opportunity cost is below the IRR, the MIRR comes out below the IRR — 18.7% against 22% in the workbook. A question stating the MIRR "improves" the reported return has it backwards for that case.
- IRR on an investment is also called the money-weighted return in the workbook's Illustration 6.1. MIRR keeps that money-weighted character and only replaces the reinvestment rate.
Check yourself
1.A fund reports an FIRR of 22 per cent. If the investor's opportunity cost is 10 per cent, the MIRR will be:
- a)higher than 22 per cent, because the opportunity cost is lower
- b)lower than 22 per cent, because the MIRR replaces the IRR's implicit assumption of reinvestment at 22 per cent with the actual 10 per cent opportunity cost
- c)exactly 22 per cent, since the MIRR is only a presentational change
- d)exactly 10 per cent, being the opportunity cost
Show the answer
Answer: (b) lower than 22 per cent, because the MIRR replaces the IRR's implicit assumption of reinvestment at 22 per cent with the actual 10 per cent opportunity cost
Essentially, the IRR uses the same rate of discounting (or compounding depending upon how you look at it) to arrive at the computation of the implicit rate of return. However, this does not fit in real life situation... the IRR is 22% which may not be the cost of capital of an investor or the opportunity cost of other investments in the market. Therefore, the MIRR considers the opportunity cost of funds at the appropriate rate and computes the return which would then be more realistic. Working the workbook's own numbers at a 10 per cent opportunity cost gives MIRR 18.7% against an FIRR of 22 per cent, and the MIRR provides a more realistic measure than the FIRR.
2.A stock with a beta of 0.8 is:
- a)more volatile and therefore riskier than the market
- b)less volatile and therefore less risky than the market
- c)uncorrelated with the market entirely
- d)guaranteed to return 80 per cent of the market return
Show the answer
Answer: (b) less volatile and therefore less risky than the market
Beta measures a stock's responsiveness or volatility to changes in the overall market volatility, often represented by a benchmark index. If a stock has a beta of 1.0, it perfectly mirrors the market volatility. If the beta of a stock is less than 1.00, it is less volatile — and therefore less risky — than the market and vice versa. Option (d) confuses a volatility measure with a return guarantee; beta says nothing about the level of return.
Where this is taught
Free preparation for NISM Series XIX-ARelated terms
- Time value of moneyThe principle that the same sum of money is worth different amounts at different points on a timeline, because money held today can be invested and because inflation erodes what it will buy.
- Direct AlphaThe IRR of an AIF's cash flows after each has been compounded at market index returns to the valuation date — the fund's out- or under-performance of the market expressed directly as a rate.
- J CurveThe shape of a private fund's returns over its life: negative in the early investing years because of fees, expenses and unripened investments, then rising steeply as exits and distributions arrive.
- Kaplan-Schoar Public Market EquivalentA market-adjusted TVPI: capital calls, distributions and NAV compounded at an index's returns to the valuation date. Above 1 means the AIF beat the market; below 1 means it lagged.
- Total Value to Paid-in CapitalA fund's investment multiple: cumulative distributions plus the residual value of unsold investments, divided by paid-in capital — equivalently, DPI plus RVPI.
- Internal Rate of ReturnThe rate at which the present value of an investor's cash outflows equals the present value of inflows — an annualised return that, unlike ROI, accounts for when each cash flow happened.
- Opportunity CostThe benefit given up on the next-best alternative when money is committed to one investment instead of another — the yardstick an AIF return has to beat before it counts as a good return.