Economic Internal Rate of Return

Two different questions can be asked about the same road, the same solar park, the same rural clinic.

What did the fund make? That is the financial internal rate of return — FIRR, or just "IRR" in investment conversation. It counts only the money the fund put in and the money the fund got back.

What did the country make? That is the economic internal rate of return. It counts the same project cash flows, and then adds the wider direct and indirect economic benefits the project produced for people who are not investors in the fund at all — the commuters who now save an hour a day, the factory that now gets uninterrupted power.

Both are internal rates of return. They differ only in whose benefit is allowed into the calculation.

The discounting machinery is identical. You find the rate that makes the present value of inflows equal the present value of outflows. What changes is the set of cash flows you feed it.

FIRR takes the fund's own flows: capital calls out, distributions in. It is the number that appears in the investor report, drives the J-curve, and sits under every hurdle, catch-up and carry calculation in the fund documents.

EIRR takes those flows and adds quantified economic benefits accruing to third parties — and, properly done, subtracts quantified economic costs. It is an appraisal measure, produced by the project sponsor or a development agency, not by the fund administrator.

The gap between the two is precisely why Category I exists. An infrastructure or social-impact project whose EIRR far exceeds its FIRR is one the economy wants built and the private market will underfund — which is the definition of a sector "which the government or regulators consider as socially or economically desirable", and the reason those funds are given concessions the other categories do not get.

FIRR:  Σ   Fund cash flow_t                      ÷ (1 + FIRR)^t  = 0

EIRR:  Σ ( Fund cash flow_t
           + wider economic benefit_t
           − wider economic cost_t )               ÷ (1 + EIRR)^t  = 0

The workbook defines EIRR but does not work it. The illustration below is built on that definition, not lifted from the text.

A Category I Infrastructure Fund puts Rs 400 crore into a highway SPV and exits five years later for Rs 760 crore. No interim distributions.

Financial IRR. Rs 400 crore compounding to Rs 760 crore over five years:

400 × (1 + r)^5 = 760
(1 + r)   = (1.90)^(1/5) = 1.1370
FIRR      = 13.70%

Now the economic layer. The project appraisal values fuel and travel-time savings to road users at Rs 60 crore a year for five years. Real money to the economy; not one rupee of it reaches the fund.

Economic cash flows, Rs crore:

Solving for the rate that makes this stream net to zero:

Interpolating, EIRR ≈ 25.8%.

So the same highway earns 13.7% for the fund and roughly 25.8% for the economy. The first number goes in the private placement memorandum and drives the hurdle and the carry. The second explains why the fund is in Category I and why the state cared whether the road got built at all.

Chapter 7 (Fund Performance and Benchmarking of AIFs), section 7.3 "Return Measures in Alternative Investments". The workbook introduces IRR as the Financial Internal Rate of Return precisely so it can tell you to distinguish it from the Economic Internal Rate of Return, "which also consider wider direct and indirect economic benefits".

The examinable content is definitional, and the question shape is a distinguishing one: which measure includes wider economic benefit, which measure goes into an investor report, which one the distribution waterfall runs off. Do not expect to be asked to compute an EIRR.

• EIRR is not FIRR. FIRR is the fund's return and belongs to the investors. EIRR is a public-appraisal measure and belongs to nobody's bank account.
• EIRR is not "gross IRR". Gross versus net IRR is about whether fees and expenses have been deducted. EIRR versus FIRR is about whose benefit is counted at all. Two entirely different distinctions.
• Nobody is paid in EIRR. Hurdle, catch-up, clawback and carried interest all run off realised cash, which means FIRR.
• For infrastructure and social ventures EIRR is typically higher than FIRR — which is the economic case for Category I concessions, and the reason a fund can be worth backing publicly while looking thin privately.
• Both are internal rates of return, so both inherit IRR's weaknesses: sensitivity to the timing of flows, and the fact that a 20% IRR over two years is a very different proposition from 25% over eight years on illiquid assets.
• The workbook gives EIRR a single sentence. Learn the distinction, not a formula.