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What a subscription line actually does to the IRR

The IRR rises by eighteen points and the multiple falls, on the same asset. Both numbers are correct, and the price of a point of headline return is not constant.

A fund buys an asset for 100 and sells it a year later for 120. Without a facility that is a 20% return. Run the same deal with a subscription line for the first six months, call 102 from investors at month six to repay principal and interest, and distribute 120 at month twelve. The annualised IRR is 38.41%.

Almost every explanation of subscription lines stops at “much higher”. It is worth printing the number, because the size of it is the argument: same asset, same buyer, same 20 of gross gain, and the headline return has nearly doubled.

Why it happens, in one line

The holding period is six months, not twelve. 120 against 102 over half a year annualises to 38.41%. Nothing about the asset changed; the measurement window did.

Without the facilityWith a six-month facility
Called from investors100 at month zero102 at month six
Distributed120 at month twelve120 at month twelve
Investor holding period12 months6 months
Money multiple1.200×1.176×
Annualised IRR20.00%38.41%
Net cash to the investor2018
Same asset, same buyer, same 20 of gross gain.

And the multiple goes the other way

This is the half that gets left out. Without the facility investors put in 100 and got back 120: 1.20 times. With it they put in 102 and got back 120: 1.176 times.

The IRR rose by 18.4 points while the multiple fell by 0.0235. Investors are 2 poorer and the marketing document is eighteen points better. Nothing improper has happened and both numbers are correct — which is exactly why a report has to separate asset return, leverage effect, fee drag and timing effect rather than presenting one number.

The price of a point of headline return

Two dollars of interest bought 18.4 points of IRR, so a point of headline return cost about 11 cents per hundred invested. That is a number worth having, because it makes the trade explicit rather than rhetorical. It is also not constant.

Months on the lineInterest accruedCapital calledInvestor holding periodMoney multipleAnnualised IRRCost per point of IRR
00.00100.001.00 yr1.2000×20.00%
31.00101.000.75 yr1.1881×25.84%17.1c
62.00102.000.50 yr1.1765×38.41%10.9c
93.00103.000.25 yr1.1650×84.24%4.7c
124.00104.00zero or negativenot a quantity
155.00105.00zero or negativenot a quantity
186.00106.00zero or negativenot a quantity
Cents of interest per hundred invested, per percentage point of headline return.

Read the last column down. Run the line three months and a point of IRR costs 17.1 cents. Run it nine months and it costs 4.7. The later the capital is called, the cheaper each point of headline return becomes — interest accrues in a straight line while the annualisation effect explodes as the remaining holding period shrinks toward zero.

That is the uncomfortable part, and it is arithmetic rather than an accusation. A manager optimising for the headline is pushed toward calling capital as late as the facility permits, and the arithmetic keeps rewarding him for it right up to the point where the holding period reaches zero and the measure stops meaning anything. The last rows of the table are the reductio: hold the line twelve months on a twelve-month deal and the investor’s holding period is zero. An IRR on a zero holding period is not a small distortion. It is not a quantity.

A worked case, and the components that are not numbers

Take a fund that draws 120 for twelve months at a cost of 8, over a period in which the investments rose 25, and a manager who calls the facility accretive. Both the manager and a sceptical investor can be right, and the way to see it is to lay out the components rather than argue about the verdict.

The four components a report should separate$m
Operational benefit — one capital call instead of threenot a number
Asset appreciation over the period25
Financing cost−8
Net economic effect17
Risk carried — twelve months of drawn debtnot a number
Timing effect on investor IRRreal, and not economic value
120 drawn for twelve months, 8 of cost, 25 of appreciation.

The net economic effect is 17, and the financing cost took 32% of the appreciation. Two of the six lines deliberately carry no figure: the operational benefit of one capital call instead of three is real and nobody prices it, and twelve months of drawn debt is a risk that did not materialise but still had a price the accounts never show. A report that assigns those a number is inventing one; a report that omits the lines entirely is pretending they are zero.

What to ask for, and what to publish

If you are an investor: ask for the IRR both ways — as reported, and recomputed on the date capital would have been called without the facility. The gap is the timing effect, and it is the only honest way to compare a manager who uses a line with one who does not. Ask for the multiple next to it, because the multiple is the number the facility cannot flatter.

If you are the one reporting: publish the four components. It costs a row each and it forecloses the argument. The alternative is a headline that is correct, incomplete, and impossible for the reader to unpick — which is the more serious failure, because it is the harder one to catch.

None of this is an argument against subscription lines. They shorten the administrative burden, they let a manager transact quickly, and the operational benefit is real. It is an argument against reporting one number when the mechanism moves two in opposite directions.

The workbook behind this article

Every figure above is a live formula in the companion file for The Fund Finance Professional, which also holds the calculator at seven facility lengths, the price of a point of IRR, and the four-component breakdown of the worked case. It is free, and it needs no account and no email address.

Open the companion file →

Also on this site

This note is drawn from The Fund Finance Professional. The book is on Amazon.

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