A subscription line is leverage on time: it magnifies whatever the investment does relative to its cost, and the IRR can move either way.
A subscription line raises a fund's IRR only when the investment it bridges returns more than the line costs. Below that, it lowers the IRR, and by more the longer the line is drawn. On an illustrative $50.0m deal bridged for nine months at 7.00 per cent and sold after four years, the line adds 1.29 points of IRR at an $80.0m exit, does nothing at the break-even exit of $65.69m, a 7.06 per cent unlevered return, and takes 2.67 points off at $40.0m.
Worked in full in The Private Equity Fund Controller Playbook by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The usual description of a subscription line says it increases investor IRR. As a rule of thumb it is true in a good vintage and false in a bad one, and the controller who reports the fund's IRR should know exactly where the line crosses over, because the investors will ask why a losing deal looks even worse on the report.
| Input | Value |
|---|---|
| Acquisition cost, paid at month 0 | 50.0 |
| Subscription line interest, simple, all-in | 7.00% |
| Months on the line before investors are called | 9 |
| Exit, after | 4.0 years |
Without the line, investors pay $50.0m at month 0 and hold for 4.0 years. With it, the fund borrows, and nine months later calls $50.0m plus $2.625m of interest, $52.625m, to repay the line. Investors then hold for 3.25 years. Fees and carry are left out so the effect stands alone.
IRR without the line = (Exit ÷ Cost)1/T − 1
IRR with the line = (Exit ÷ (Cost × (1 + r × h)))1/(T − h) − 1
Break-even exit = Cost × (1 + reff)T, with reff = (1 + r × h)1/h − 1
In Excel, with dated cash flows: =XIRR(Flows,Dates) on both series; the break-even exit is =Cost*(1+r*h)^(T/h).
Step 1: the line's effective annual cost. 7.00 per cent simple for nine months is 5.25 per cent for the period, 7.06 per cent a year compounded.
Step 2: the break-even. The two IRRs are equal when the deal's own return equals that rate: 50.0 × 1.07064 = $65.69m, a multiple of 1.314. At that exit both series give 7.06 per cent.
Step 3: each side of it. Above $65.69m, the shorter holding period annualises a gain over fewer years, and the IRR rises. Below it, the interest outweighs what the shorter period adds to a small gain, and on a loss the interest makes the loss larger while the shorter period annualises it over fewer years: the IRR falls.
| Exit | IRR, no line | IRR, with line | Difference, points | Multiple, no line | Multiple, with line |
|---|---|---|---|---|---|
| 40.00 | −5.43% | −8.09% | −2.67 | 0.800 | 0.760 |
| 50.00 | 0.00% | −1.56% | −1.56 | 1.000 | 0.950 |
| 60.00 | 4.66% | 4.12% | −0.55 | 1.200 | 1.140 |
| 65.69 | 7.06% | 7.06% | 0.00 | 1.314 | 1.248 |
| 80.00 | 12.47% | 13.75% | 1.29 | 1.600 | 1.520 |
| 100.00 | 18.92% | 21.84% | 2.92 | 2.000 | 1.900 |
The multiple falls in every row, because $2.625m of interest is a real cost whatever the exit. The IRR rises only in the top two rows. At a $40.0m exit investors lose $12.62m instead of $10.0m, and the reported IRR is −8.09 per cent instead of −5.43.
The 1.29 points at $80.0m split into two parts that pull in opposite directions. Timing alone, the same $50.0m called nine months later, would lift the IRR to 15.56 per cent, +3.09 points; the interest takes back 1.81. At $40.0m both work against the investor: timing costs 1.21 points and interest 1.46.
| Months on line | Called | Exit 45 | Exit 60 | Exit 80 |
|---|---|---|---|---|
| 3 | 50.88 | −3.22% | 4.50% | 12.83% |
| 9 | 52.62 | −4.70% | 4.12% | 13.75% |
| 12 | 53.50 | −5.60% | 3.90% | 14.35% |
| 18 | 55.25 | −7.88% | 3.35% | 15.96% |
A longer line widens the fan in both directions. Eighteen months adds 3.49 points to a good deal and takes 5.28 off a poor one. A fund that bridges every acquisition for a year reports a more dispersed track record, not simply a better one.
The fund controller's companion workbook runs the same test on the book's own case, where fees are included: there the facility helps investors only above a $96.68m sale, and the case sells at $78.0m, so the facility lowers investor IRR.
Treating the line as an IRR enhancer in general. It is leverage on time: it magnifies whatever the deal does relative to the line's cost, gains and losses alike. The second mistake is to report only the IRR with the line. Investors increasingly ask for the IRR without it as well; the gap between the two is the facility effect, and it should carry a sign. For the good-deal case in full, see what a subscription line actually does to the IRR, and for the date mechanics, IRR vs XIRR for fund cash flows.
The line raises IRR only when the investment beats the line's effective cost, here 7.06 per cent, and it always lowers the multiple. Compute the break-even exit, report both IRRs, and expect the facility to make a bad deal look worse. The free workbook for this case separates the timing effect from the interest on the book's own fund.
No. It increases IRR only when the investment returns more than the line's effective cost. On an illustrative $50.0m deal bridged for nine months at 7.00 per cent, the break-even return is 7.06 per cent a year, an exit of $65.69m after four years. At $60.0m the line lowers IRR from 4.66 to 4.12 per cent; at $40.0m from -5.43 to -8.09.
Yes, always downward, because interest is a real cost. On an illustrative $50.0m deal, nine months at 7.00 per cent costs $2.625m, so investors are called $52.625m instead of $50.0m. At an $80.0m exit the multiple falls from 1.600 to 1.520 while the IRR rises from 12.47 to 13.75 per cent.
Grow the cost at the line's effective annual rate over the whole holding period. Nine months at 7.00 per cent simple is 5.25 per cent for the period, 7.06 per cent a year compounded, so a $50.0m deal held four years breaks even at 50.0 times 1.0706 to the fourth power, $65.69m, a 1.314 multiple.
This article is one calculation from The Private Equity Fund Controller Playbook. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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