Weighted Average

What does weighted average mean?

Weighted average (German: gewichteter Durchschnitt) denotes an anti-dilution protection that lowers an investor's entry price, when a later round is priced lower, to a weighted mean of the old and the new price. Such a round is called a down round; the entry price is the price per share that the investor itself paid. The weighting depends on how many shares already exist and how many are newly issued. A small issue at a low price therefore changes the entry price only a little, a large one considerably. In English contract language, the term is weighted average anti-dilution, and with a broad base broad-based weighted average.

The principle corresponds to the average price when refuelling at changing prices. Anyone who fills 40 litres at EUR 2.00 and 10 litres at EUR 1.50 has paid EUR 1.90 per litre on average. A few cheap litres lower the average only a little.

The weighted average is the form of anti-dilution protection widespread in German funding rounds, usually with a broad calculation base. The formula is in the participation agreement or the shareholders' agreement. In a GmbH (German limited liability company), the adjustment is implemented through additional shares (compensation shares) that the protected investor takes up in a capital increase at the nominal amount, usually EUR 1 per share. The stricter alternative is the full ratchet, which lowers the entry price completely to the new price.

The weighted average formula

In practice, the adjusted price is usually calculated using the following formula:

Formula: P2 = P1 × (A + B) / (A + C)

• P1: the protected investor's previous entry price per share
• P2: adjusted entry price
• A: number of shares before the new issue, measured on the agreed calculation base
• B: number of shares that the new total amount would have yielded at the previous price, that is, new amount / P1
• C: number of shares actually newly issued

Because the new price is below P1, C is greater than B, and P2 falls below P1. Equivalently, the formula can be written as a mean: P2 = (A × P1 + C × new price) / (A + C). The old price enters with the weight of the existing shares, the new price with the weight of the new shares, hence the name.

The compensation follows from the adjusted price. The protected investor's investment amount divided by P2 gives the shares it would have received at that price; less its previous shares, the number of compensation shares remains. Contracts additionally regulate rounding to whole shares, for example by rounding down. The formula is also widespread in US contract practice, where it adjusts the conversion price of preferred stock; in a GmbH, it works through the number of compensation shares.

Broad-based and narrow-based: broad and narrow calculation base

The value A decides the strength of the adjustment. The larger A is, the more weight the old price carries and the smaller the reduction.

• Broad base (broad-based): A comprises all shares on a fully diluted basis, that is, shares, virtual shares and options including the reserved pool, and conversion rights. This variant is widespread in German funding rounds.
• Narrow base (narrow-based): A comprises only a part, for example only the shares according to the list of shareholders or only the shares of the protected series. The adjustment is noticeably stronger.

How strongly the narrow base works depends on how narrowly it is drawn. If it counts all shares and leaves out only virtual shares and conversion rights, the result often deviates only slightly from the broad base. If it counts only the protected series, the compensation is considerably higher, as the worked example shows.

Which rights belong to the broad base should be determined by the same definition that applies to the price of the round (fully diluted). If the two definitions diverge, results arise that cannot be reconciled with the cap table.

Negotiation points on the weighted average

• Calculation base: expressly broad, with a list of the rights included.
• Triggers and exceptions: which events count as a new issue and which do not, for example allocations from the employee programme, agreed conversions and issues with the consent of the protected investors.
• Multiple issues: whether issues within a period, for example several tranches of one round, are counted as one issue.
• Rounding and nominal amount: how rounding to whole shares is done and whether the nominal amount that the investor pays for the compensation shares is taken into account in the calculation.
• Participation obligation: whether the investor keeps the protection only if it subscribes for its share in the down round (pay-to-play).

Worked example: weighted average with broad and narrow base

The starting position corresponds to the example on the full ratchet. Of 90,000 shares with a nominal amount of EUR 1 each, 55,000 are held by the founders, 10,000 by a business angel without protection and 25,000 by the Series A investor. The latter invested EUR 3 million at EUR 120 per share. The employee programme comprises 10,000 virtual shares. In the follow-on round, a new investor takes shares for EUR 3 million at EUR 60 each.

• Formula quantities: P1 = EUR 120; B = EUR 3 million / EUR 120 = 25,000; C = EUR 3 million / EUR 60 = 50,000
• Broad base with A = 55,000 + 10,000 + 25,000 + 10,000 = 100,000: P2 = 120 × (100,000 + 25,000) / (100,000 + 50,000) = EUR 100
• Check as a mean: (100,000 × EUR 120 + 50,000 × EUR 60) / 150,000 = EUR 15 million / 150,000 = EUR 100
• Compensation on the broad base: EUR 3 million / EUR 100 = 30,000 shares, so 5,000 compensation shares, which the investor takes at the nominal amount of EUR 5,000 in total
• Narrow base from the 25,000 Series A shares only: P2 = 120 × (25,000 + 25,000) / (25,000 + 50,000) = EUR 80; EUR 3 million / EUR 80 = 37,500 shares, so 12,500 compensation shares
• Narrow base from all 90,000 shares: P2 = 120 × 115,000 / 140,000 = around EUR 98.57; 30,434 shares (rounded down), so 5,434 compensation shares
• Percentages on the broad base: Series A investor 30,000 / 155,000 = around 19.35%, founders 55,000 / 155,000 = around 35.48%, new investor 50,000 / 155,000 = around 32.26%
• Percentages on the narrow base from the Series A shares: Series A investor 37,500 / 162,500 = around 23.08%, founders 55,000 / 162,500 = around 33.85%
• Small round of EUR 600,000 at EUR 60 on the broad base: B = 5,000, C = 10,000, P2 = 120 × 105,000 / 110,000 = around EUR 114.55; 1,190 compensation shares (rounded down)

The full ratchet yields 25,000 compensation shares in both round sizes. The weighted average with a broad base lowers the entry price to EUR 100 in the large round and to around EUR 114.55 in the small one. The compensation therefore grows with the size of the issue. Valued at the new price, the Series A investor holds, on the broad base, 30,000 × EUR 60 = EUR 1.8 million, under the full ratchet EUR 3 million. The burden of the lower price is therefore shared between the protected investor and the other shareholders.

Distinctions: weighted average, full ratchet and WACC

• Full ratchet: lowers the entry price completely to the new price and disregards the size of the new issue.
• Anti-dilution protection: the umbrella term for price-based anti-dilution protection, including triggers, exceptions and implementation in the GmbH.
• Pay-to-play: not a calculation method but a condition under which an investor keeps its protection.
• Weighted average cost of capital (WACC): a term from business valuation that describes the interest rate for discounting future payments (discount rate). It shares only the wording with anti-dilution protection.

Common mistakes

• Base not fixed. "Weighted average" without qualification leaves open whether the calculation is broad or narrow. In the example, the difference between the variants is 5,000 versus 12,500 compensation shares.
• Base departs from the round definition. If the formula counts different rights from the price calculation of the round, compensation and cap table cannot be reconciled.
• Formula quantities unclear. Without a clear definition of A, B and C there is room for divergent interpretations, for example whether conversion shares of the new round are included in C.
• Tranches not considered. If a round is paid out in several tranches, it must be regulated whether each tranche is calculated separately or all together.
• Rounding and nominal amount left open. With many participants, rounding differences add up, and without a rule on the nominal amount it is unclear whether it reduces the number of compensation shares.

Frequently asked questions

What do A, B and C mean in the formula?

A is the number of shares before the new issue on the agreed base. B is the number that the new amount would have yielded at the old price, C the number of new shares actually issued. The ratio of A + B to A + C determines by how much the entry price falls.

How are the compensation shares calculated with weighted average?

In four steps. First B (new amount divided by the old price) and C (number of shares actually newly issued) are determined, then P2 using the formula. The investment amount divided by P2 and rounded down to whole shares gives the new number of shares; less the previous shares, the compensation shares remain. In the worked example, EUR 3 million / EUR 100 = 30,000 shares less 25,000 gives exactly 5,000 compensation shares. In a spreadsheet, input cells for P1, A, the new amount and the new price are enough.

Is the broad or the narrow base usual?

In German funding rounds, the broad base. The narrow base favours the protected investors and is correspondingly agreed less often.

Does the formula also apply to a round at the same price?

No. If the new price is not below the entry price, C is not greater than B, and no compensation arises. The clause is then not triggered at all.

How does the weighted average affect the exit?

Through the higher number of shares held by the protected investor. It receives a larger share of the proceeds, unless it asserts its liquidation preference anyway. A conversion ratio as with preferred stock in the US market does not exist in a GmbH.

Are several down rounds taken into account one after another?

The contract regulates this. It is usual that each further issue below the most recently adjusted price triggers a new adjustment, calculated from the adjusted price.

The Roemer Capital view

If the draft of a participation agreement contains the formula, we first check whether the quantities A, B and C are clearly defined. We also reconcile the calculation base with the definition on which the price of the round rests. We clarify ambiguities with the company's law firm while the negotiation is still running.

For the shareholders, we run the clause through with broad and narrow base and for several round sizes. An abstract formula thereby becomes a number of compensation shares that can be discussed objectively in the negotiation.