Ownership dilution and value dilution worked on one accelerated placing, with the holder who could not participate and the one who could.
A placing dilutes existing shareholders twice, and the two numbers are very different. Ownership dilution is the new shares over the enlarged share count; value dilution is the discount times that same fraction. On an illustrative placing of 9.5 million new shares into 118 million, at EUR 40.55 against a EUR 42.60 close, a holder's stake falls by 7.45 per cent but the value of each existing share falls by only 0.36 per cent, which on the whole register is EUR 18.02 million handed to the new investors.
Worked in full in Capital Markets by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The two measures answer different questions. Ownership dilution tells a shareholder how much of the company it no longer owns. Value dilution tells it how much money it lost, and the answer is much smaller because the company receives cash for the new shares. Only the discount is a transfer; the rest is a sale at close to fair value.
| Input | Value |
|---|---|
| Shares in issue before | 118,000,000 |
| New shares placed | 9,500,000 |
| Size, % of existing shares | 8.05% |
| Reference price (last close) | EUR 42.60 |
| Placing price | EUR 40.55 |
| Discount to reference | 4.81% |
| Gross proceeds | EUR 385,225,000 |
The calculation assumes the market values the company at its pre-deal price plus the cash raised, which is the standard starting point. In practice the share price also reacts to what the money is for and to the information in the announcement; that reaction is not dilution and should be measured separately.
Step 1. Ownership dilution
New shares over enlarged count: 9,500,000 / 127,500,000 = 7.45 per cent. A holder of 1.00 per cent, 1,180,000 shares, now owns 0.925 per cent.
Step 2. Theoretical post-deal price
(Market value before + proceeds) / shares after = (5,026,800,000 + 385,225,000) / 127,500,000 = EUR 42.4473. In Excel: =(B1*B4+B2*B5)/(B1+B2).
Step 3. Value dilution per existing share
42.60 − 42.4473 = EUR 0.1527, or 0.36 per cent of the reference price. The shortcut gives the same: discount × new / (old + new) = 4.81% × 7.45% = 0.359 per cent.
Step 4. The transfer in money
118,000,000 existing shares × EUR 0.1527 = EUR 18,023,922, and the new investors gain exactly the same amount: 9,500,000 × (42.4473 − 40.55).
| Shares | Stake | Value, EUR | |
|---|---|---|---|
| Before | 1,180,000 | 1.00% | 50,268,000 |
| After, not participating | 1,180,000 | 0.925% | 50,087,761 |
| Loss | 180,239 |
The holder gave up 7.45 per cent of its stake and lost 0.36 per cent of its money. Had it been allowed to buy its pro rata 95,000 new shares at EUR 40.55, for EUR 3,852,250, it would have held 1,275,000 shares worth EUR 54,120,250, exactly its EUR 50,268,000 before plus the cash it paid: no loss at all. That is the arithmetic case for pre-emption rights, and the reason non-pre-emptive placings are usually limited in size.
The EUR 18.02 million transferred is 4.25 times the 1.10 per cent commission of EUR 4,237,475. The discount is the largest cost of the placing, and it appears on no invoice: the full bill is broken down in how much of a placement is uninvoiced, and how much the discount itself depends on the reference chosen is worked in how a placing discount is calculated.
| Discount | 5% of shares | 10% | 15% | 20% |
|---|---|---|---|---|
| 2.00% | 0.10 | 0.18 | 0.26 | 0.33 |
| 4.81% | 0.23 | 0.44 | 0.63 | 0.80 |
| 7.00% | 0.33 | 0.64 | 0.91 | 1.17 |
| 10.00% | 0.48 | 0.91 | 1.30 | 1.67 |
Value dilution rises with both inputs but never approaches the ownership figure. A 20 per cent placing at a 10 per cent discount, an aggressive deal, still costs existing holders only 1.67 per cent of value, while their stake falls by a sixth. Doubling the discount roughly doubles the value dilution; doubling the size does a little less, because the new shares also carry part of the dilution.
The theoretical price is a benchmark, not a forecast. If the market reads the placing as a sign that management thinks the shares are fully valued, the price can trade below EUR 42.45 for reasons that have nothing to do with the arithmetic of dilution. If the proceeds fund an acquisition the market likes, it can trade above. Either way, the 0.36 per cent is the part of the move that the terms of the deal caused, and it is the part a board can control by negotiating the discount and the size.
Two errors run in opposite directions. The first is quoting ownership dilution as if it were a loss: "a 7 per cent dilutive placing" sounds like 7 per cent of value destroyed when the figure is 0.36. The second is using the discount in euros, 9,500,000 × EUR 2.05 = EUR 19,475,000, as the existing holders' loss. That figure is the right one for the issuer's cost bill, the proceeds forgone against the reference price, but it is EUR 1.45 million more than the value the existing holders lose, because once the new shares are issued they bear their own share of the dilution: the new investors buy at 40.55 and hold at 42.45, not at 42.60. The shareholders' loss is EUR 18.02 million. Both errors matter when a board weighs a placing against a rights issue or a bond; the bond side of that comparison is in how to calculate the all-in cost of a bond issue.
Report both numbers, and label them. Ownership dilution is new over enlarged shares, 7.45 per cent here; value dilution is the discount times that fraction, 0.36 per cent, EUR 18.02 million on the register. The second is the cost; the first is the governance question. The free workbook for this case splits a placement's full cost into commission, discount and the leak, under four reference prices.
Discount times new shares over the enlarged share count. A 4.81 per cent discount on a placing that adds 7.45 per cent of the enlarged capital gives 0.359 per cent. Equivalently, compare the reference price with the theoretical post-deal price, (old value + proceeds) / shares after: EUR 42.60 against EUR 42.4473, a loss of EUR 0.1527 a share.
No. A 1.00 per cent holder that buys 95,000 of the 9,500,000 new shares at EUR 40.55 pays EUR 3,852,250 and ends with 1,275,000 shares worth EUR 54,120,250, exactly its EUR 50,268,000 before plus the cash paid. The discount only transfers value from holders who cannot participate to those who can.
In value, less than it sounds. The enlarged capital is 9.09 per cent new shares, so a 10.00 per cent discount costs existing holders 0.91 per cent of value per share. Their ownership falls by 9.09 per cent. At 20 per cent of the shares and the same discount the value dilution is 1.67 per cent.
This article is one calculation from Capital Markets. 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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: corporate finance, valuation and markets → · All 1340 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.