The theoretical ex-rights price, the value of a nil-paid right and the holder who does nothing, worked on one illustrative rights issue.
The theoretical ex-rights price is the market value of the company after the issue divided by the enlarged number of shares: (existing shares × share price + new shares × subscription price) / (existing + new shares). On an illustrative 2-for-5 rights issue at EUR 30.00 with the shares at 42.60, the TERP is EUR 39.00. The right to buy one new share is worth 9.00, and the honest discount is 23.08 per cent to TERP, not the 29.58 per cent to the last close that headlines tend to quote.
Worked in full in Capital Markets by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A listed company raises EUR 1.2 billion from its existing shareholders, in proportion to their holdings. All figures are illustrative.
| Term | Value |
|---|---|
| Shares in issue | 100,000,000 |
| Share price, last close before announcement (EUR) | 42.60 |
| Ratio | 2 new for every 5 held |
| New shares | 40,000,000 |
| Subscription price (EUR) | 30.00 |
| Gross proceeds (EUR) | 1,200,000,000 |
Before the issue the market values the equity at 100,000,000 × 42.60 = 4,260,000,000. The issue adds 1,200,000,000 of cash. Absent any change in how the market values the business, the enlarged company is worth the sum, spread over 140,000,000 shares.
TERP = (N × P + n × S) / (N + n)
= (4,260,000,000 + 1,200,000,000) / 140,000,000 = 5,460,000,000 / 140,000,000 = EUR 39.00
Per ratio block: (5 × 42.60 + 2 × 30.00) / 7 = 273.00 / 7 = 39.00
Excel, with price in B1, subscription price in B2, new shares per block in B3 and old shares per block in B4: =(B4*B1+B3*B2)/(B4+B3)
The TERP is theoretical because the market will price the shares ex-rights on its own, and it will move with the news, the use of proceeds and the market. It is the reference against which the issue's terms are measured, and the price at which a holder who follows the rights is left exactly where it started.
Nil-paid right, per new share = TERP − S = 39.00 − 30.00 = 9.00
Per existing share = 9.00 × 2 / 5 = 3.60, and 42.60 − 3.60 = 39.00, the TERP again
Discount to TERP = 1 − 30.00 / 39.00 = 23.08%
Discount to last close = 1 − 30.00 / 42.60 = 29.58%
The discount to the last close overstates the transfer of value, because part of that gap is simply the dilution of the price by the cheap new shares, which every holder takes back if it subscribes. The discount to TERP is the comparable figure, and it is the one to set beside other rights issues. For a placing, where existing holders are not offered the shares, the discount to the last close is the right measure and the arithmetic is different: see how much a discounted placing dilutes shareholders.
A holder of 10,000 shares, worth 426,000 before the issue, is entitled to 4,000 new shares at a cost of 120,000.
| Choice | Shares after | Value of shares | Cash in or out | Net position |
|---|---|---|---|---|
| Take up in full | 14,000 | 546,000 | −120,000 | 426,000 |
| Sell the rights nil-paid | 10,000 | 390,000 | 36,000 | 426,000 |
| Do nothing, no compensation | 10,000 | 390,000 | 0 | 390,000 |
Taking up or selling leaves the holder whole. Doing nothing costs 36,000, 8.45 per cent of the holding, and cuts its share of the company from 0.0100 to 0.0071 per cent, a 28.57 per cent dilution. In UK-style issues the lapsed shares are placed in the market after the offer closes and any premium over the subscription price is paid to those who lapsed: if the rump were placed at 37.50, the holder would receive 7.50 a share, 30,000 of the 36,000, before expenses. The protection is real but not complete.
For a fixed EUR 1.2 billion, a lower price means more new shares and a deeper discount. The table holds the proceeds constant.
| Subscription price | New shares | Ratio, per 5 held | TERP | Discount to TERP | Right per existing share | Loss if lapsed |
|---|---|---|---|---|---|---|
| 20.00 | 60,000,000 | 3.00 | 34.12 | 41.39% | 8.47 | 19.89% |
| 25.00 | 48,000,000 | 2.40 | 36.89 | 32.23% | 5.71 | 13.40% |
| 30.00 | 40,000,000 | 2.00 | 39.00 | 23.08% | 3.60 | 8.45% |
| 35.00 | 34,285,714 | 1.71 | 40.66 | 13.92% | 1.94 | 4.55% |
| 40.00 | 30,000,000 | 1.50 | 42.00 | 4.76% | 0.60 | 1.41% |
A deep discount does not cost a shareholder who acts: at 20.00 the holder still ends at 426,000 by taking up or selling. What it does is raise the stakes of inaction and make the issue more robust, since the share price has to fall a long way before 20.00 is above the market and nobody subscribes. A shallow discount limits the cost of inaction but leaves the issue exposed to a falling share price, so it normally needs a full underwriting, which costs commission.
The placement alternative, priced against four reference prices with its commission and the cost of the leak kept separate, is in the free workbooks for this book.
The discount to the last close compares the subscription price with the price before the issue; the discount to TERP compares it with the price after the new shares are blended in. On a 2-for-5 issue at 30.00 with the shares at 42.60, the first is 29.58 per cent and the second 23.08 per cent. Rights issues are compared with each other on the discount to TERP.
Theoretically it is the TERP minus the subscription price, per new share: 39.00 minus 30.00 is 9.00 in the worked case. Per existing share it is that times the ratio, 9.00 times 2 / 5, or 3.60, which is exactly the fall from 42.60 to the TERP of 39.00. In the market, nil-paid rights trade close to this value, adjusted for moves in the share price.
It is TERP divided by the cum-rights share price, 39.00 / 42.60 = 0.9155 here. Historic share prices and earnings per share are multiplied by it so that they are comparable after the issue. Earnings per share of 2.40 become 2.20. Dividing by the enlarged share count instead, giving 1.71, wrongly treats the cash raised as if it were a free bonus issue.
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.
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