Rights issues and dilution
New shares sold to existing holders at a discount. The price falls, but a holder who acts loses nothing. The only way to lose is to do nothing.
- Calculate the theoretical ex-rights price and the value of a right
- Work out the new shares and the money raised
- Find the subscription price that gives a target ex-rights price
- Show that taking up and selling the rights leave a holder equally well off
The intuition
A pizza is cut into 4 slices worth $10 each. The owner adds a fifth slice's worth and sells that slice to the same eaters for $5. Now there are 5 slices worth $45 in total, $9 each. Every slice got cheaper, but whoever bought the $5 slice got a $9 slice for it: the $4 gained makes up exactly for the $1 lost on each of the other four.
A rights issue works the same way. A company offers its existing shareholders new shares, one for every k they own, at a subscription price below the market. Afterwards every share is worth the same blended price, the theoretical ex-rights price (TERP). The right to buy a cheap share is itself worth money, and exactly makes up for the fall.
TERP = (k × price before + subscription price) ÷ (k + 1). Value of a right, per new share = TERP − subscription price. Headline dilution = 1 − TERP ÷ price before. Money raised = shares ÷ k × subscription price.
Why it works
- The conventions here: a 1-for-k issue (one new share for every k held) at a stated subscription price; no fees; rights valued at their theoretical value.
- TERP is a weighted average: k old shares at the old price and one new share at the subscription price.
- Taking up the rights (paying for the new shares) and selling them both leave a holder exactly as wealthy as before. Letting them lapse loses their value.
- The subscription discount is much bigger than the fall in price, because only one share in k + 1 is sold at the discount: the price falls by the discount ÷ (k + 1).
- A deep discount makes the issue self-underwriting: the rights stay worth using even if the shares fall during the offer.
- The arithmetic is neutral; the reason is not. A company raising equity at a discount usually needs the money, and that is what moves the share price.
| TERP: (4 × 20 + 15) ÷ 5 | $19.00 |
| Right per new share: 19 − 15 | $4.00, or $1.00 per old share |
| Headline dilution: 1 − 19 ÷ 20 | 5% |
| New shares: 100M ÷ 4, at $15 | 25M, raising $375M |
| Take up: 5,000 × 19 − 1,000 × 15 | $80,000, the same as before |
| Sell the rights: 4,000 × 19 + 1,000 × 4 | $80,000 |
| Let them lapse: 4,000 × 19 | $76,000, a $4,000 loss |
For a TERP 10% below $20 in a 1-for-4: 5 × 18 − 4 × 20 = $10, a 50% subscription discount.
The formulas
The blended price of the old and new shares.
What the right to buy cheaply is worth.
The mechanical fall in the share price.
What the company gets.
Run it backwards.
Worked example
Blend k old shares at the market price with one new share at the subscription price. The right is worth the gap between TERP and the subscription price.
See it move
Same company and the same holder. Change the subscription discount, how many old shares earn one new share, and the share price before the issue.
- Deepen the discount. The subscription price and TERP fall, each right is worth more, and doing nothing costs more.
- Raise k, so fewer new shares per old share. TERP moves closer to the old price and the fall in price shrinks.
- Whatever you move, taking up and selling the rights stay level with the wealth before the issue.
- Change the price before the issue. The percentage fall in price does not move.
Run it backwards
Same company, reversed: it wants the ex-rights price to be no more than a set percentage below today's. What subscription price does that allow?
Fix TERP at the target, then rearrange the TERP formula: subscription price = (k + 1) × TERP − k × price before.
The discount that gives is much deeper than the fall in TERP, because it applies to one share in k + 1. A bigger k lets a company offer a deeper discount for the same fall in price.
Traps
Say it in the interview
“A company announces a rights issue at a 30% discount. Are its shareholders being diluted?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- TERP = (k × price + subscription price) ÷ (k + 1).
- Right = TERP − subscription price.
- Take up or sell: wealth unchanged. Lapse: lose the rights' value.
- The price falls by the discount ÷ (k + 1).