Rights per new share
N = S0 / s
where s = Amount to be raised / Subscription price
The first step of every rights problem. Get s from the money to be raised and the subscription price, never from the market price.
- S0
- Number of shares outstanding before the issue
- s
- Number of new shares issued
- N
- Rights required to buy one new share; need not be a whole number
After-rights price
Px = (S0 x P0 + s x Ps) / (S0 + s)
The ex-rights or theoretical after-rights price. It is a weighted average of the old market price and the subscription price, weighted by share counts.
- P0
- Cum-rights market price, before the rights go ex
- Ps
- Subscription price of the new shares
- Px
- After-rights (ex-rights) price
Value of one right
Ps + N x R = Px -> R = (Px - Ps) / N
Identity: P0 = Px + R
To value a right, and to check any rights calculation. The value of a right always equals the fall in the share price from cum-rights to ex-rights.
- R
- Value of one right
- N
- Rights needed per new share
Shareholder wealth under the three options
Exercise: (holding + new shares) x Px - (new shares x Ps)
Sell rights: holding x Px + rights held x R
Do nothing: holding x Px
To show that a rights issue is wealth-neutral. The first two give the same answer as holding x P0; only the third is lower, by exactly the value of the lapsed rights.
- holding
- Shares owned before the issue
- rights held
- One per existing share