Ex-Right Value Formula

I’m confused as to why we need to compensate for the stock’s falling price. If the stock is worth less, doesn’t it make sense that the right should be worth less because it’s giving less of a “discount”?

For example, say the stock is trading at $10 cum-rights. Subscription price is $9.10 and 2 rights are required to buy a share. The cum-rights formula gives us 30¢. This is less than the true savings on the subscription per right - which is 45¢.

Now, let’s say the stock ex-rights is trading at $9.70. If we use the ex-rights formula, that gives us 30¢ as well. But the true savings on the subscription is only 30¢ per right in this case.

Why don’t we keep this formula the same as the cum-rights formula, which would give us a 20¢ right value - which makes sense considering that the true savings of a right is only 30¢ in this case as opposed to 45¢ when the stock was trading cum-rights?

Hi @Mass_coffee_louse - the difference between the ex and cum-rights formulas is due to the falling market price of the stock after they trade without rights (ex-rights). Let’s demonstrate the math with your numbers:

  • Stock market price = $10
  • 2 rights needed to buy 1 new share at $9.10

Cum-rights value = (Stock market price - subscription price) / (# of rights needed + 1)
Cum-rights value = ($10 - $9.10) / (2+1)
Cum-rights value = ($0.90) / (3)
Cum-rights value = $0.30

Now, let’s assume it’s the ex-rights date (the day the stock starts trading without the rights). The stock’s market price will fall by the value of one right ($0.30), down to $9.70 per share. Now, let’s calculate the ex-right formula:

Ex-rights value = (Stock market price - subscription price) / (# of rights needed)
Ex-rights value = ($9.70 - $9.10) / (2)
Ex-rights value = ($0.60) / (2)
Ex-rights value = $0.30

While the reasoning behind the formulas is unimportant for the exam, you weren’t factoring the stock’s “amped up” value when trading cum-rights. The stock is trading at $10 initially, but $0.30 of that $10 value is attributed to the value of a right. The addition of the “+1” in the denominator adjusts for this.

I wouldn’t get too caught up in the reasoning for the formulas, as exam questions will only test your knowledge of the formulas (not the “why” behind them).