# How to find the share price with respect to the type of share?

As someone coming from a mathematical background who has started reading into some basic finance, there are a few concepts that I am struggling to understand and would be grateful if I could check to see whether or not my understanding of these is correct.

The first concerns the distinction between ordinary and preference shares. I understand the theoretical difference between the two, but I am confused about what this diagram for ordinary shares means And similarly, there is also a diagram for preference shares: My guess is that (based on the above diagrams), this seems to suggest the following result:

• $$P_t = P_0 - \sum_{i=1}^{t-1} D_i$$ for ordinary shares

• As for Preference Shares, I am quite confused as to what the relationship is here between $$P_t$$ and $$P_0$$. The removal of $$D$$, then $$0$$, then $$2D$$ doesn’t seem to display a clear pattern and so I’m not entirely sure what this diagram illustrates here.

The text gives no numerical examples (as it is more focussed on the theoretical side), however, I’m interested in what the mathematical relationship is between these quantities and what these diagrams are trying to show.

I don't claim to be an expert on this so if someone else who knows more corrects me, I yield graciously.

Side note: The term is "preferred stock", not "preference stock". Though perhaps you are in a different country where it has a different name. Or maybe this is an accepted alternative name. But anyway ...

"Preferred stock" is sort of half way between owning a share of a company and owning a debt. On preferred stock, the company typically promises a specific dividend. On common stock, dividends are declared each quarter (or sometimes another schedule) depending on the company's profits. So your income from preferred stock should be constant while your income from common stock could go up and down.

Except if the company doesn't make any money this quarter, then they won't pay the promised dividend on the preferred stock. That's how it's different from a debt. With a debt, if the debtor doesn't pay, the creditors can seize assets or force them into bankruptcy. With preferred stock, the stockholders are just out of luck.

Again typically, because details can vary, if the company doesn't make money one quarter and does not pay a dividend on the preferred stock, but the next quarter it makes a ton of money, they will make up the missing dividend. That's what the diagram meant by the D / 0 / 2D. The first quarter they make reasonable earnings and pay the promised dividend. The second quarter they lose money so pay nothing. The third quarter they make money again so they pay twice the normal dividend to make up for the missing dividend the previous quarter.

Also, preferred stockholders have no voting rights.

• Thanks, that clarifies a lot. In terms $P_0$ and $P_t$, how do they fit in with this model? Is there a relationship between the two that links in with the dividend payments? Otherwise, I’m a bit confused as to why they’re mentioned in the diagram @Jay Nov 22, 2022 at 7:06
• @FD_bfa Today's value of the share is the present value of (expected) future dividends: $P_0=\sum_t (1+i)^{-t}D_t$, where $i$ is the discount rate. en.wikipedia.org/wiki/Net_present_value Nov 22, 2022 at 10:06
• @VARulle does this apply to both ordinary and preferred shares? Nov 22, 2022 at 18:01
• @FD_bfa I suppose that the market value of a share of preferred stock would equal the net present value of future dividends summed to infinity, or the anticipated future life of the stock, and multiplied by the probability that those dividends will actually be paid. As in, if a company promises to pay whatever per year but they're going bankrupt, the stock would be worth considerably less than if they promised the same dividend and they are doing well and have a bright future. I wouldn't say the value is the sum of future dividends. You have to adjust for net present value of money. ...
– Jay
Nov 23, 2022 at 1:29
• ... If a stock promised to pay \$1 per year forever, well over the course of "forever" that would mean an infinite amount of money, but the stock would not trade for infinity dollars.
– Jay
Nov 23, 2022 at 1:30