The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


dividend rate would then be $0.35 per share. Yet Jason would still own 51%, Dave would
still own 49%, and each man would still receive the same overall dividend. The dividend per
share can be a misleading measure of how desirable a stock investment is.

Distributing Profits of a Partnership


If a business is not set up as a corporation, how are the profits to be distributed among its
owners? The technical and legal details of how other businesses are structured fall outside
the scope of this book, but however the details are set up, there must be some agreement as
to how much each owner is entitled to receive.
If a business is set up as a partnership, the partners may agree to distribute all profits
equally. In that case, dividing them up is just a matter of dividing the profits to be distrib-
uted by the number of equal partners. This would not be unusual if all the partners of a
business contribute essentially the same effort, skills, and capital to the business. However,
it is also not unusual for the partners in a business to agree that some should receive a larger
share than others. One partner might work more hours or contribute more valuable exper-
tise or more financial capital than another. In those cases, there is no formula that must be
used to determine how the profits would be split up; it is a matter of whatever distribution
the partners can agree is fair.
The partners may agree on a split of the profits based on the percent each will receive.
In that case, finding each individual’s take is simple a matter of applying her percent to the
total profit. Sometimes, rather than use percents, the partners may decide to split the profits
based on “parts” each is to receive. Mathematically, we treat each part as though it were a
share of stock. The following example will illustrate.

Example 6.1.3 Suppose that TJ, Rudy, Eric, and Kevin have a band, which they
have set up as a business partnership. They agree to distribute their profi ts in unequal
shares, because Rudy owns most of the band’s equipment and Eric wrote most of the
songs. They agree to distribute the profi ts as follows: TJ gets 3 parts, Rudy 5 parts,
Eric 4 parts, and Kevin gets 3 parts. (This sort of distribution can be abbreviated as
3:5:4:3 split, as long as it is clear which number goes with which person.)

The band earned $7,250 last month, and all four partners agree to distribute this
entire amount among them. How much does each person receive?

Even though this is not a corporation, we can pretend that each part is a share of stock for
the purposes of distributing the profi ts. So there are a total of 3  5  4  3  15 “shares,”
and so each share should receive $7,250/15  $483.33.

Thus, TJ would receive 3($483.33)  $1,449.49, as would Kevin. Similarly, Eric gets
4($483.33)  $1,933.32, and Rudy gets 5($483.33)  $2,416.65.

This could also be done with percents. Since he gets 3 parts out of 15, we could instead say that
TJ gets 3/15  20%. Applying this 20% to the total profit, we get (20%)($7,250)  $1,450.
(The penny difference is due to rounding.) Likewise, the other three bandmates would
receive 33.3%, 26.7%, and 20%, respectively, and their shares could be calculated with
percents in the same way.

Dividend Yields


It is often desirable to express a company’s dividend rate as a percent, to make comparisons
more meaningful. This rate is called the stock’s dividend yield.
The difficulty here is what that percent should be of. The most common way to do this
is to express the dividend as a percent of the current fair market value of a share of the
company’s stock. It is also common practice to express this as a rate per year, making it
more comparable to an interest rate.
The shares of many large corporations can be bought and sold through any stock broker.
Large companies, with many shares of stock outstanding, typically have their shares listed
on a major stock exchange such as the New York Stock Exchange or NASDAQ. There are

6.1 Stocks 253
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