MathematicsPosted: November 19, 2011
I was fairly advanced in my math education. Revisit the topic here if you wish. Yup, I’m a geek.
My nephew Zach believes mathematics have little if any practical application. Oh, contrare, my friend.
If a corporation wants additional funds to expand, it can raise money in at least two ways. First, it can borrow the money. Second, it can sell common stock for cash and issue ownership to a new shareholder.
Say a corporation has one shareholder who owns 100 shares. It wishes to sell a 20% ownership interest to an investor. So how many shares should it issue to the investor? Many people answer “20 shares”.
Is that correct? No. That’d give the investor a 16.67% ownership interest. (20 divided by 120.)
Let’s employ some algebra. Here’s our formula:
X = 100 + (0.20 * X)
X is the unknown number of total shares after the issuance to the investor. The (0.20 * X) piece accounts for the investor owning 20% of the corporation after the issuance of new shares. (I’m open to other formulae if you have a suggestion.)
OK, back to the formula.
Let’s subtract (0.20 * X) from each side. Now our formula is:
X – (0.20 * X) = 100.
Or 0.80 * X = 100.
Now let’s divide each side by 0.80. Now our formula is:
X = 100 / 0.80.
Ergo, X = 125.
The corporation needs to issue 25 shares to the investor. 25 divided by 125 total shares = 20%.