Textbook

If a company feels its stock price is too expensive or too cheap, it can consider performing a **stock split**. There are two types of stock splits - forward and reverse. Forward stock splits increase the number of outstanding shares, while reverse stock splits decrease the number of outstanding shares.

**Forward stock splits** are pursued when a company feels its stock price is too expensive for the average investor. Let’s assume ABC company’s stock price has risen to $500 per share, which is relatively expensive (most stocks trade between $30 - $150). ABC company could consider decreasing its stock price through a forward stock split. This would increase the number of shares a stockholder owns, but the stock price decreases proportionately. Let’s work through a few examples.

A stockholder owns 100 shares of ABC Company at a current market price of $500 per share. How will a 4:1 forward stock split impact shareholders?

Each stockholder receives four shares for every one share owned.

To find the stock split factor, divide the first number by the second number

$SS factor=second SS numberfirst SS number $

$SS factor=14 $

$SS factor=4$

To find the number of shares adjustment, multiply the original number of shares by the stock split factor

$New shares=old shares x SS factor$

$New shares=100 x 4$

$New shares=400$

To find the price per share adjustment, divide the original price per share by the stock split factor

$New price=SS factorold price $

$New price=4$500 $

$New price=$125$

Put it all together and compare before and after to confirm

$Before the split:$

- 100 shares @ $500 =
**$50,000**

$After the split:$

- 400 shares @ $125 =
**$50,000**

To further your confidence with stock split calculations, let’s take a look at the real-world story of Apple’s 7:1 stock split back in 2014:

Let’s see if you can do one on your own now.

A stockholder owns 300 shares at a current market price of $90 per share. The issuer performs a 3:2 stock split. What adjustment is made to the investor’s position?

**What is the stock factor?**

(spoiler)

$SS factor=second SS numberfirst SS number $

$SS factor=23 $

$SS factor=1.5$

**How many shares will the stockholder end up with?**

(spoiler)

$New shares=old shares x SS factor$

$New shares=300 x 1.5$

$New shares=450$

**What is the new price per share?**

(spoiler)

$New price=SS factorold price $

$New price=1.5$90 $

$New price=$60$

**Summarize the final result.**

(spoiler)

$Before the split:$

- 300 shares @ $90 =
**$27,000**

$After the split:$

- 450 shares @ $60 =
**$27,000**

As you can see in these examples, the stockholder always ends up with the same overall value ($27,000 in the last example). It’s the number of shares owned and the market price that changes. As an analogy, imagine you have an apple pie, which we’ll consider as one unit of pie. If you were to cut that apple pie in half, you technically have two units of pie. While you have more pie units, you don’t end up with more overall pie.

**Reverse stock splits** are pursued when a company feels its stock price is too low (the opposite of forward splits). Instead of waiting for market demand to increase its stock price, a company could do a reverse stock split and achieve an immediate stock price increase.

Let’s go through a reverse split example together.

An investor owns 100 shares of stock at a current market price of $10. How will a 1:5 reverse stock split impact the position?

Each stockholder receives one share for every five shares owned.

To find the stock split factor, divide the first number by the second number

$SS factor=second SS numberfirst SS number $

$SS factor=51 $

$SS factor=0.2$

To find the number of shares adjustment, multiply the original number of shares by the stock split factor

$New shares=old shares x SS factor$

$New shares=100 x 0.2$

$New shares=20$

To find the price per share adjustment, divide the original price per share by the stock split factor

$New price=SS factorold price $

$New price=0.2$10 $

$New price=$50$

Put it all together and compare before and after to confirm

$Before the split:$

- 100 shares @ $10 =
**$1,000**

$After the split:$

- 20 shares @ $50 =
**$1,000**

Before you work through an example on your own, let’s learn about the real-world story of Citigroup’s reverse stock split in 2011:

Try one on your own now.

A stockholder owns 400 shares at a current market price of $20 per share. The issuer performs a 4:5 reverse stock split. What will the investor’s stock position become?

**What is the stock factor?**

(spoiler)

$SS factor=second SS numberfirst SS number $

$SS factor=54 $

$SS factor=0.8$

**How many shares will the stockholder end up with?**

(spoiler)

$New shares=old shares x SS factor$

$New shares=400 x 0.8$

$New shares=320$

**What is the new price per share?**

(spoiler)

$New price=SS factorold price $

$New price=0.8$20 $

$New price=$25$

**Summarize the final result.**

(spoiler)

$Before the split:$

- 400 shares @ $20 =
**$8,000**

$After the split:$

- 320 shares @ $25 =
**$8,000**

As you can see, the stockholder always ends up with the same overall value ($8,000 in the last example) after a stock split occurs.

Stock splits (forward and reverse) affect all stockholders, so there is never a change in proportionate ownership. If an investor owns 25% of the outstanding shares in a company before a stock split, they’ll still own 25% of the shares after the stock split. Back to our pie analogy - imagine you and three of your friends slice a pie into fourths, giving each person a 25% pie stake. Cutting your slice in half would resemble a 2:1 forward stock split. Do you have more pie slices? Yes. Is there less pie per slice? Yes. Regardless, you still own 25% of the overall pie!

To summarize, stock splits do not affect overall investment value. However, the price per share and the number of shares will change. Although stock splits are relatively insignificant in the long run, they require approval* from stockholders.

**Stock splits (forward and reverse) affect a common stock’s par value. While par value on common stock is a relatively unimportant accounting measure, actions impacting par value generally require shareholder approval.*

**Stock dividends** also offer an opportunity to obtain extra shares. Like stock splits, stock dividends are simply a “reshuffling” of numbers for the company to manipulate its stock price. If a company pays a stock dividend of 25%, each investor will end up with 25% more shares. However, each share will fall proportionally in price. Ultimately, a stock dividend does not increase the overall value of a stock position. Good news - if you understand the math behind stock split calculations, you will likely understand stock dividend math. Here’s an example of a stock dividend question:

An investor owns 100 shares of stock at $20/share. The investor receives a 25% stock dividend. What changes?

Let’s go through the math. The first step is to find the stock dividend factor.

To find the stock dividend factor, add the stock dividend percent (in decimal form) to 1

$SD factor=SD (decimal form) + 1$

$SD factor=0.25 + 1$

$SD factor=1.25$

To find the number of shares adjustment, multiply the original number of shares by the stock split factor

$New shares=old shares x SD factor$

$New shares=100 x 1.25$

$New shares=125$

To find the price per share adjustment, divide the original price per share by the stock dividend factor

$New price=SD factorold price $

$New price=1.25$20 $

$New price=$16$

Put it all together and compare before and after to confirm

$Before the split:$

- 100 shares @ $20 =
**$2,000**

$After the split:$

- 125 shares @ $16 =
**$2,000**

As you can see, the investor ends with the same overall value they started with ($2,000). You can use this comparison to confirm your calculation was done correctly.

Let’s see if you can navigate a stock dividend scenario successfully on your own.

An investor owns 300 shares of JPM stock @ $115. They receive a 15% stock dividend. What changes?

(spoiler)

Answer = **345 shares @ $100**

Step 1: stock dividend factor

$SD factor=SD (decimal form) + 1$

$SD factor=0.15 + 1$

$SD factor=1.15$

Step 2: shares adjustment

$New shares=old shares x SD factor$

$New shares=300 x 1.15$

$New shares=345$

Step 3: price adjustment

$New price=SD factorold price $

$New price=1.15$115 $

$New price=$100$

Step 4: confirm the same overall value

$Before the split:$

- 300 shares @ $115 =
**$34,500**

$After the split:$

- 345 shares @ $100 =
**$34,500**

In conclusion, stock splits and dividends change the number of outstanding shares but don’t result in shareholders gaining or losing overall value. Both accomplish the same thing (manipulating the price upward or downward), but some differences exist.

The most significant difference to be aware of relates to voting. Stock splits require shareholder approval, while stock dividends do not (similar to cash dividends). With the consent of the Board of Directors, a stock dividend can occur whether the stockholders want it or not.

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