3-for-1 split. After the split, the price of one share was $39.24. What was the pre-split price per share?

Explanation:

Let's say that the company is valued at $300 just as a simple example.

Also, let's say there are 100 shares each worth $3, so we have 100*3 = 300 as the total value of the company.

A 3-for-1 split means that for each share, it will get turned into 3 shares. So you turn in 1 share and in return you get 3 shares back. Or put another way, each share is ripped/cut into 3 equal pieces.

After doing this split, we would have 3*100 = 300 shares and each share would be now worth (1/3)*3 = 1 dollar. Note the new number of shares multiplied with the new value per share is still the same total valuation of $300. Doing a stock split, or a reverse stock split, will not change the value of the company. This is a good thing or else companies would simply do (reverse) splits all the time to increase their value however large they wanted without actually contributing anything to society.

So quite simply, when we do a 3-for-1 split, we multiply the old price per share by 1/3 to get the new price per share.

Let

x = old price per share

y = new price per share

So x happens before the split and y is after the split.

For a 3-to-1 split, we can form this equation

y = (1/3)x

which solves to

x = 3y

when we multiply both sides by 3

We know that y = 39.24, which means,

x = 3y

x = 3*39.24

x = 117.72

The pre-split price per share was $117.72

So in short, all we did was multiply the given number (39.24) by 3.

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