Problem 20 - Accounting

Question

Rolling Pin Corporation wholesales ovens and ranges to restaurants throughout the Midwest. Rolling Pin Corporation, which had 50,000 shares of common stock outstanding, declared a 3 -for-1 stock split ( 2 additional shares for each share issued). a. What will be the number of shares outstanding after the split? b. If the common stock had a market price of \(\$ 180\) per share before the stock split, what would be an approximate market price per share after the split?

Step-by-Step Solution

Answer

a. 150,000 shares b. Approximately \(\$ 60\) per share.

Step 1: Understand the Stock Split

A 3-for-1 stock split means that for every 1 share owned, shareholders receive 2 additional shares, making it a total of 3 shares for each initial share.

Step 2: Calculate the New Number of Shares

With the stock split ratio known, multiply the existing number of shares by the factor of the split. Rolling Pin Corporation originally had 50,000 shares. After the 3-for-1 split, the number of shares will be: \[ 50,000 \times 3 = 150,000 \] So, there will be 150,000 shares outstanding after the split.

Step 3: Understand Market Price Adjustment

Stock splits do not change the overall value of a shareholder's investment. Therefore, if the total number of shares increases by a factor of 3, the market price should decrease by the same factor to maintain the same total value.

Step 4: Calculate the New Market Price per Share

The original market price per share was \(\\( 180\). After the split, the approximate new market price will be the original price divided by the split factor of 3: \[ \frac{180}{3} = 60 \] Thus, the approximate market price per share after the split will be \(\\) 60\).

Key Concepts

Market Price Adjustment

When a company issues a stock split, the main impact is on the market price of its shares. A stock split does not change the overall value of a shareholder's investment, rather it affects how the value is distributed among the number of shares.
For example, if a company originally had shares priced at \(\\(180\) per share and undergoes a 3-for-1 stock split, each share is divided into three parts to maintain the total value. Therefore, to calculate the new market price after a split, you need to divide the original price by the split ratio.
This means the new price of each share after a 3-for-1 split will be:

• Original Price: \(\\)180\)
• Split Ratio: 3
• New Price: \(\frac{180}{3} = \$60\)

Although the price of each individual share decreases, the total market value of all shares together remains the same. It's essential for investors to understand this mechanism to see that the investment value does not change post-split.

Number of Shares Outstanding

The number of shares outstanding refers to the total shares currently held by all shareholders, including insiders and the public, but excluding the company's treasury shares.
During a stock split, the company increases the number of shares outstanding to decrease the price of each individual share, making them more affordable to a broader range of investors.
In a 3-for-1 stock split, every share is split into three shares. This increases the total number of outstanding shares by a factor of three.
For instance, if a corporation began with 50,000 shares and executes a 3-for-1 stock split:

• Original Shares Outstanding: 50,000
• New Number of Shares (after split): \(50,000 \times 3 = 150,000\)

This increase in shares does not reflect a change in the company's market capitalization, merely a division of existing shares into more shares.

Shareholder Investment Value

A shareholder's investment value in a company is determined by the number of shares owned multiplied by the current market price per share. During a stock split, this overall investment value remains consistent, even though the individual share count and price change.
Let's say a shareholder owns 1,000 shares at \(\\(180\) per share. The total investment value before a split is:

• Original Total Value: \(1,000 \times 180 = \\)180,000\)

After a 3-for-1 stock split, the shareholder will have 3,000 shares, but the price per share reduces:

• New Price per Share: \(\\(60\)
• New Total Value: \(3,000 \times 60 = \\)180,000\)

The shareholder's total investment remains \(\$180,000\), showing that while the stock split increases the share count and decreases the price, the actual value held by a shareholder does not change.