Problem 20 - Accounting

Question

Mia Restaurant Corporation wholesales ovens and ranges to restaurants throughout the Southwest. Mia Restaurant Corporation, which had 40,000 shares of common stock outstanding, declared a 4 -for-1 stock split (3 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 \(\$ 300\) per share before the stock split, what would be an approximate market price per share after the split?

Step-by-Step Solution

Answer

After the split, there will be 160,000 shares outstanding, and the approximate market price per share would be \$75.

Step 1: Understanding the Stock Split

A 4-for-1 stock split means each existing share is divided into 4 shares. This means for every 1 share you originally own, you will now own 4 shares.

Step 2: Calculating New Shares Outstanding

Mia Restaurant Corporation had 40,000 shares originally. After a 4-for-1 stock split, each original share is split into 4. Thus, the new number of shares is calculated as \( 40,000 \times 4 = 160,000 \) shares.

Step 3: Understanding Market Price Post Split

The stock split increases the number of shares, but the total market value of all shares remains the same. Therefore, the market price per share typically decreases to reflect the increased number of shares.

Step 4: Calculating New Market Price Per Share

Before the split, the market price was \( \\(300 \) per share. After the split, since each share is now split into 4, the new price per share is calculated as \( \frac{300}{4} = \\)75 \) per share.

Key Concepts

Shares Outstanding

When a company like Mia Restaurant Corporation declares a stock split, it's a way of increasing the number of shares available. In this scenario, the company executed a 4-for-1 stock split. This means for every one share an investor held, they now own four shares.

Let's break it down further. Originally, Mia Restaurant Corporation had 40,000 shares outstanding. After the stock split, the number of shares increases. To calculate the new number of shares, you multiply the original shares by the split ratio. That is:

• Original shares: 40,000
• Stock split: 4-for-1
• New shares outstanding: 40,000 * 4 = 160,000

The increase in shares doesn't change the ownership percentages of shareholders, but each share now represents a smaller percentage of the company. This can attract more investors because the share price post-split is typically more affordable.

Market Price Adjustment

A stock split also leads to an adjustment in the market price per share. While the number of shares has increased, the overall market capitalization of the company remains unchanged. This means the value of the company as a whole doesn't change, only the number of shares available does.

Before the stock split, each share of Mia Restaurant Corporation was valued at $300. With the 4-for-1 split, each share must now represent a smaller fraction of the total company value. Here's how the market price adjusts:

• Pre-split price per share: $300
• Split factor: 4
• New price per share: $300 ÷ 4 = $75

Thus, after the split, the market price adjusts to $75 per share. The key is to remember that the market price adjustment keeps the overall value constant – it's the same pie, just with more slices.

Financial Calculations

To fully understand stock splits, it's crucial to grasp some simple financial calculations involved. A stock split doesn't inherently change the company's market value. Instead, it adjusts the share metrics, aiding liquidity and potentially attracting investors by making shares more affordable.

In this exercise, we saw:

• To calculate the new shares outstanding, use: Original shares x Split factor = New shares
• For new market price per share: Pre-split price ÷ Split factor = New price

These calculations show the relative changes in shares and price, helping investors understand how their investment might be reshaped. While the numerical value per share changes, the total value of holdings remains the same, maintaining investor confidence.

It’s important that students understand these calculations as they provide the foundation for grasping more complex financial topics in the future.