Math Problem Statement

The authorized share capital of the Alfred Cake Company is 120,000 shares. The equity is currently shown in the company’s books as follows:

Common stock ($2 par value) $ 69,000 Additional paid-in capital 19,000 Retained earnings 39,000 Common equity $ 127,000 Treasury stock (4,000 shares) 13,000 Net common equity $ 114,000 How many shares are issued? How many shares are outstanding? How many more shares can be issued without the approval of shareholders?

Solution

To find the required values, let's break down the information step by step:

  1. How many shares are issued?

    • Common stock ($2 par value) is reported as $69,000.
    • The par value of each share is $2.

    The number of shares issued can be calculated as: Shares issued=Common stockPar value=69,0002=34,500 shares\text{Shares issued} = \frac{\text{Common stock}}{\text{Par value}} = \frac{69,000}{2} = 34,500 \text{ shares}

  2. How many shares are outstanding?

    • Treasury stock is 4,000 shares. Treasury shares are shares that have been issued but are no longer outstanding because the company has repurchased them.

    The number of outstanding shares is: Shares outstanding=Shares issuedTreasury shares=34,5004,000=30,500 shares\text{Shares outstanding} = \text{Shares issued} - \text{Treasury shares} = 34,500 - 4,000 = 30,500 \text{ shares}

  3. How many more shares can be issued without the approval of shareholders?

    • The authorized share capital is 120,000 shares.
    • The company has already issued 34,500 shares.

    The number of shares that can be issued without shareholder approval is: Shares available for issue=Authorized sharesShares issued=120,00034,500=85,500 shares\text{Shares available for issue} = \text{Authorized shares} - \text{Shares issued} = 120,000 - 34,500 = 85,500 \text{ shares}

Summary:

  • Shares issued: 34,500 shares
  • Shares outstanding: 30,500 shares
  • Shares that can be issued without shareholder approval: 85,500 shares

Would you like further clarification on any part of this solution?

Here are some related questions to expand on this topic:

  1. What is the difference between common stock and treasury stock?
  2. How does issuing additional shares affect a company’s equity?
  3. What is the significance of par value in share capital?
  4. How does retained earnings relate to the overall equity of a company?
  5. What are the potential implications of repurchasing shares for a company?

Tip: Issuing new shares dilutes existing ownership, so companies need to consider the balance between raising capital and shareholder interest.

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Math Problem Analysis

Mathematical Concepts

Basic Arithmetic
Corporate Finance
Equity and Shares Calculation

Formulas

Shares issued = Common stock / Par value
Shares outstanding = Shares issued - Treasury shares
Shares available for issue = Authorized shares - Shares issued

Theorems

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Suitable Grade Level

Grades 11-12, College Level