Math Problem Statement

  1. Shining Star Company’s current balance sheet shows total common equity of $6,225,000. The company has 600,000 shares of stock outstanding, and they sell at a price of $29.20 per share. By how much do the firm’s market and book values per share differ?

Question 7 options:

a)

$21.67

b)

$19.96

c)

$20.13

d)

$22.76

e)

$18.83

Solution

To determine how much the firm's market and book values per share differ, we need to calculate both the market value per share and the book value per share, then find the difference.

Step 1: Calculate the Book Value per Share

The book value per share is calculated as:

Book Value per Share=Total Common EquityShares Outstanding\text{Book Value per Share} = \frac{\text{Total Common Equity}}{\text{Shares Outstanding}}

Given:

  • Total Common Equity = $6,225,000
  • Shares Outstanding = 600,000

Book Value per Share=6,225,000600,000=10.375\text{Book Value per Share} = \frac{6,225,000}{600,000} = 10.375

Step 2: Calculate the Market Value per Share

The market value per share is given as the price of the stock:

Market Value per Share=29.20\text{Market Value per Share} = 29.20

Step 3: Find the Difference Between Market and Book Value per Share

Difference=Market Value per ShareBook Value per Share\text{Difference} = \text{Market Value per Share} - \text{Book Value per Share}

Difference=29.2010.375=18.825\text{Difference} = 29.20 - 10.375 = 18.825

Rounding to two decimal places, the difference is $18.83.

Answer:

e) $18.83


Would you like further clarification on the steps? Here are a few related questions to explore:

  1. What factors could cause the market value per share to be higher or lower than the book value per share?
  2. How is total common equity related to a company’s overall financial health?
  3. What is the significance of market value versus book value in stock analysis?
  4. How would you calculate the price-to-book (P/B) ratio?
  5. What happens to market value and book value if the company's equity changes (e.g., due to new stock issuance or repurchases)?

Tip: The market value of a share reflects investor sentiment and future prospects, while the book value is based on historical costs and may not represent a company’s current worth.

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Math Problem Analysis

Mathematical Concepts

Financial Mathematics
Equity Valuation
Market Value vs. Book Value

Formulas

Book Value per Share = Total Common Equity / Shares Outstanding
Difference = Market Value per Share - Book Value per Share

Theorems

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Suitable Grade Level

Undergraduate Finance/Accounting