Math Problem Statement

. Roy purchased 4,000 shares of Ernst stock for $148,920 one year ago. The stock pays annual dividends of $0.35 a share. Today, he sold all of his shares for $42.78 a share. What is his total return on this investment?

Solution

To calculate Roy's total return on his investment, we need to account for both the capital gain (or loss) from selling the stock and the dividends he received during the year. Here's how to compute it step-by-step:

Step 1: Calculate the initial purchase price

Roy bought 4,000 shares for a total of $148,920, so the purchase price per share is: Purchase price per share=148,9204,000=37.23\text{Purchase price per share} = \frac{148,920}{4,000} = 37.23

Step 2: Calculate the total selling price

Roy sold all 4,000 shares for $42.78 each, so the total amount he received from selling the shares is: Selling price=4,000×42.78=171,120\text{Selling price} = 4,000 \times 42.78 = 171,120

Step 3: Calculate the capital gain

The capital gain (or loss) is the difference between the selling price and the purchase price: Capital gain=171,120148,920=22,200\text{Capital gain} = 171,120 - 148,920 = 22,200

Step 4: Calculate the dividend income

Roy received annual dividends of $0.35 per share. Therefore, his total dividend income for the year is: Total dividends=4,000×0.35=1,400\text{Total dividends} = 4,000 \times 0.35 = 1,400

Step 5: Calculate the total return

Roy's total return includes both the capital gain and the dividend income. Therefore, his total return is: Total return=22,200+1,400=23,600\text{Total return} = 22,200 + 1,400 = 23,600

Thus, Roy's total return on his investment is $23,600.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

  1. How can the percentage return on Roy's investment be calculated?
  2. What happens to the total return if the dividend is increased to $0.50 per share?
  3. How do you calculate total return if there is a loss instead of a gain?
  4. What is the difference between realized gains and unrealized gains in investments?
  5. How does dividend yield impact total return in stocks?

Tip: Always consider both capital gains and dividends when calculating the total return on an investment.

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Math Problem Analysis

Mathematical Concepts

Investment Return Calculation
Capital Gains
Dividend Income

Formulas

Total purchase price per share = Total purchase cost / Number of shares
Total selling price = Number of shares × Selling price per share
Capital gain = Total selling price - Total purchase cost
Dividend income = Number of shares × Dividend per share
Total return = Capital gain + Dividend income

Theorems

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Suitable Grade Level

Undergraduate Finance or Investment