Math Problem Statement
(Calculating rates of return)****
Blaxo BalloonsBlaxo Balloons
manufactures and distributes birthday balloons. At the beginning of the year,
BlaxoBlaxo's
common stock was selling for
$19.6219.62,
but by year end, it was only
$18.0818.08.
a. If the firm paid a total cash dividend of
$1.861.86
during the year, what rate of return would you have earned if you had purchased the stock exactly one year ago?
b. What would your rate of return have been if the firm had paid no cash dividend?
Question content area bottom
Part 1
The rate of return you would have earned is
enter your response here%.
(Round to two decimal places.)
Part 2
The rate of return you would have earned if the firm paid no cash dividend is
enter your response here%.
(Round to two decimal places.)
Solution
To calculate the rate of return, we’ll consider both the dividend payment and the price change over the year. Here’s how we can break down the calculations:
Part (a): Rate of Return with Dividend
The total rate of return can be calculated as:
Given:
- Beginning Price = $19.62
- Ending Price = $18.08
- Dividend = $1.86
Let's plug in these values:
Calculating inside the numerator first:
= \frac{0.32}{19.62} \times 100$$ $$= 0.0163 \times 100 = 1.63\%$$ So, the rate of return with the dividend is: **1.63%** --- ### Part (b): Rate of Return without Dividend If no dividend was paid, the rate of return would only depend on the price change: $$\text{Rate of Return without Dividend} = \frac{\text{Ending Price} - \text{Beginning Price}}{\text{Beginning Price}} \times 100$$ Plugging in the prices: $$= \frac{18.08 - 19.62}{19.62} \times 100$$ $$= \frac{-1.54}{19.62} \times 100$$ $$= -0.0785 \times 100 = -7.85\%$$ So, the rate of return without the dividend is: **-7.85%** --- ### Summary of Results - **Part (a)**: Rate of Return with Dividend = **1.63%** - **Part (b)**: Rate of Return without Dividend = **-7.85%** Would you like further details on any part of this solution? Here are five follow-up questions related to rate of return: 1. How does dividend yield factor into the rate of return calculation? 2. What would the rate of return be if the dividend were higher, say $2.00? 3. How would an increased ending price, for instance $19.00, change the rate of return? 4. What other factors could affect the actual realized return for an investor? 5. Why is it important to distinguish between returns with and without dividends? **Tip**: Dividends can significantly impact the overall return on an investment, especially when the stock price movement is minimal.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Finance
Rate of Return
Dividend Calculation
Formulas
Total Rate of Return = ((Ending Price - Beginning Price + Dividend) / Beginning Price) * 100
Rate of Return without Dividend = ((Ending Price - Beginning Price) / Beginning Price) * 100
Theorems
-
Suitable Grade Level
Grades 11-12