The following graph shows the value of a stock's dividends over time. The stock's current dividend is $1.00 per share, and dividends are expected to grow at a constant rate of 4.50% per year. The intrinsic value of a stock should equal the sum of the present value (PV) of all of the dividends that a stock is supposed to pay in the future, but many people find it difficult to imagine adding up an infinite number of dividends. Calculate the present value (PV) of the dividend paid today (D) and the discounted value of the dividends expected to be paid 10, 20, and 50 years from now (D10, D20, D50). Assume that the stock's required return (rs) is 5.40%. Note: Carry and round the calculations to four decimal places. Time Period Now End of Year 10 End of Year 20 End of Year 50 Dividend's Expected Future Value Dividend's Expected Present Value

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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The graphic presents information regarding the value of a stock’s dividends over time. The current dividend is $1.00 per share, with dividends projected to grow at a constant rate of 4.50% per year. The intrinsic value of a stock should be equivalent to the sum of the present value (PV) of all future dividends. This concept can be challenging due to the idea of calculating an infinite number of dividends.

This exercise involves calculating the present value (PV) of the dividend paid today (D₀) and the discounted value of dividends expected at 10, 20, and 50 years in the future (D₁₀, D₂₀, D₅₀). The required return rate (rₛ) for the stock is given as 5.40%.

**Note:** Ensure all calculations are accurate to four decimal places.

**Table Explanation:**

- **Time Period:** Lists the specific points in time for which the dividend values are calculated (Now, End of Year 10, End of Year 20, End of Year 50).
  
- **Dividend’s Expected Future Value:** This column requires calculating the expected future value of dividends at each specific time period.

- **Dividend’s Expected Present Value:** This column requires finding the present value of the expected future dividends for each time period. 

The table provides dropdowns for interaction, allowing for the calculation or display of specific expected values based on the input conditions.
Transcribed Image Text:The graphic presents information regarding the value of a stock’s dividends over time. The current dividend is $1.00 per share, with dividends projected to grow at a constant rate of 4.50% per year. The intrinsic value of a stock should be equivalent to the sum of the present value (PV) of all future dividends. This concept can be challenging due to the idea of calculating an infinite number of dividends. This exercise involves calculating the present value (PV) of the dividend paid today (D₀) and the discounted value of dividends expected at 10, 20, and 50 years in the future (D₁₀, D₂₀, D₅₀). The required return rate (rₛ) for the stock is given as 5.40%. **Note:** Ensure all calculations are accurate to four decimal places. **Table Explanation:** - **Time Period:** Lists the specific points in time for which the dividend values are calculated (Now, End of Year 10, End of Year 20, End of Year 50). - **Dividend’s Expected Future Value:** This column requires calculating the expected future value of dividends at each specific time period. - **Dividend’s Expected Present Value:** This column requires finding the present value of the expected future dividends for each time period. The table provides dropdowns for interaction, allowing for the calculation or display of specific expected values based on the input conditions.
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