A stock’s current dividend is $1.00, and dividends are expected to grow at a constant rate of 2.70% 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 PV of the dividend paid today (D0D0) and the PV of the dividends expected to be paid 10, 20, and 50 years from now (Dˆ10D^10, Dˆ20D^20, and Dˆ50D^50). Assume that the stock’s required return (rsrs) is 8.40%.

Essentials Of Investments
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ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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A stock’s current dividend is $1.00, and dividends are expected to grow at a constant rate of 2.70% 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 PV of the dividend paid today (D0D0) and the PV of the dividends expected to be paid 10, 20, and 50 years from now (Dˆ10D^10, Dˆ20D^20, and Dˆ50D^50). Assume that the stock’s required return (rsrs) is 8.40%.
A stock’s current dividend is $1.00, and dividends are expected to grow at a constant rate of 2.70% 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 PV of the dividend paid today (\(D_0\)) and the PV of the dividends expected to be paid 10, 20, and 50 years from now (\(\hat{D}_{10}\), \(\hat{D}_{20}\), and \(\hat{D}_{50}\)). Assume that the stock’s required return (\(r_s\)) is 8.40%.

| Time Period | Expected Dividend’s |       |       |
|-------------|---------------------|-------|-------|
|             | Future Value        | Present Value         |
| Now     | \<\>                   | \<\>              |
| End of Year 10 | \<\>                   | \<\>              |
| End of Year 20 | \<\>                   | \<\>              |
| End of Year 50 | \<\>                   | \<\>              |

Using the grey curve (star symbols), plot the present value of each of the expected future dividends for years 10, 20, and 50. The resulting curve will illustrate how the PV of a particular dividend payment will decrease depending on how far from today the dividend is expected to be received.

**Note:** Round each of the discounted values of the dividends to the nearest tenth decimal place before plotting it on the graph. (Tool tip: Mouse over the points in the graph to see their coordinates.)
Transcribed Image Text:A stock’s current dividend is $1.00, and dividends are expected to grow at a constant rate of 2.70% 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 PV of the dividend paid today (\(D_0\)) and the PV of the dividends expected to be paid 10, 20, and 50 years from now (\(\hat{D}_{10}\), \(\hat{D}_{20}\), and \(\hat{D}_{50}\)). Assume that the stock’s required return (\(r_s\)) is 8.40%. | Time Period | Expected Dividend’s | | | |-------------|---------------------|-------|-------| | | Future Value | Present Value | | Now | \<\> | \<\> | | End of Year 10 | \<\> | \<\> | | End of Year 20 | \<\> | \<\> | | End of Year 50 | \<\> | \<\> | Using the grey curve (star symbols), plot the present value of each of the expected future dividends for years 10, 20, and 50. The resulting curve will illustrate how the PV of a particular dividend payment will decrease depending on how far from today the dividend is expected to be received. **Note:** Round each of the discounted values of the dividends to the nearest tenth decimal place before plotting it on the graph. (Tool tip: Mouse over the points in the graph to see their coordinates.)
### Understanding the Graph of Dividend Growth

#### Graph Overview
The graph presented displays the growth of dividends over a specific period, demonstrating both the Present Value (PV) and Future Value (FV) of dividends. 

#### Axes Details
- **X-Axis (Horizontal):** Represents the time in years, ranging from 0 to 60.
- **Y-Axis (Vertical):** Represents the dividends in dollars, ranging from 0 to 5.00.

#### Data Plot
- **Line Graph:** The blue line connects three data points reflecting the progression of dividends over time.
  - **First Point:** At around 10 years, the dividend value is slightly above $1.00.
  - **Second Point:** Around 25 years, with a dividend value above $2.00.
  - **Third Point:** At 50 years, the dividend value surpasses $4.00.

#### Key Terminology
- **PV of Dividends:** Present Value, indicating the value of dividends at the initial time.
- **FV of Dividends:** Future Value, showing the expected value of dividends over time.

#### Additional Notes
- The graph includes a notation for "Discounted Dividends," which likely signifies the adjusted value considering factors such as inflation or interest rates.

This graph is instrumental in understanding how dividends are expected to appreciate in value over the long term and serves as a financial modeling tool for future investment decisions.
Transcribed Image Text:### Understanding the Graph of Dividend Growth #### Graph Overview The graph presented displays the growth of dividends over a specific period, demonstrating both the Present Value (PV) and Future Value (FV) of dividends. #### Axes Details - **X-Axis (Horizontal):** Represents the time in years, ranging from 0 to 60. - **Y-Axis (Vertical):** Represents the dividends in dollars, ranging from 0 to 5.00. #### Data Plot - **Line Graph:** The blue line connects three data points reflecting the progression of dividends over time. - **First Point:** At around 10 years, the dividend value is slightly above $1.00. - **Second Point:** Around 25 years, with a dividend value above $2.00. - **Third Point:** At 50 years, the dividend value surpasses $4.00. #### Key Terminology - **PV of Dividends:** Present Value, indicating the value of dividends at the initial time. - **FV of Dividends:** Future Value, showing the expected value of dividends over time. #### Additional Notes - The graph includes a notation for "Discounted Dividends," which likely signifies the adjusted value considering factors such as inflation or interest rates. This graph is instrumental in understanding how dividends are expected to appreciate in value over the long term and serves as a financial modeling tool for future investment decisions.
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