Synovec Company is growing quickly. Dividends are expected to grow at a rate of 20 percent for the next three years, with the growth rate falling off to a constant 4 percent thereafter. If the required return is 10 percent, and the company just paid a dividend of $3.70, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Current share price

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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**Problem Statement: Estimating Current Share Price**

*Synovec Company is growing quickly. Dividends are expected to grow at a rate of 20 percent for the next three years, with the growth rate falling off to a constant 4 percent thereafter. If the required return is 10 percent, and the company just paid a dividend of $3.70, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)*

**Input Data:**

- Dividend growth rate: 20% for the next three years
- Long-term growth rate: 4%
- Required return rate: 10%
- Most recent dividend paid: $3.70

**Output Field:**

- Current Share Price: A field where users can input or see the calculated current share price based on the provided data.

(Note: The placeholder in the interface prompts the user to enter the calculated share price.)

**Visual Explanation:**

On the interface, there is a box titled "Current share price" for users to input their answer after calculations. The prompt emphasizes not to round intermediate calculations and to provide the final answer to two decimal places.

**Example Solution Steps:**

1. **Calculate the expected dividends for the next three years:**
   - D1 = $3.70 * (1 + 0.20) = $4.44
   - D2 = $4.44 * (1 + 0.20) = $5.33
   - D3 = $5.33 * (1 + 0.20) = $6.40

2. **Calculate the expected dividend at the end of year 4 using the long-term growth rate:**
   - D4 = $6.40 * (1 + 0.04) = $6.66

3. **Calculate the present value of the expected dividends for the first three years:**
   - PV(D1) = $4.44 / (1 + 0.10)^1
   - PV(D2) = $5.33 / (1 + 0.10)^2
   - PV(D3) = $6.40 / (1 + 0.10)^3

4. **Calculate the price of the stock at the end of year 3 (P3) using the perpetual growth formula:**
   - P3
Transcribed Image Text:**Problem Statement: Estimating Current Share Price** *Synovec Company is growing quickly. Dividends are expected to grow at a rate of 20 percent for the next three years, with the growth rate falling off to a constant 4 percent thereafter. If the required return is 10 percent, and the company just paid a dividend of $3.70, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)* **Input Data:** - Dividend growth rate: 20% for the next three years - Long-term growth rate: 4% - Required return rate: 10% - Most recent dividend paid: $3.70 **Output Field:** - Current Share Price: A field where users can input or see the calculated current share price based on the provided data. (Note: The placeholder in the interface prompts the user to enter the calculated share price.) **Visual Explanation:** On the interface, there is a box titled "Current share price" for users to input their answer after calculations. The prompt emphasizes not to round intermediate calculations and to provide the final answer to two decimal places. **Example Solution Steps:** 1. **Calculate the expected dividends for the next three years:** - D1 = $3.70 * (1 + 0.20) = $4.44 - D2 = $4.44 * (1 + 0.20) = $5.33 - D3 = $5.33 * (1 + 0.20) = $6.40 2. **Calculate the expected dividend at the end of year 4 using the long-term growth rate:** - D4 = $6.40 * (1 + 0.04) = $6.66 3. **Calculate the present value of the expected dividends for the first three years:** - PV(D1) = $4.44 / (1 + 0.10)^1 - PV(D2) = $5.33 / (1 + 0.10)^2 - PV(D3) = $6.40 / (1 + 0.10)^3 4. **Calculate the price of the stock at the end of year 3 (P3) using the perpetual growth formula:** - P3
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