Your broker offers to sell you shares of Wingler & Company common stock, which paid a dividend of $2 yesterday. You expect the dividend to grow at a rate of 5 percent per year into perpetuity. If the appropriate rate of return for the stock is 12 percent, what is the market value of Wingler's stock?
Your broker offers to sell you shares of Wingler & Company common stock, which paid a dividend of $2 yesterday. You expect the dividend to grow at a rate of 5 percent per year into perpetuity. If the appropriate rate of return for the stock is 12 percent, what is the market value of Wingler's stock?
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
Problem 1PS
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I need help with this question in the picture, please. (7-6)
![### Problem 7-6
Your broker offers to sell you shares of Wingler & Company common stock, which paid a dividend of $2 yesterday. You expect the dividend to grow at a rate of 5 percent per year into perpetuity. If the appropriate rate of return for the stock is 12 percent, what is the market value of Wingler’s stock?
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**Explanation for Educational Context:**
This problem involves calculating the market value of a stock using the Gordon Growth Model (also known as the Dividend Discount Model). The model helps determine the present value of an infinite series of future dividends that are expected to grow at a constant rate.
- **Dividend Paid (D₀):** $2
- **Growth Rate (g):** 5% (0.05)
- **Required Rate of Return (r):** 12% (0.12)
The formula for the price of the stock (P₀) is:
\[ P₀ = \frac{D₁}{r - g} \]
Where \( D₁ \) is the dividend expected next year, calculated as:
\[ D₁ = D₀ \times (1 + g) \]
Substitute the known values into the formula to find the price of the stock.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F148aeaed-9d27-47af-9574-163d35f55f55%2F37096936-d76f-424e-a862-6e85b82bead5%2Ffvyqd8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 7-6
Your broker offers to sell you shares of Wingler & Company common stock, which paid a dividend of $2 yesterday. You expect the dividend to grow at a rate of 5 percent per year into perpetuity. If the appropriate rate of return for the stock is 12 percent, what is the market value of Wingler’s stock?
---
**Explanation for Educational Context:**
This problem involves calculating the market value of a stock using the Gordon Growth Model (also known as the Dividend Discount Model). The model helps determine the present value of an infinite series of future dividends that are expected to grow at a constant rate.
- **Dividend Paid (D₀):** $2
- **Growth Rate (g):** 5% (0.05)
- **Required Rate of Return (r):** 12% (0.12)
The formula for the price of the stock (P₀) is:
\[ P₀ = \frac{D₁}{r - g} \]
Where \( D₁ \) is the dividend expected next year, calculated as:
\[ D₁ = D₀ \times (1 + g) \]
Substitute the known values into the formula to find the price of the stock.
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