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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![**Stock Valuation Problem**
**Question 3. (10 points):** The Northwest Athletic Equipment Company has undergone tremendous growth over the past several years. Things are slowing now but they still anticipate a 3% annual rate in the growth of dividends per year indefinitely. If the market requires a 14% rate of return on comparable securities, and Northwest Athletic currently pays an annual dividend of $0.50 per share, estimate a current per share price of the stock.
---
**Explanation:**
To estimate the current per share price of the stock of Northwest Athletic Equipment Company, we can use the Gordon Growth Model (also known as the Dividend Discount Model for a growing perpetuity). This model is used to determine the present value of a stock based on its expected future dividends that grow at a constant rate.
**Formula:**
\[ P = \frac{D_0 \times (1 + g)}{r - g} \]
Where:
- \( P \) = current stock price
- \( D_0 \) = current dividend ($0.50)
- \( g \) = growth rate of dividends (3% or 0.03)
- \( r \) = required rate of return (14% or 0.14)
**Steps:**
1. Calculate next year's expected dividend: \( D_1 = D_0 \times (1 + g) = 0.50 \times (1 + 0.03) = 0.50 \times 1.03 = 0.515 \).
2. Plug the values into the formula:
\[ P = \frac{0.515}{0.14 - 0.03} = \frac{0.515}{0.11} \].
3. Calculate the result to find the estimated current stock price.
Through these steps, you can determine the current per share price based on the given dividend, growth rate, and required return. This example illustrates the application of financial models in evaluating investment opportunities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3b6f7a8-1c05-4a35-8233-778155cd0503%2Fb3c300d8-c9f6-43b8-8c2d-90f9e4ee3ef2%2Fsceoofw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Stock Valuation Problem**
**Question 3. (10 points):** The Northwest Athletic Equipment Company has undergone tremendous growth over the past several years. Things are slowing now but they still anticipate a 3% annual rate in the growth of dividends per year indefinitely. If the market requires a 14% rate of return on comparable securities, and Northwest Athletic currently pays an annual dividend of $0.50 per share, estimate a current per share price of the stock.
---
**Explanation:**
To estimate the current per share price of the stock of Northwest Athletic Equipment Company, we can use the Gordon Growth Model (also known as the Dividend Discount Model for a growing perpetuity). This model is used to determine the present value of a stock based on its expected future dividends that grow at a constant rate.
**Formula:**
\[ P = \frac{D_0 \times (1 + g)}{r - g} \]
Where:
- \( P \) = current stock price
- \( D_0 \) = current dividend ($0.50)
- \( g \) = growth rate of dividends (3% or 0.03)
- \( r \) = required rate of return (14% or 0.14)
**Steps:**
1. Calculate next year's expected dividend: \( D_1 = D_0 \times (1 + g) = 0.50 \times (1 + 0.03) = 0.50 \times 1.03 = 0.515 \).
2. Plug the values into the formula:
\[ P = \frac{0.515}{0.14 - 0.03} = \frac{0.515}{0.11} \].
3. Calculate the result to find the estimated current stock price.
Through these steps, you can determine the current per share price based on the given dividend, growth rate, and required return. This example illustrates the application of financial models in evaluating investment opportunities.
Expert Solution
Step 1
The constant growth model is a method for valuing the share price of a stock. It calculates the intrinsic value of a stock. It is also known as the Dividend Discount Model (DDM) or Gordon’s Growth Model (GGM).
It is an important tool in comparing various companies across industries while making an investment decision.
It is calculated as:
Calculate the expected dividend:
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