What would you pay today, in dollars, for a stock that is expected to make a $2 dividend in one year if the expected dividend growth rate is 5% and you require a 12% return on your investment? O 28.57 29.33 O 31.43 O 43.14 O 54.30
What would you pay today, in dollars, for a stock that is expected to make a $2 dividend in one year if the expected dividend growth rate is 5% and you require a 12% return on your investment? O 28.57 29.33 O 31.43 O 43.14 O 54.30
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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Question
![**Investment Valuation Problem**
What would you pay today, in dollars, for a stock that is expected to make a $2 dividend in one year if the expected dividend growth rate is 5% and you require a 12% return on your investment?
- Option A: $28.57
- Option B: $29.33
- Option C: $31.43
- Option D: $43.14
- Option E: $54.30
In this question, you're asked to determine the present value of a stock based on expected future dividends and growth rates, given a required rate of return. This involves assessing the stock using the Gordon Growth Model (also known as the Dividend Discount Model).
**Gordon Growth Model Formula:**
\[ P = \frac{D_1}{r - g} \]
Where:
- \( P \) is the price you're willing to pay for the stock today.
- \( D_1 \) is the dividend expected in one year ($2 in this case).
- \( r \) is the required rate of return (12% or 0.12 here).
- \( g \) is the growth rate of the dividend (5% or 0.05 here).
Using this formula, you can calculate the option that matches the theoretical fair price of the stock.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F537cca7c-787a-475d-9aba-926e9a602de3%2Fe4c8a0f7-4756-4982-a72b-a3d42eda901f%2Fysfl0yw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Investment Valuation Problem**
What would you pay today, in dollars, for a stock that is expected to make a $2 dividend in one year if the expected dividend growth rate is 5% and you require a 12% return on your investment?
- Option A: $28.57
- Option B: $29.33
- Option C: $31.43
- Option D: $43.14
- Option E: $54.30
In this question, you're asked to determine the present value of a stock based on expected future dividends and growth rates, given a required rate of return. This involves assessing the stock using the Gordon Growth Model (also known as the Dividend Discount Model).
**Gordon Growth Model Formula:**
\[ P = \frac{D_1}{r - g} \]
Where:
- \( P \) is the price you're willing to pay for the stock today.
- \( D_1 \) is the dividend expected in one year ($2 in this case).
- \( r \) is the required rate of return (12% or 0.12 here).
- \( g \) is the growth rate of the dividend (5% or 0.05 here).
Using this formula, you can calculate the option that matches the theoretical fair price of the stock.
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