Humana Inc.'s last dividend (Do) was $1.12, and its earnings and dividends are expected to increase at a constant growth rate of 12 percent. Humana's market beta is 1.16. If the current risk-free rate is 5 percent and the required rate of return on the market portfolio is 12 percent, what is the company's current expected stock price?
Humana Inc.'s last dividend (Do) was $1.12, and its earnings and dividends are expected to increase at a constant growth rate of 12 percent. Humana's market beta is 1.16. If the current risk-free rate is 5 percent and the required rate of return on the market portfolio is 12 percent, what is the company's current expected stock price?
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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![**Humana Inc.'s Expected Stock Price Calculation**
Humana Inc.'s last dividend (\(D_0\)) was $1.12, and its earnings and dividends are expected to increase at a constant growth rate of 12 percent. Humana's market beta is 1.16. If the current risk-free rate is 5 percent and the required rate of return on the market portfolio is 12 percent, what is the company's current expected stock price?
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**Explanation:**
To find the expected stock price, we use the Gordon Growth Model (also known as the Dividend Discount Model for constant growth), which is:
\[ P_0 = \frac{D_1}{r_s - g} \]
Where:
- \( P_0 \) is the current stock price
- \( D_1 \) is the dividend expected next year
- \( r_s \) is the required rate of return
- \( g \) is the growth rate
First, calculate \( D_1 \) (the expected dividend next year):
\[ D_1 = D_0 \times (1 + g) \]
Next, calculate the required rate of return (\( r_s \)) using the Capital Asset Pricing Model (CAPM):
\[ r_s = \text{Risk-free rate} + \beta \times (\text{Market return} - \text{Risk-free rate}) \]
Finally, plug these values into the Gordon Growth Model to find the expected stock price \( P_0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0bc9ff5-4fd1-4a68-8564-3d0282184e7c%2F35602c9c-c3f4-4176-ad98-c29a928c20d7%2F30f2j0p_processed.png&w=3840&q=75)
Transcribed Image Text:**Humana Inc.'s Expected Stock Price Calculation**
Humana Inc.'s last dividend (\(D_0\)) was $1.12, and its earnings and dividends are expected to increase at a constant growth rate of 12 percent. Humana's market beta is 1.16. If the current risk-free rate is 5 percent and the required rate of return on the market portfolio is 12 percent, what is the company's current expected stock price?
---
**Explanation:**
To find the expected stock price, we use the Gordon Growth Model (also known as the Dividend Discount Model for constant growth), which is:
\[ P_0 = \frac{D_1}{r_s - g} \]
Where:
- \( P_0 \) is the current stock price
- \( D_1 \) is the dividend expected next year
- \( r_s \) is the required rate of return
- \( g \) is the growth rate
First, calculate \( D_1 \) (the expected dividend next year):
\[ D_1 = D_0 \times (1 + g) \]
Next, calculate the required rate of return (\( r_s \)) using the Capital Asset Pricing Model (CAPM):
\[ r_s = \text{Risk-free rate} + \beta \times (\text{Market return} - \text{Risk-free rate}) \]
Finally, plug these values into the Gordon Growth Model to find the expected stock price \( P_0 \).
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