A Person Is Considering Buying The Stock Of Two Home Health
A Person Is Considering Buying The Stock Of Two Home Health Companies
A person is considering buying the stock of two home health companies that are similar in all respects except the proportion of earnings paid out as dividends. Both companies are expected to earn $6 per share in the coming year, but company D (for dividends) is expected to pay out the entire amount as dividends, while company G (for growth) is expected to pay out only one-third of its earnings, or $2 per share. The companies are equally risky; their required rate of return is 15 percent. D’s constant growth rate is zero, and G’s is 8.33 percent. What are the intrinsic values of stocks D and G?
Paper For Above instruction
The valuation of stocks fundamentally hinges on the expected dividends and the growth prospects of the companies in question. Given the scenario, we are asked to calculate the intrinsic values of two home health companies—one paying out dividends in entirety and the other retaining earnings for growth—using the dividend discount model (DDM). These calculations will underscore the importance of dividend payout strategies and growth expectations in determining stock value.
For company D, which pays all earnings as dividends with no growth, the valuation model simplifies to the perpetuity formula since dividends are expected to remain constant indefinitely. The intrinsic value per share, therefore, is the annual dividend divided by the required rate of return. Conversely, company G retains two-thirds of earnings to finance growth, leading to an increasing dividend stream, which is best valued using the Gordon Growth Model (GGM), a form of the DDM for stocks with constant growth.
Intrinsic Value of Company D
Company D pays out all of its earnings ($6 per share) as dividends and has no growth in dividends. The formula for the intrinsic value of a no-growth stock is:
\[ P_D = \frac{D}{r} \]
where:
- \( D = \$6 \),
- \( r = 15\% \) or 0.15.
Plugging in the values:
\[ P_D = \frac{\$6}{0.15} = \$40 \]
Thus, the intrinsic value of company D is $40 per share.
Intrinsic Value of Company G
Company G pays out only one-third of its earnings, i.e., \( D_1 = \$2 \) per share, and retains two-thirds to finance growth. Its expected growth rate \( g \) is 8.33%, or 0.0833. Using the Gordon Growth Model:
\[ P_G = \frac{D_1}{r - g} \]
where:
- \( D_1 = \$2 \),
- \( r = 15\% \),
- \( g = 8.33\% \).
Substituting:
\[ P_G = \frac{\$2}{0.15 - 0.0833} = \frac{\$2}{0.0667} \approx \$30 \]
The intrinsic value of company G is approximately $30 per share.
Summary
Under the given assumptions, the intrinsic value per share for company D with no growth is $40, while for company G, considering its growth and payout policy, is approximately $30. These valuations emphasize how dividend payout and growth expectations influence stock valuation; the company's policy to retain earnings for growth significantly reduces its immediate dividend payout but enhances its future value due to expected growth.
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Additional Valuations
Medical Corporation of America (MCA):
Given data:
- Current stock price \( P_0 = \$36 \),
- Last dividend \( D_0 = \$2.40 \),
- Required rate of return \( r = 12\% \),
- Growth rate \( g \) is to be determined, assuming dividends grow constantly.
Using the Gordon Growth Model:
\[ P_0 = \frac{D_1}{r - g} \]
where:
\[ D_1 = D_0 \times (1 + g) \]
Rearranged to find \( g \):
\[ g = r - \frac{D_0}{P_0} \]
Calculate \( D_1 \):
\[ D_1 = 2.40 \times (1 + g) \]
Expressing \( P_0 \):
\[ 36 = \frac{2.40 \times (1 + g)}{0.12 - g} \]
Solving for \( g \) involves rearranging:
\[ 36(0.12 - g) = 2.40(1 + g) \]
\[ 4.32 - 36g = 2.40 + 2.40g \]
\[ 4.32 - 2.40 = 36g + 2.40g \]
\[ 1.92 = 38.40g \]
\[ g = \frac{1.92}{38.40} = 0.05 \text{ or } 5\% \]
The dividend growth rate \( g \) is 5%. To find the expected stock price in five years:
\[ P_5 = P_0 \times (1 + g)^5 \]
\[ P_5 = 36 \times (1.05)^5 \approx 36 \times 1.2763 = \$45.93 \]
Hence, the expected stock price in five years is approximately \$45.93.
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Bay Area Healthcare Stock Valuation
Given data:
- Last dividend \( D_0 = \$2 \),
- Growth rate \( g = 5\% \),
- Required rate of return \( r = 12\% \),
- Dividends grow perpetually at a constant rate.
a. Dividends over the next three years:
\[ D_1 = 2 \times 1.05 = \$2.10 \]
\[ D_2 = 2.10 \times 1.05 = \$2.205 \]
\[ D_3 = 2.205 \times 1.05 = \$2.315 \]
b. Current value and forecasted dividends:
Current stock value:
\[ P_0 = \frac{D_1}{r - g} = \frac{2.10}{0.12 - 0.05} = \frac{2.10}{0.07} = \$30 \]
Value at each of the next three years incorporates the growing dividend:
\[ P_1 = \frac{D_2}{r - g} = \frac{2.205}{0.07} \approx \$31.50 \]
\[ P_2 = \frac{D_3}{r - g} = \frac{2.315}{0.07} \approx \$33.07 \]
\[ P_3 = \frac{D_4}{r - g} = \frac{2.4315}{0.07} \approx \$34.74 \]
c. Dividend yield and capital gains yield:
- Dividend yield each year:
\[ \text{Dividend Yield} = \frac{D_{t+1}}{P_t} \]
- Capital gains yield:
\[ \text{Gains} = g = 5\% \]
- Total return:
\[ \text{Total Return} = \text{Dividend Yield} + g \]
d. Expected total returns:
- Year 1:
\[ \frac{\$2.205}{\$30} \approx 7.35\% \]
plus 5% growth, total approximately 12.35%
- Year 2:
\[ \frac{\$2.315}{\$31.50} \approx 7.35\% \]
plus 5%, total ~12.35%
- Year 3:
\[ \frac{\$2.4315}{\$33.07} \approx 7.35\% \]
plus 5%, total ~12.35%
This consistent total return aligns with the required rate of return, confirming the model's internal consistency.
e. Comparison with required rate of return:
The total expected return over each year (~12.35%) matches the required rate of return (12%), indicating the stock price valuation based on dividend growth assumptions is appropriate. This consistency underscores the efficiency of dividend discount models in reflecting market expectations and supports rational investment decision-making.
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Lucas Clinics Dividend Expectations
Given:
- Last dividend \( D_0 = \$1.50 \),
- Current stock price \( P_0 = \$15.75 \),
- Growth rate \( g = 5\% \),
- Required return \( r = 15\% \).
Expected dividend for the next year:
\[ D_1 = D_0 \times (1 + g) = 1.50 \times 1.05 = \$1.575 \]
Dividend yield:
\[ \frac{D_1}{P_0} = \frac{1.575}{15.75} \approx 10\% \]
Capital gains yield:
Since the stock grows at 5%, the capital gains yield is 5%. The total expected return, therefore, is:
\[ \text{Dividend Yield} + \text{Capital Gains Yield} = 10\% + 5\% = 15\% \]
This matches the investor's required rate of return, confirming the valuation and expectations derived from the dividend discount model operate coherently.
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Conclusion
Stock valuation, whether for home health companies or healthcare firms like MCA, depends critically on dividend payout policies, earnings growth rates, and investor required returns. The models applied here, including the perpetuity and Gordon Growth Model, provide a framework for estimating intrinsic values and future prices, which align well with market dynamics when assumptions hold true. Understanding these principles helps investors make rational decisions based on fundamental data, ensuring they comprehend the impact of payout policies and growth prospects on stock valuation.
References
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