Problem 4: The Baron Basketball Company Earned $1,000

Problem 4 The Baron Basketball Company Bbc Earned 1000 A Shares

Problem 4: The Baron Basketball Company (BBC) earned $10.00 a share last year and paid a dividend of $6.00 a share. Next year, you expect BBC to earn $11.00 and continue its payout ratio. Assume that you expect to sell the stock for $132.00 a year from now. If you require 12 percent on this stock, how much would you be willing to pay for it?

Problem 6: Over the long run, you expect dividends for BBC in problem 4 to grow at 8 percent and you require 11 percent on the stock. Using the infinite period DDM, how much would you pay for this stock?

Problem 8: The Shamrock Dogfood Company (SDC) has consistently paid out 40 percent of its earnings in dividends. The company's return on equity is 16 percent. What would you estimate as its dividend growth rate?

Problem 10: What P/E ratio would you apply if you learned that SDC had decided to increase its payout to 50 percent? (Hint: This change in payout has multiple effects.)

Paper For Above instruction

The valuation of stocks is a fundamental aspect of investment analysis, requiring a clear understanding of financial metrics such as earnings, dividends, growth rates, and required rates of return. This paper aims to analyze the specific problems related to stock valuation through dividend discount models (DDM), growth assumptions, and price-to-earnings (P/E) ratios, focusing on the hypothetical companies Baron Basketball Company (BBC) and Shamrock Dogfood Company (SDC).

Problem 4: valuation based on next year’s expected dividend and price

The first scenario involves calculating how much an investor should be willing to pay for BBC stock based on expected earnings, dividends, and sale price after one year. BBC earned $10.00 per share last year with a corresponding dividend of $6.00. The analyst expects earnings to increase to $11.00 per share, maintaining the same payout ratio. Therefore, the projected dividend for the next year would be 60% of $11.00, which is $6.60 per share. Assuming the dividend payout remains consistent, investors anticipate selling the stock for $132.00 after one year, with a required rate of return of 12%.

Using this data, the maximum price an investor should be willing to pay today can be calculated with the present value of the expected sale price, dividends, and future value. The valuation formula incorporates the expected dividend, the future stock price, and the investor's required rate of return:

\[ P_0 = \frac{D_1 + P_1}{1 + r} \]

Where \( D_1 \) is the dividend next year, \( P_1 \) is the expected sale price, and \( r \) is the required rate of return. Substituting the values, \( D_1 = 6.60 \), \( P_1 = 132 \), and \( r = 0.12 \), the calculation yields:

\[ P_0 = \frac{6.60 + 132}{1.12} = \frac{138.60}{1.12} \approx \$123.75 \]

Therefore, an investor should be willing to pay approximately \$123.75 today for the stock.

Problem 6: valuation with perpetual dividend growth (constant growth DDM)

The second scenario involves applying the Gordon Growth Model (a variant of the dividend discount model) to determine the fair value of BBC stock under perpetual growth assumptions. Assuming dividends grow at an 8% rate indefinitely, and the required rate of return is 11%, the stock's value can be calculated using the formula:

\[ P_0 = \frac{D_1}{r - g} \]

In this context, \( D_1 \) is the expected dividend next year, which is \$6.60, as previously calculated. The growth rate \( g \) is 8%, or 0.08, and the required rate \( r \) is 11%, or 0.11. Substituting into the formula:

\[ P_0 = \frac{6.60 \times (1 + 0.08)}{0.11 - 0.08} = \frac{6.60 \times 1.08}{0.03} = \frac{7.13}{0.03} \approx \$237.67 \]

This indicates that, based on perpetual growth of dividends at 8%, an investor would be willing to pay approximately \$237.67 for BBC stock.

This valuation underscores the importance of growth prospects and the relationship between the required rate of return and dividend growth in stock valuation.

Problem 8: estimating dividend growth rate based on payout and ROE

The third problem examines the dividend growth rate of Shamrock Dogfood Company (SDC), which pays out 40% of its earnings, with a return on equity (ROE) of 16%. The dividend growth rate \( g \) can be estimated using the retention growth model, which relates payout ratio and ROE:

\[ g = \text{Retention Ratio} \times \text{ROE} \]

Since payout ratio is 40%, the retention ratio is 60%. Therefore,:

\[ g = 0.60 \times 0.16 = 0.096 \text{ or } 9.6\% \]

This indicates that SDC's dividends are expected to grow at approximately 9.6% annually, assuming the company maintains its payout ratio and ROE.

This growth rate highlights how retained earnings contribute to dividend increases over time, which is vital in valuation models that account for growth.

Problem 10: implications of payout policy change on P/E ratio

The final problem considers how increasing the payout ratio from 40% to 50% influences the P/E ratio. The price-to-earnings ratio is influenced by the company's growth rate, payout policy, and risk factors. When a firm increases its payout ratio, several effects emerge:

• Higher payout ratio often signals confidence in earnings stability, potentially reducing perceived risk and increasing valuation multiples.
• However, it leaves less retained earnings for reinvestment, which could slow future growth, reducing the P/E ratio.
• The overall effect on P/E depends on how investors perceive these trade-offs and the company's growth versus dividend payout).

Theoretically, the P/E ratio can be approximated using the Gordon Growth Model as:

\[ P/E = \frac{1-b}{r - g} \]

Where \( b \) is the payout ratio, and \( g \) is the growth rate. Increasing payout from 40% to 50% reduces the retention ratio from 60% to 50%, which might decrease growth if retained earnings drive growth. If the growth rate reduces accordingly, the P/E ratio might adjust proportionally. Moreover, investors may value higher payout ratios more favorably if they prefer dividends over capital gains, leading to higher P/E ratios.

Thus, the decision impacts valuation multiple by affecting expected growth and investor perceptions, illustrating the interconnectedness of payout policies and valuation multiples.

Conclusion

Stock valuation involves analyzing expected dividends, earnings, growth rates, and investor required returns. The problems examined exemplify the application of models like the discounted dividend model and P/E ratios to estimate fair stock prices under different assumptions. Recognizing how payout policies influence growth and valuation is essential for making informed investment decisions. As demonstrated, the interactive effects of payout ratios, growth expectations, and required returns critically shape stock valuations, guiding investors in their assessments.

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