Over The Long Run, You Expect Dividends For BBC In Problem 4

6 Over The Long Run You Expect Dividends For Bbc In Problem 4 To Gr

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? 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? 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 based on dividend discount models (DDM) is a fundamental approach in financial analysis. This paper addresses three core questions related to stock valuation and dividend policy: (1) the intrinsic value of BBC stock given its expected dividend growth, (2) the dividend growth rate for Shamrock Dogfood Company (SDC) based on its payout policy and return on equity, and (3) the impact on the price-to-earnings (P/E) ratio if SDC increases its payout ratio.

Valuation of BBC Stock Using the Infinite Period DDM

In the context of long-term stock valuation, the Gordon Growth Model, a specific form of the Dividend Discount Model (DDM), is often utilized. It assumes dividends grow at a constant rate indefinitely. The formula for the current stock price (P) using the DDM is:

P = D1 / (r - g)

Where:

  • D1 = dividend in the next period
  • r = required rate of return (11% in this case)
  • g = dividend growth rate (8%)

Based on the problem, if the current dividend (D0) is known, D1 can be calculated as D0*(1 + g). However, since D0 is not explicitly provided, we focus directly on the valuation formula. Assuming that the dividend growth rate and required return are aligned with the expectations in the problem, and considering that the company is expected to grow at 8% and investors require an 11% return, the stock price under these assumptions is:

P = D1 / (r - g) = D0*(1 + g) / (r - g)

Without the current dividend D0, the valuation links to expected future dividends and growth assumptions. This calculation indicates that to find the intrinsic value, the actual dividend payments would need to be specified. Nonetheless, the model underscores the importance of the growth rate and the required rate of return in stock valuation.

Estimating the Dividend Growth Rate of SDC

Shamrock Dogfood Company’s payout policy and its return on equity provide insights into its dividend growth rate. The payout ratio, which is the proportion of earnings paid out as dividends, combined with the company's return on equity (ROE), can be used to estimate the company's dividend growth rate (g).

Given data:

  • Payout ratio (b) = 40% or 0.4
  • ROE = 16% or 0.16

The growth rate of dividends (g) can be approximated using the retained earnings growth approach:

g = (ROE) (1 - payout ratio) = ROE (1 - b)

Substituting the values:

g = 0.16 (1 - 0.4) = 0.16 0.6 = 0.096 or 9.6%

This suggests that, under the current payout policy, SDC's dividends are expected to grow at approximately 9.6% annually, assuming consistent earnings and payout policies.

Impact on P/E Ratio if SDC Increases Its Payout

Considering SDC’s decision to increase its payout ratio from 40% to 50%, this change influences the company's earnings retention, growth prospects, and the valuation multiples applied by investors. The P/E ratio reflects investor expectations of future earnings growth and risk.

When payout ratios increase:

  • Less retained earnings are reinvested into the company, potentially slowing future growth.
  • Higher dividends may attract income-oriented investors, potentially increasing the stock price temporarily.

Mathematically, the P/E ratio can be linked to the growth rate (g) and return on equity (ROE) as:

P/E = (1 - b) / (r - g)

where r is the required rate of return. Increasing the payout ratio b from 0.4 to 0.5 reduces the retention ratio (1 - b) from 0.6 to 0.5, thus potentially lowering the P/E ratio if growth slows.

Furthermore, a higher payout ratio reduces the growth rate since g = ROE * (1 - b). With increased payout, the growth rate decreases from 9.6% to:

g_new = 0.16 * (1 - 0.5) = 0.08 or 8%

Therefore, the new P/E ratio would be approximately:

P/E = (1 - 0.5) / (r - 0.08) = 0.5 / (r - 0.08)

Assuming the same required rate of return, the P/E ratio declines due to reduced expected growth, reflecting lower capital reinvestment and future earnings potential. This illustrates the trade-offs involved in increasing payout ratios.

Conclusion

Stock valuation involves understanding dividend growth, payout policies, and investors’ required rates of return. The DDM provides a useful framework for estimating stock prices when dividends grow at a steady rate. For SDC, maintaining an appropriate payout policy can balance immediate income with long-term growth, directly impacting valuation multiples like the P/E ratio. Investors need to consider how payout decisions influence future earnings growth and, consequently, stock valuations, as evidenced by the changes in payout ratio and growth rates discussed.

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