A Stock Pays No Dividend And Is Expected To Be Sold For $50

1a Stock Pays No Dividend And Is Expected To Be Sold For 50 After 4

1. A stock pays no dividend and is expected to be sold for $50 after 4 years. If the investor’s required rate of return (RRR) is 12%, at what price is he/she willing to buy it?

2. ABC company has its return on equity (ROE) = 10% and a retention rate of 30%. It recently paid a dividend of $2. The stock’s current selling price is $50. What is the expected rate of return for the stock? If your RRR is 12%, will you be willing to buy it? If your RRR is 15%, will you be willing to buy?

3. A common stock sells for $50 and will pay a dividend of $3.5 next period. The firm has a constant growth rate of 15%. What is the expected rate of return? If your RRR is 20%, will you buy it?

4. You’re planning to buy between preferred Stock A and B. Stock A pays an annual dividend of $6 and is currently selling for $60. Stock B pays an annual dividend of $8 and is selling for $75. Which one will you buy?

Paper For Above instruction

Investment decisions hinge on evaluating the value of securities relative to the investor’s required rate of return (RRR). This analysis involves understanding present and future cash flows, dividend policies, growth prospects, and risk assessments. In the following, each scenario will be addressed with detailed calculations and interpretations, illustrating the core principles of valuation and investment choice.

Scenario 1: Valuation of a Non-Dividend Stock with a Future Sale Price

The first scenario involves a stock with no dividends paid during its holding period, expected to be sold for $50 after four years. The main question is: at what initial purchase price will an investor with a RRR of 12% be willing to buy the stock? This is fundamentally a discounted future value problem. Since the stock does not pay dividends, the only cash flow the investor considers is the sale proceeds at the end of year four.

The formula to determine the present value (PV) of a future sum is:

PV = Future Price / (1 + RRR)^n

where Future Price = $50, RRR = 12% or 0.12, and n = 4 years.

Applying the data:

PV = 50 / (1 + 0.12)^4 = 50 / (1.12)^4 ≈ 50 / 1.5748 ≈ $31.78

Therefore, an investor willing to require a 12% return should be willing to pay approximately $31.78 today for this stock.

Scenario 2: Expected Rate of Return for ABC Company Stock

Next, we analyze ABC Company’s stock, which has a return on equity (ROE) of 10% and a retention ratio of 30%. The dividend was recently $2, and the current stock price is $50. The goal is to compute the expected rate of return, considering the company’s growth in dividends and earnings.

The dividend growth model (Gordon Growth Model) relates the stock price (P) to dividends (D) and growth rate (g):

P = D1 / (k_e - g)

where D1 is the dividend next period, k_e is the expected rate of return, and g is the growth rate of dividends.

First, calculate the growth rate g using the ROE and retention ratio:

g = ROE × retention ratio = 10% × 30% = 3% or 0.03.

The next dividend, D1, is:

D1 = D0 × (1 + g) = $2 × (1 + 0.03) = $2.06

Applying the Gordon Growth Model:

50 = 2.06 / (k_e - 0.03)

Rearranged to find k_e:

k_e = (2.06 / 50) + 0.03 = 0.0412 + 0.03 = 0.0712 or 7.12%

Hence, the expected rate of return is approximately 7.12%. Comparing this to investor RRR thresholds:

  • At RRR = 12%, the stock’s expected return (7.12%) is below the requirement. Therefore, it would not be an attractive buy based on RRR.
  • At RRR = 15%, the stock still offers a lower expected return than the investor’s requirement, so again, it would not meet the threshold for purchase.

Scenario 3: Expected Rate of Return for a Growth Stock

In this scenario, a stock is selling at $50, with a next-period dividend of $3.5, and the firm’s dividend grows perpetually at a rate of 15%. The question is: what is the expected rate of return?

Using the Gordon Growth Model, the expected rate of return is the sum of the dividend yield and growth rate:

Expected Return = (D1 / P) + g

Calculations:

Dividend yield = 3.5 / 50 = 0.07 or 7%

Adding the growth rate:

Expected Return = 7% + 15% = 22%

Thus, investors can expect a 22% return based on current dividend and growth estimates.

Comparing to an RRR threshold of 20%:

  • Since 22% exceeds 20%, the stock appears to be an attractive investment for a risk-averse investor seeking at least 20% returns.

Scenario 4: Comparison of Preferred Stock A and B

Finally, the choice between preferred stocks A and B is based on dividend yield and investment return considerations. Stock A pays a $6 dividend, priced at $60:

Dividend Yield A = 6 / 60 = 10%

Stock B pays an $8 dividend, priced at $75:

Dividend Yield B = 8 / 75 ≈ 10.67%

Assuming both stocks are relatively similar in risk and market conditions, the higher dividend yield indicates a potentially better income return, making Stock B more attractive from a yield perspective.

However, investors should also consider growth prospects, stability, and other qualitative factors. Based purely on dividend yield, Stock B offers a higher immediate income yield and would be the preferred choice.

Conclusion

Investment valuation involves a careful analysis of expected future cash flows, growth estimates, and risk premiums. As demonstrated, the valuation of a no-dividend stock hinges solely on its anticipated sale price discounted at the investor’s RRR. Similarly, dividend growth models facilitate understanding expected returns and guiding buying decisions. Comparing preferred stocks involves assessing dividend yields relative to prices, but broader factors must also be considered. Ultimately, successful investing relies on aligning valuation insights with individual risk tolerance and return requirements.

References

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  • Damodaran, A. (2012). Damodaran on Valuation: Security Analysis for Investment and Corporate Finance. Wiley Finance.
  • Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance (12th ed.). McGraw-Hill Education.
  • Gordon, M. J. (1959). Dividends, earnings, and stock prices. The Review of Economics and Statistics, 41(2), 99-105.
  • Fama, E. F., & French, K. R. (2002). The equity premium. The Journal of Finance, 57(2), 637-659.
  • Lintner, J. (1956). Distributed dividend payments and stock prices. The American Economic Review, 46(2), 971-978.
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  • McKinsey & Company. (2021). Dividend investing: Strategies for building income streams. Retrieved from https://www.mckinsey.com
  • Investopedia. (2023). The Gordon Growth Model. Retrieved from https://www.investopedia.com
  • Morningstar. (2023). Preferred Stock Data and Analysis. Retrieved from https://www.morningstar.com

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