A Share Of Stock With A Beta Of 69 Now Sells

A Share Of Stock With A Beta Of 69 Now Sells

Chapter 12, Question 5- A share of stock with a beta of .69 now sells for $50. Investors expect the stock to pay a year-end dividend of $4. The T-bill rate is 6%, and the market risk premium is 9%. a. Suppose investors believe the stock will sell for $52 at year-end. Is the stock a good or bad buy? What will investors do? The stock is a buy and the investors . b. At what price will the stock reach an “equilibrium†at which it is perceived as fairly priced today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Sample Paper For Above instruction

The valuation of stocks using the Capital Asset Pricing Model (CAPM) hinges on the relationship between expected returns and perceived risk, represented by beta (β). In this context, we analyze whether a stock with a beta of 0.69, currently trading at $50, constitutes a good investment based on future expectations and determine its fair value considering market conditions.

Firstly, calculating the expected return based on the anticipated year-end stock price and dividend provides a concrete basis for investment decision-making. The expected end-of-year stock price is forecasted at $52, and with an expected dividend of $4, the total expected return combines both capital gains and dividends. Specifically, the total expected amount received by investors at year-end is $52 + $4 = $56. Since the current stock price is $50, the implied rate of return based on this expectation is (56 - 50)/50 = 12%. This suggests a significant potential return, but its desirability depends on the risk-adjusted required return as indicated by the CAPM.

The CAPM states that the expected return (E[r]) on a security is Rf + β * Market Risk Premium, where Rf is the risk-free rate, which is 6%, and the market risk premium is 9%. Incorporating the beta of 0.69, the expected return becomes:

E[r] = 6% + 0.69 * 9% = 6% + 6.21% = 12.21%

Thus, the stock's expected return, based on CAPM, is approximately 12.21%. Comparing this with our estimated return of 12%, we find they are very close, suggesting the stock is fairly priced under these assumptions. However, since the expected return slightly falls short of the CAPM-required return, investors may view the stock as slightly overvalued or fairly valued, depending on their risk preferences and market outlook.

Furthermore, the fair or equilibrium price of the stock can be derived by equating the dividend discount model with CAPM expectations. The commonly used Gordon Growth Model, adjusted for the expected stock price and dividend, is:

P = (D1 + P1)/ (1 + E[r])

where D1 is the dividend, P1 is the expected stock price at year-end. Rearranged for the current price, the fair value considering the expected dividend and price is:

P0 = (D1 + P1) / (1 + E[r])

Plugging in values:

P0 = ($4 + $52) / (1 + 0.1221) ≈ $56 / 1.1221 ≈ $49.89

This suggests that the fair price of the stock today, considering the expected dividend and future stock price, is approximately $49.89. Since the current market price is $50, which is very close, the stock is nearly fairly valued, and investors might consider it a neutral or slightly undervalued opportunity depending on transaction costs and other factors.

In conclusion, based on the expected future price, dividends, and the CAPM, the stock with a beta of 0.69 appears to be fairly valued or a marginal buy at the current price of $50. Investors assessing risk-adjusted returns would find this stock an acceptable investment, given its alignment with observed market expectations and risk profile.

References

  • Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25-46.
  • Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). Wiley.
  • Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47(1), 13-37.
  • Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425-442.
  • Ross, S. A. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13(3), 341-360.
  • Ross, S. A., Westerfield, R., & Jaffe, J. (2016). Corporate Finance (11th ed.). McGraw-Hill Education.
  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
  • Scholes, M., & Williams, J. (1977). Estimating betas from nonsynchronous data. Journal of Financial Economics, 5(3), 309-345.
  • Clark, P. K. (1973). A subordinated stochastic process model with finite variance for speculative prices. Econometrica, 41(5), 877-888.

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