Stock Valuation Infographic With Expected Return

Problem:

A stock with a beta of .75 currently sells for $50. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 4%, and the market risk premium is 7%. If the stock is perceived to be fairly priced today, what must be investors’ expectation of the price of the stock at the end of the year?

We’re given a stock priced at $50 today, with the following details:

Given:

• Beta, $\beta = 0.75$
  

• Current price, $P_0 = 50$
  

• Expected dividend at year-end, $D_1 = 2$
  

• Risk-free rate, $R_f = 4\% = 0.04$
  

• Market risk premium, $R_m - R_f = 7\% = 0.07$
  

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Step 1: Calculate Required Rate of Return using CAPM

$$r = R_f + \beta (R_m - R_f)$$
$$r = 0.04 + 0.75(0.07) = 0.04 + 0.0525 = \boxed{0.0925 \text{ or } 9.25\%}$$

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Step 2: Use the Required Return Formula

For a fairly priced stock:

$$P_0 = \frac{D_1 + P_1}{1 + r}$$

Where:

• $P_1$ is the expected price at the end of the year

Rearranging to solve for $P_1$:

P1​ = (1+0.0925)⋅50−2 = 1.0925⋅50−2 = 54.625−2 = $52.625​

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✅ Answer:

Investors must expect the stock price at year-end to be $52.63 (rounded) if the stock is fairly priced today.