To estimate the expected return on the stock if you hold it for exactly one year, we can use the Capital Asset Pricing Model (CAPM) to find the required return and then factor in the dividend growth model for the stock price appreciation. Here are the steps:

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Step 1: Calculate the Required Return Using CAPM

The formula for CAPM is:

$r_e = r_f + \beta (r_m - r_f)$

Where:

• $r_e$ = Required return (expected return under CAPM)
• $r_f$ = Risk-free rate (T-bill yield = 4.1% or 0.041)
• $\beta$ = Beta of the stock (1.5)
• $r_m - r_f$ = Market risk premium (7.1% or 0.071)

Substituting the values:

$r_e = 0.041 + 1.5 \times 0.071$

$r_e = 0.041 + 0.1065 = 0.1475 \, (14.75\%)$

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Step 2: Estimate the Stock Price in One Year

Using the dividend growth model, the price of the stock at any time $t$ is given by:

$P_t = \frac{D_{t+1}}{r_e - g}$

Where:

• $P_t$ = Price at time $t$
• $D_{t+1}$ = Dividend expected next year
• $r_e$ = Required return (from CAPM = 0.1475)
• $g$ = Dividend growth rate (4.2% or 0.042)

The dividend next year, $D_{t+1}$, is calculated as:

$D_{t+1} = D_0 \times (1 + g)$

Substitute $D_0 = 4$ and $g = 0.042$:

$D_{t+1} = 4 \times (1 + 0.042) = 4 \times 1.042 = 4.168$

Now calculate the expected price in one year ($P_1$):

$P_1 = \frac{4.168}{0.1475 - 0.042}$

$P_1 = \frac{4.168}{0.1055} \approx 39.49$

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Step 3: Estimate the Total Expected Return for One Year

The total return consists of:

1. Dividend Yield: $\frac{D_{t+1}}{P_0}$
2. Capital Gain: $\frac{P_1 - P_0}{P_0}$

Here:

• $P_0 = 39.51$
• $D_{t+1} = 4.168$
• $P_1 \approx 39.49$

Dividend Yield:

$\text{Dividend Yield} = \frac{D_{t+1}}{P_0} = \frac{4.168}{39.51} \approx 0.1055 \, (10.55\%)$

Capital Gain:

$\text{Capital Gain} = \frac{P_1 - P_0}{P_0} = \frac{39.49 - 39.51}{39.51} \approx -0.00051 \, (-0.051\%)$

Total Return:

$\text{Total Return} = \text{Dividend Yield} + \text{Capital Gain}$

$\text{Total Return} = 0.1055 - 0.00051 \approx 0.1050 \, (10.50\%)$

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Final Answer:

The expected return on the investment if you hold the stock for one year is approximately:

$\boxed{10.50\%}$

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Additional Questions:

1. How does the dividend growth rate impact the expected return?
2. Why is the capital gain negative in this scenario despite the dividend payment?
3. Can the CAPM model be applied to predict returns over a longer time horizon?
4. What assumptions are made in using the dividend growth model?
5. How sensitive is the expected return calculation to changes in the beta or market risk premium?

Tip: When estimating stock returns, always combine both the capital appreciation and dividend components for a complete picture.