Assume that risk free rate is currently 6 percent. The expected return on the average stocks in the market is 12 percent. You are evaluating the prospect of ABC stock which is currently paying Rs 20…

a. Required Rate of Return on ABC Stock

Using the Capital Asset Pricing Model (CAPM): $$r=r_f+\beta (r_m-r_f)$$ where:

• $r_f=6\%$ (risk-free rate),
• $\beta =1.5$ (beta of ABC stock),
• $r_m=12\%$ (expected market return).

Substitute the values: $$r=6\%+1.5(12\%-6\%)=6\%+1.5\times 6\%=6\%+9\%=\text{15\%}$$

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b. Expected Dividends per Share for Next Two Years

Given:

• Current dividend ($D_0$) = Rs 20,
• Growth rate for next 2 years ($g_1,g_2$) = 20%.

Year 1 Dividend ($D_1$):

$$D_1=D_0\times (1+g_1)=20\times 1.20=\text{Rs 24}$$

Year 2 Dividend ($D_2$):

$$D_2=D_1\times (1+g_2)=24\times 1.20=\text{Rs 28.80}$$

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c. Expected Stock Price at the End of Year 2 ($P_2$)

After Year 2, dividends grow at a normal rate ($g_3=5\%$) indefinitely. The stock price at $t=2$ is the present value of future dividends and terminal value: $$P_2=\frac{D_3}{r-g_3}$$ where:

• $D_3=D_2\times (1+g_3)=28.80\times 1.05=\text{Rs 30.24}$,
• $r=15\%$, $g_3=5\%$.

$$P_2=\frac{30.24}{0.15-0.05}=\frac{30.24}{0.10}=\text{Rs 302.40}$$

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d. Intrinsic Value of the Stock Today

The intrinsic value ($P_0$) is the present value of all future cash flows: $$P_0=\frac{D_1}{(1+r)}+\frac{D_2}{(1+r{)}^2}+\frac{P_2}{(1+r{)}^2}$$ Substitute: $$P_0=\frac{24}{1.15}+\frac{28.80}{(1.15{)}^2}+\frac{302.40}{(1.15{)}^2}$$

Calculate each term:

1. $\frac{24}{1.15}=20.87$
2. $\frac{28.80}{1.3225}=21.78$
3. $\frac{302.40}{1.3225}=228.70$

Sum: $$P_0=20.87+21.78+228.70=\text{Rs 271.35}$$

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e. Is the Stock Underpriced or Overpriced?

• Intrinsic value = Rs 271.35,
• Market price = Rs 260.

Since Rs 260 < Rs 271.35, the stock is underpriced.

Recommendation: Yes, the stock should be bought because its market price is below its intrinsic value, indicating potential capital appreciation.

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Key Formulas Used