Part (a): Calculate the intrinsic value of ABC Corporation's stock using the Dividend Discount Model (DDM).

The Dividend Discount Model (DDM) is used to calculate the intrinsic value of a stock based on the present value of expected future dividends. The formula for the DDM, assuming dividends grow at a constant rate (Gordon Growth Model), is:

$\text{Intrinsic Value} = \frac{D_1}{r - g}$

Where:

• $D_1$ is the dividend expected in the next year.
• $r$ is the required rate of return.
• $g$ is the growth rate of the dividend.

Given:

• Annual dividend, $D_0 = 3$ (current dividend).
• Dividend growth rate, $g = 4\% = 0.04$.
• Required rate of return, $r = 8\% = 0.08$.

First, calculate $D_1$:

$D_1 = D_0 \times (1 + g) = 3 \times (1 + 0.04) = 3 \times 1.04 = 3.12$

Now, use the DDM formula to find the intrinsic value:

$\text{Intrinsic Value} = \frac{3.12}{0.08 - 0.04} = \frac{3.12}{0.04} = 78$

Part (b): Determine whether the stock is overvalued, undervalued, or fairly valued.

The intrinsic value calculated is $78. The current stock price is $75.

• If the intrinsic value > current stock price, the stock is undervalued.
• If the intrinsic value < current stock price, the stock is overvalued.
• If the intrinsic value = current stock price, the stock is fairly valued.

Since $78 > $75, the stock is undervalued.

Part (c): Recalculate the intrinsic value if the dividend growth rate increases to 5%.

Now, the new growth rate $g$ is 5% or 0.05. Recalculate $D_1$:

$D_1 = D_0 \times (1 + g) = 3 \times (1 + 0.05) = 3 \times 1.05 = 3.15$

Using the DDM formula with the new growth rate:

$\text{Intrinsic Value} = \frac{3.15}{0.08 - 0.05} = \frac{3.15}{0.03} = 105$

Effect on Valuation

With the increased growth rate, the intrinsic value of the stock rises to $105. Compared to the current price of $75, the stock becomes even more undervalued.

Summary

1. Intrinsic Value with 4% growth: $78 (Stock is undervalued).
2. Intrinsic Value with 5% growth: $105 (Stock is even more undervalued).

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Would you like further details on any of the steps or concepts involved?

Related Questions:

1. How does the required rate of return affect the intrinsic value in the DDM model?
2. What assumptions are critical for the Dividend Discount Model to be accurate?
3. How would the intrinsic value change if the required rate of return increased?
4. What happens to the stock valuation if the dividend growth rate is less than the required rate of return?
5. Can the Dividend Discount Model be applied to companies with no dividend payments?
6. How does inflation impact the required rate of return?
7. What are alternative methods to DDM for stock valuation?
8. How would changes in market conditions impact the required rate of return?

Tip:

When using the Dividend Discount Model, it's important to ensure that the dividend growth rate is realistic and sustainable over the long term, as this has a significant impact on the calculated intrinsic value.