To calculate the value of the stock using the Gordon Growth Model (Dividend Discount Model), the formula is:

$P = \frac{D_1}{r - g}$

Where:

• $P$ = Price (value) of the stock
• $D_1$ = Dividend next year
• $r$ = Required rate of return
• $g$ = Growth rate of dividends

Step 1: Compute $D_1$

The dividend next year ($D_1$) is calculated as: $D_1 = D_0 \times (1 + g)$

Given:

• $D_0 = 1.41$
• $g = 5.10\% = 0.051$

$D_1 = 1.41 \times (1 + 0.051) = 1.41 \times 1.051 = 1.48271$

Step 2: Calculate the Stock Value ($P$)

Using the formula: $P = \frac{D_1}{r - g}$

Given:

• $r = 7.40\% = 0.074$
• $g = 5.10\% = 0.051$

$P = \frac{1.48271}{0.074 - 0.051} = \frac{1.48271}{0.023} = 64.47$

Final Answer for Part a:

The value of the stock is: $P = \mathbf{\$64.47}$

Part b: Should you make the investment?

Compare the calculated stock value ($P = 64.47$) with the current market price:

• If the current market price is less than $64.47, the stock is undervalued, and you should invest.
• If the current market price is greater than $64.47, the stock is overvalued, and you should not invest.

Let me know if you'd like clarification on any steps or assistance with related calculations!

Related Questions:

1. What if the growth rate ($g$) were different? How would it affect the stock's value?
2. How would a change in the required rate of return ($r$) impact the stock value?
3. How can external market conditions affect the growth rate of dividends ($g$)?
4. What factors determine a realistic required rate of return ($r$) for investors?
5. How does the model adjust if dividends are expected to grow non-constantly?

Tip:

The Gordon Growth Model assumes constant growth. For stocks with varying growth rates, consider using a multi-stage dividend discount model for more accuracy.