JRN enterprises just announced that it plans to cut its dividend from $2.5 to $1.50 per share and use the extra funds to expand its operations. Prior to this announcement, JRN’s dividends were expected to grow at 4% per year and JRNs stock was trading at $25.00 per share. With the new expansion, JRNs dividends are expected to grow at 8% per year indefinitel. Assuming that JRNs risk is unchanged by the expansion, the value of a share of JRN after the announcement is closest to: 
A $25.00 
B $31.25
C $27.50 
D $15.00

To determine the new value of a share of JRN Enterprises after the dividend cut and the change in the growth rate, we can use the Gordon Growth Model (also known as the Dividend Discount Model):

\[
P = \frac{D_1}{r - g}
\]

Where:
- $ P $ = Price of the stock
- $ D_1 $ = Dividend in the next period
- $ r $ = Required rate of return
- $ g $ = Growth rate of dividends

### Step 1: Calculate the required rate of return ($r$) before the announcement
Before the announcement:
- Dividend $D_0$ = $2.50
- Growth rate $g$ = 4% = 0.04
- Stock price $P_0$ = $25.00

The required rate of return is calculated as:

\[
P_0 = \frac{D_0 \times (1 + g)}{r - g}
\]

\[
25.00 = \frac{2.50 \times (1 + 0.04)}{r - 0.04}
\]

\[
25.00 = \frac{2.60}{r - 0.04}
\]

\[
r - 0.04 = \frac{2.60}{25.00}
\]

\[
r - 0.04 = 0.104
\]

\[
r = 0.144 = 14.4\%
\]

### Step 2: Calculate the new stock price after the announcement
After the announcement:
- New Dividend $D_1$ = $1.50
- New Growth rate $g$ = 8% = 0.08
- The required rate of return $r$ remains the same at 14.4% = 0.144

Now, using the Gordon Growth Model again:

\[
P = \frac{1.50}{0.144 - 0.08}
\]

\[
P = \frac{1.50}{0.064}
\]

\[
P = 23.4375
\]

This price does not directly match any of the provided options. However, the closest option to this calculated price is **D) $15.00**.

Given the discrepancy, it might be worth rechecking the input values or considering other factors such as potential changes in market perception or additional impacts of the dividend cut that could affect the stock price beyond the straightforward application of the Dividend Discount Model. 

Would you like further clarification on this or any other related concepts?

**Related Questions:**
1. What are the assumptions underlying the Gordon Growth Model?
2. How would a change in the required rate of return affect the stock price?
3. What could be the reasons for a discrepancy between calculated stock value and actual market price?
4. How do investors typically react to dividend cuts in the stock market?
5. How can changes in growth expectations impact a company's stock price?

**Tip:** When applying the Dividend Discount Model, it's essential to ensure that the growth rate is less than the required rate of return, otherwise the model might not be valid.

Learn how to calculate the new stock value of JRN Enterprises after a dividend cut and expansion using the Dividend Discount Model. Given initial dividend, growth rate, and stock price, understand the impact of financial decisions on stock valuation.

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