Big Time Cell Phone Corporation just announced a cut in their annual dividend from $3.11 to $2.23 per share (year 1 dividend). Big Time has announced the investment in a new indestructible smart phone. Prior to this announcement, analysts believe dividends would grow at 2.50% into the foreseeable future, and the stock was priced at $17.72. After the announcement, the expectation is that dividends will now grow at a 3.65% rate.

Answer 1

To analyze the situation with Big Time Cell Phone Corporation's dividend cut and the new growth expectations, we can begin by determining the fair value of the stock using the Gordon Growth Model (dividend discount model), which is given by the formula:

\[ P_0 = \frac{D_1}{r - g} \]

Where:

• \( P_0 \) = price of the stock today
• \( D_1 \) = dividend next year
• \( r \) = required rate of return
• \( g \) = growth rate of dividends

Step 1: Identify the Variables

• The new dividend announced, \( D_1 \), is $2.23.
• After the announcement, the expected growth rate \( g \) is 3.65%.

Step 2: Estimate Required Rate of Return \( r \)

Before we can calculate the new stock price, we need the required rate of return. Since the stock was priced at $17.72 with a dividend of $3.11 and a growth rate of 2.5%, we can back-calculate \( r \) using the old situation:

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

Where \( D_0 \) is the previous dividend, which is $3.11.

Using the previous values:

• \( g = 0.025 \) (2.5%)
• \( P_0 = 17.72 \)

Substituting the known values:

\[ 17.72 = \frac{3.11(1 + 0.025)}{r - 0.025} \]

Calculating \( D_1 \):

\[ D_1 = 3.11 \times 1.025 = 3.18 \]

Now set up the equation:

\[ 17.72 = \frac{3.18}{r - 0.025} \]

Cross-multiplying gives:

\[ 17.72(r - 0.025) = 3.18 \]

Distributing:

\[ 17.72r - 0.443 = 3.18 \]

Adding 0.443 to both sides:

\[ 17.72r = 3.623 \]

Dividing by 17.72:

\[ r = \frac{3.623}{17.72} \approx 0.204 (or \approx 20.4%) \]

Step 3: Calculate the New Stock Price

Now that we have \( r \approx 0.204 \) and the new dividend \( D_1 = 2.23 \) with the growth rate \( g = 0.0365 \):

\[ P_0 = \frac{2.23}{0.204 - 0.0365} \]

Calculating the denominator:

\[ r - g = 0.204 - 0.0365 = 0.1675 \]

Now substitute into the price formula:

\[ P_0 = \frac{2.23}{0.1675} \approx 13.30 \]

Conclusion

Given the new expected growth rate and the dividend cut, the calculated fair value of Big Time Cell Phone Corporation's stock is approximately $13.30. This suggests the stock may have been overvalued at $17.72 prior to the announcement of the dividend cut.