Big Time Cell Phone Corporation just announced a cut in their annual dividend from $3.10 to $2.13 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 $15.59. After the announcement, the expectation is that dividends will now grow at a 3.60% rate.

Answer 1

To analyze the situation and the impact of the dividend cut and growth rate adjustment for Big Time Cell Phone Corporation, we can calculate the new expected price of the stock based on the Gordon Growth Model (also known as the Dividend Discount Model).

1. Calculate the expected dividend for Year 1:

Given that the new dividend is $2.13 per share.

2. Calculate the expected dividend for Year 2:

The new expected growth rate is 3.60%.

\[ \text{Year 2 Dividend} = \text{Year 1 Dividend} \times (1 + \text{Growth Rate}) \]

\[ \text{Year 2 Dividend} = 2.13 \times (1 + 0.036) = 2.13 \times 1.036 = 2.20768 \]

3. Calculate the expected dividend for Year 3:

Using the Year 2 dividend as a base:

\[ \text{Year 3 Dividend} = \text{Year 2 Dividend} \times (1 + \text{Growth Rate}) \]

\[ \text{Year 3 Dividend} = 2.20768 \times (1 + 0.036) = 2.20768 \times 1.036 = 2.28163 \]

4. Calculate the price of the stock using Gordon Growth Model:

The formula for the Gordon Growth Model is:

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

Where:

• \(P_0\) = Price of the stock today
• \(D_1\) = Dividend expected next year (which is $2.13 for Year 1)
• \(r\) = Required rate of return
• \(g\) = Growth rate of dividends (3.60%)

Since we need the required rate of return, we will estimate it using the previous pricing and growth assumption. Let's assume the original growth rate of 2.50% and the original price of $15.59:

\[ 15.59 = \frac{3.10}{r - 0.025} \]

Rearranging gives us:

\[ r - 0.025 = \frac{3.10}{15.59} \] \[ r - 0.025 \approx 0.198 \] \[ r \approx 0.2 + 0.025 = 0.225 = 22.5% \]

5. Using the new growth rate to find the new stock price:

Now we can use the required return (\(0.225\)) and new growth rate (\(0.036\)) in the Gordon Growth Model:

\[ P_0 = \frac{2.13}{0.225 - 0.036} \]

Calculating the denominator:

\[ 0.225 - 0.036 = 0.189 \]

Calculating the stock price:

\[ P_0 = \frac{2.13}{0.189} \approx 11.27 \]

Conclusion:

Based on the new dividend and the expected growth rate, the estimated price of Big Time Cell Phone Corporation stock is approximately $11.27. This is a decrease from its previous price of $15.59 following the dividend cut and revised growth expectations.

Answer 2

What is the new price of the stock after the announcement?

Answer 3

To find the new price of the stock after the announcement of the dividend cut and the adjustment in the growth rate, we can use the Gordon Growth Model (Dividend Discount Model).

Relevant Information:

• New Dividend (D1): $2.13 (the announced annual dividend)
• Growth Rate (g): 3.60% or 0.036
• Estimated Required Rate of Return (r): We can estimate this as approximately 9.5% based on prior performance if necessary, but for this calculation, we'll use the previously determined rate of return from the stock's current price before the announcement.

Calculating the Required Rate of Return (r):

Using the previous stock price and dividend yield:

1. Previous Dividend (D0): $3.10 (old dividend)
2. Previous Price: $15.59

Using the previously suggested \(r\):

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

Here, the original model gives us an approximate required rate of return (\(r\)). But since we have a new dividend and new growth rate, we can estimate \(r\) again based on the previous market price of $15.59 and old growth.

Deriving \(r\) from the original price:

1. We already derived an approximate \(r\) of 22.5% for the old conditions (if we still consider the higher growth potential previously assumed).

Now we will still use this method to find \(r\) because the market conditions can fluctuate. However, since we want a stable price,

To simply calculate the new price based on a previously estimated rate close to common market rates, let's use 9.5% or more accurately assume a reasonable rate (or our previous \(r\) found before).

Assuming \(r ≈ 9.5%\):

Using the Gordon Growth Model:

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

Substituting the values into the formula:

\[ P_0 = \frac{2.13}{0.095 - 0.036} \] Calculating the denominator: \[ 0.095 - 0.036 = 0.059 \]

Then, calculating the price: \[ P_0 = \frac{2.13}{0.059} \approx 36.14 \]

Final Result:

Thus, the new price of the stock after the dividend cut and the announcement of the revised growth expectations is approximately $36.14. This reflects the expectations of future cash flows from the adjusted dividend trajectory.

If further adjustments or a more precise rate of return (which could be derived from market conditions) was needed, the real market behaviors may influence the stock's trading price accordingly. The market often significantly reacts to such an announcement, and investor sentiment can sway the actual trading price.