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Tattletale News Corporation has been growing at a rate of $20 \%$ per year, and you expect this growth rate in earnings and dividends to continue for another three years.


AIf the last dividend paid was \$6, what will the next dividend be?
BIf the discount rate is 23\% and the steady growth rate after three years is 3\%, what should the stock price be today?



Note: For all requirements, do not round intermediate calculations. Round your answer to 2 decimal places.



a. Dividend

b. Stock price

Verified Answer :

  • The dividend for the next year (\(D_1\)) is calculated as \(D_0 \times (1 + g_1) = 6 \times 1.20 = \boxed{\$7.20}\).
  • Future dividends \(D_2\) and \(D_3\) are determined to be \(\$8.64\) and \(\$10.368\), respectively.
  • The terminal price at the end of year 3 (\(P_3\)) is found using the Gordon Growth Model: \(P_3 = \frac{D_3 \times (1 + g_2)}{r - g_2} = \boxed{\$53.40}\).
  • The stock price today is the sum of the present values of dividends (\(D_1, D_2, D_3\)) and the present value of the terminal price, resulting in \(\boxed{\$45.83}\).

Explanation

  1. Problem Analysis

To determine the next dividend and the current stock price of Tattletale News Corporation, we begin by analyzing the provided data. The company paid a last dividend of \(D_0 = \$6\). It is expected to grow at a rate of \(g_1 = 20\%\) (or \(0.20\)) for the next three years. After these three years, the company will reach a steady growth rate of \(g_2 = 3\%\) (or \(0.03\)) indefinitely. The required discount rate is \(r = 23\%\) (or \(0.23\)). To calculate the current stock price, we need to find the dividends for years 1, 2, and 3, and then determine the terminal value at the end of year 3.

  1. Calculating the Next Dividend

First, we calculate the dividend for next year (\(D_1\)):
\[D_1 = D_0 \times (1 + g_1) = 6 \times (1 + 0.20) = \$7.20\]
The next dividend, \(D_1\), is \(\$7.20\).

  1. Calculating Dividends and Terminal Value

Next, we calculate the dividends for years 2 and 3 using the growth rate \(g_1\):
\[D_2 = D_1 \times (1 + g_1) = 7.20 \times 1.20 = \$8.64\]
\[D_3 = D_2 \times (1 + g_1) = 8.64 \times 1.20 = \$10.368\]
To find the terminal value at the end of year 3, we first calculate the dividend for year 4 (\(D_4\)) using the steady growth rate \(g_2\):
\[D_4 = D_3 \times (1 + g_2) = 10.368 \times (1 + 0.03) = 10.67904\]
Now, we calculate the terminal price at the end of year 3 (\(P_3\)) using the Gordon Growth Model:
\[P_3 = \frac{D_4}{r - g_2} = \frac{10.67904}{0.23 - 0.03} = \frac{10.67904}{0.20} = 53.3952\]

  1. Calculating the Stock Price Today

Finally, we find the present value of the stock today (\(P_0\)) by discounting the cash flows (dividends for years 1, 2, 3 and the terminal price at year 3) to the present using the discount rate \(r = 0.23\):
\[PV(D_1) = \frac{7.20}{(1.23)^1} \approx 5.8537\]
\[PV(D_2) = \frac{8.64}{(1.23)^2} \approx 5.7109\]
\[PV(D_3) = \frac{10.368}{(1.23)^3} \approx 5.5716\]
\[PV(P_3) = \frac{53.3952}{(1.23)^3} \approx 28.6937\]
Summing these present values:
\[P_0 = 5.8537 + 5.7109 + 5.5716 + 28.6937 = 45.8299\]
Rounding the final stock price to two decimal places, we get \(\$45.83\). The next dividend is \(\$7.20\).

Examples

Financial models like the one used here are essential for investors trying to determine the fair value of a company's stock. By forecasting future dividend growth and discounting those payments to today's value, investors can make informed decisions about whether a stock is overvalued or undervalued. This methodology, known as the Dividend Discount Model, is a cornerstone of fundamental analysis and helps in allocating capital efficiently in the stock market.

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