Question

The ABX News Co. paid the last dividend of $1/share and the dividend is expected to grow at a rate of 20% over the next three years. It will then grow at a normal constant rate of 5% for the future. The rate of return is 12%. What should the stock price be today?

Answer 1

The last dividend was $1.

Next year's dividend will be 20% more. So $1 + 20% of $1

= $1.2 (This will be after end of year 1)

End of year 2 it will grow by another 20%. So $1.2 + 20% of $1.2

= $1.44 (This is after end of year 2)

End of 3rd year it will grow by another 20%. So $1.44 + 20% of $1.44

= $1.728

After 3rd year the dividend will grow at a constant rate of 5%.

When dividend grows at a constant rate, then we apply the constant dividend growth model to find the IIntrinsic value of the share.

Formula: Dividend in the next period / (Rate of Return - Growth)

Dividend in the next period means the 4th year. So the dividend will grow by 5%.

= (1.728) + 5% of 1.728

= 1.8144

Intrinsic value of the stock at the end of year 3 using Constant dividend growth model

= 1.8144 / (0.12 - 0.05)

= 1.8144 / 0.07

$25.92

Now we need to do present value of expected dividends and Intrinsic value that we found at the end of year 3.

We are discounting using the discount rate of 12%.

Intrinsiv value of stock now = Present value of dividend after year 1 + Present value of dividend after year 2 + (Present value of dividend after year 3 + Present Value of Intrinsic Value)

= 1.2 / 1.12 + 1.44 / (1.12)^2 + (1.728 + 25.92) / (1.12)^3

= 1.0714 + 1.1479 + 19.6793

= 21.8986

So the stock price today should be $21.8986