Question

Consider a firm that has just paid a dividend of $2. An analyst expects dividends to grow at a rate of 8% per year for the next five years. After that, dividends are expected to grow at a normal rate of 5% per year. Assume that the appropriate discount rate is 7%. How much is the intrinsic value of the stock (v0)?

Answer 1

The intrinsic value of the stock can be calculated by discounting the predicted growing dividends to their present value using a two-stage dividend growth model: the first stage covers the first five years of 8% growth and the second stage accounts for the perpetual growth at 5%.

Step-by-step explanation:

To calculate the intrinsic value of the stock (v0), we need to discount the expected future dividends to the present value using the given discount rate. Since the firm has just paid a dividend of $2 and we expect this to grow by 8% for the next five years and then by 5% perpetually thereafter, we use a two-stage dividend growth model to estimate the stock's present value.

The present value (PV) of dividends during the first stage (years 1-5) is calculated using the formula for present value of a growing annuity. For the second stage (from year 6 onwards), we calculate the perpetual growth using the Gordon Growth Model (also known as a dividend discount model). Finally, we sum these present values to get the intrinsic value of the stock.