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 terminal value of the stock in year 5 (V5)?

Answer 1

The terminal value of the stock in year 5 (V5) is calculated by using the formula TV = D5 * (1 + g) / (r - g), where D5 is the dividend at year 5, g is the long-term growth rate, and r is the discount rate. First, find the dividend in year 5 by compounding the initial $2 dividend by the 8% growth rate, and then use this in the terminal value formula with a growth rate of 5% and a discount rate of 7%.

Step-by-step explanation:

To calculate the terminal value of the stock in year 5 (V5), we need to consider the dividend growth rates and the discount rate. Since the dividends are expected to grow at a rate of 8% per year for the first five years and then at a normal rate of 5% per year thereafter, the terminal value at the end of year 5 can be found by calculating the present value of all future dividends from year 6 onwards, discounted back to year 5. The formula for calculating the terminal value (TV) at the end of year 5 is: TV = D5 * (1 + g) / (r - g)

Where D5 is the dividend in year 5, g is the growth rate from year 6 onwards (5%), and r is the discount rate (7%). First, we find D5, which is the dividend in year 5: D5 = D0 * (1 + g)^5

So, D5 = $2 * (1 + 0.08)^5. We then use D5 in the terminal value formula: TV = (D5 * 1.05) / (0.07 - 0.05)

After calculating D5, you plug the value into the TV formula to find the terminal value at the end of year 5.