Question

Connect Only Problem 8-16 Variable Growth (LG8-6) A fast-growing firm recently paid a dividend of $0.70 per share. The dividend is expected to increase at a 30 percent rate for the next four years. Afterwards, a more stable 11 percent growth rate can be assumed. If a 12.5 percent discount rate is appropriate for this stock, what is its value? Note: Do not round intermediate calculations. Round your answer to 2 decimal places.

Answer 1

The value of the stock can be calculated using the dividend growth model. The present value of each expected dividend is calculated and then summed up to get the total value of the stock. The final value is approximately $31.594.

Step-by-step explanation:

The value of the stock can be calculated using the dividend growth model. First, we need to calculate the present value of each dividend received at different time periods.

Using the formula for the present value of a dividend, the present value of the expected dividends for the next four years can be calculated as follows:

1. Year 1: $0.70 / (1 + 0.125)^1 = $0.623
2. Year 2: $0.70 * (1 + 0.30) / (1 + 0.125)^2 = $0.874
3. Year 3: $0.70 * (1 + 0.30)^2 / (1 + 0.125)^3 = $1.222
4. Year 4: $0.70 * (1 + 0.30)^3 / (1 + 0.125)^4 = $1.706

Then, we need to calculate the present value of the dividends beyond the fourth year using the stable growth rate:

Year 5 onwards: $1.706 * (1 + 0.11)^1 / (0.125 - 0.11) = $27.169

Finally, we can sum up the present values of all the dividends to get the total value of the stock: $0.623 + $0.874 + $1.222 + $1.706 + $27.169 = $31.594

Therefore, using the dividend growth model, the value of the stock is approximately $31.594.