Let's lopk at a company that is currently notpaying dividends. You predict that in five years the company will pay a dividend for the first time. The dividend will be \( \$ 0.50 \) per share. You expect the dividend to grow at an \( 8 \% \) rate per year indefinitely at that time. The required return on companies like this one is \( 15 \% \). What is the price of the stock today?

To calculate the price of the stock today, we can use the Gordon Growth Model (also known as the Dividend Discount Model). First, we need to find the expected dividend in year five, which is \( \$0.50 \). As the dividend is expected to grow at an \( 8 \% \) rate indefinitely, we can find the future dividends and then find their present value. First, calculate the expected dividends for years six and beyond: - Year 6: \( D_6 = 0.50 \times (1 + 0.08) = \$0.54 \) - Year 7: \( D_7 = 0.54 \times (1 + 0.08) = \$0.5832 \) And so on. The formula for the dividend in year \( n \) is \( D_n = D_{n-1} \times (1 + g) \). We can calculate the stock price at the end of year five using \( P_5 \): \[ P_5 = \frac{D_6}{r - g} = \frac{\$0.54}{0.15 - 0.08} = \frac{\$0.54}{0.07} = \$7.7143 \] Now, we need to find today’s price \( P_0 \) by discounting \( P_5 \) back to present value: \[ P_0 = \frac{P_5}{(1 + r)^5} = \frac{7.7143}{(1 + 0.15)^5} = \frac{7.7143}{2.011357} \approx \$3.83 \] So, the price of the stock today is approximately **\$3.83**.