Sports Novelties, Inc., has experienced an explosion in demand for its feathered football novelties. The firm currently (time 0) pays a dividend of $0.25 per share. This dividend is expected to increase to $0.75 per share 1 year from now. It is expected to grow at a rate of 15 percent per year for the following 7 years. Coley, a naïve investor, seeks your advice regarding the current value of this stock. Coley plans to purchase this stock today, if the price is right, and to hold it for 3 years. He believes that the stock will increase in value to $30 at the end of 4 years. What is the current value of this stock to Coley if he requires a 20 percent rate of return on stocks of this risk level?
To determine the current value of the stock, we can use the dividend discount model (DDM) and the future value of the stock at the end of 4 years.
Step 1: Calculate the present value of the future dividends:
- The dividend at time 1 is $0.75 per share.
- The dividend at time 2 is $0.75 * (1 + 15%) = $0.8625 per share.
- This continues for the following 7 years, so we need to calculate the present value of each dividend using a discount rate of 20%.
Present value of dividends = [($0.75 / (1 + 0.20))^1] + [($0.8625 / (1 + 0.20))^2] + ... + [($0.75 * (1 + 0.15)^7) / (1 + 0.20)^7]
Step 2: Calculate the future value of the stock at the end of 4 years:
- Coley believes the stock will increase in value to $30 at the end of 4 years.
Future value of stock = $30
Step 3: Calculate the present value of the future stock value at the end of 4 years:
- Since Coley plans to hold the stock for 3 years, we need to calculate the present value of the future stock value using a discount rate of 20%.
Present value of future stock value = $30 / (1 + 0.20)^4
Step 4: Calculate the current value of the stock:
- Add the present value of the future dividends and the present value of the future stock value to get the current value of the stock.
Current value of stock = Present value of dividends + Present value of future stock value
Please note that without specific information about the dividends beyond year 8, we will only calculate the present value for the given time horizon.
Once we calculate these values, we can determine the current value of the stock to Coley.
To calculate the current value of the stock, we can use the dividend discount model (DDM). The DDM values a stock based on the present value of its expected future dividends.
Step 1: Determine the dividends for each year. We know that the dividend will increase from $0.25 per share currently to $0.75 per share in 1 year. After that, it will grow at a rate of 15% per year for the following 7 years.
Year 0 (current): $0.25 per share
Year 1: $0.75 per share
Year 2: $0.75 * (1 + 0.15) = $0.8625 per share
Year 3: $0.8625 * (1 + 0.15) = $0.99188 per share
Year 4: $0.99188 * (1 + 0.15) = $1.14062 per share
Year 5: $1.14062 * (1 + 0.15) = $1.31172 per share
Year 6: $1.31172 * (1 + 0.15) = $1.50948 per share
Year 7: $1.50948 * (1 + 0.15) = $1.74091 per share
Year 8: $1.74091 * (1 + 0.15) = $1.93104 per share
Step 2: Calculate the present value of each dividend using the required rate of return of 20%. We will be discounting each dividend back to the present value for Coley's holding period of 3 years.
Present Value = Dividend / (1 + Required Rate of Return) ^ Number of Years
PV Year 1 = $0.75 / (1 + 0.20) ^ 1 = $0.625
PV Year 2 = $0.8625 / (1 + 0.20) ^ 2 = $0.6131
PV Year 3 = $0.99188 / (1 + 0.20) ^ 3 = $0.5602
Step 3: Calculate the present value of the expected stock price at the end of 4 years. We can use the same formula as in Step 2.
PV Year 4 = $30 / (1 + 0.20) ^ 4 = $19.008
Step 4: Calculate the sum of the present values.
Current Value of the Stock = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4
= $0.625 + $0.6131 + $0.5602 + $19.008
= $20.8063
Therefore, the current value of this stock to Coley, considering his required rate of return of 20%, is approximately $20.81 per share.