1. Simpkins Corporation does not pay any dividends because it is expanding rapidly and needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends, with the first dividend of $0.50 coming 3 years from today. The dividend should grow rapidly—at a rate of 80% per year—during Years 4 and 5. After Year 5, the company should grow at a constant rate of 7% per year. If the required return on the stock is 16%, what is the value of the stock today? (Assume the market is in equilibrium with the required return equal to the expected return.)
2. Several years ago, Rolen Riders issued preferred stock with a stated annual dividend of 10% of its $100 par value. Preferred stock of this type currently yields 8%. Assume dividends are paid annually.
To determine the value of Simpkins Corporation’s stock today, we can use the dividend discount model (DDM) under the assumption that the stock will eventually start paying dividends. Given the information provided, we can break down the problem into several steps:
Step 1: Calculate the dividends for Years 4 and 5, taking into account the rapid growth rate of 80% per year:
Year 4 Dividend = $0.50 * (1 + 0.80) = $0.90
Year 5 Dividend = $0.90 * (1 + 0.80) = $1.62
Step 2: Calculate the dividends after Year 5, assuming a constant growth rate of 7%:
Year 6 Dividend = $1.62 * (1 + 0.07) = $1.74
Year 7 Dividend = $1.74 * (1 + 0.07) = $1.86
And so on…
Step 3: Calculate the present value of these future dividends using the required return of 16%. We will discount each year’s dividend back to present value.
Step 4: Calculate the present value of the first dividend of $0.50 received in Year 3.
Step 5: Sum the present values of all future dividends and the first dividend to find the total value of the stock today.
Now, let’s do the calculations:
Year 3 Dividend (First Dividend) = $0.50 / (1 + 0.16)^3 ≈ $0.344
Year 4 Dividend = $0.90 / (1 + 0.16)^4 ≈ $0.587
Year 5 Dividend = $1.62 / (1 + 0.16)^5 ≈ $0.896
To calculate the present value of dividends beyond Year 5 with the constant growth rate of 7%, we can use the Gordon Growth Model:
Year 6 Dividend = $1.62 * (1 + 0.07) / (0.16 – 0.07) ≈ $17.82
Year 7 Dividend = $1.74 * (1 + 0.07) / (0.16 – 0.07) ≈ $19.74
And so on…
Now, calculate the present values of these dividends back to today using the 16% required return. Once you have the present values for all future dividends, add them to the present value of the first dividend:
Stock Value = $0.344 + $0.587 + $0.896 + $17.82 + $19.74 + …
You would continue this pattern for all future years, but since the dividends are growing indefinitely at a constant rate, you can use the Gordon Growth Model formula to calculate the infinite series:
Stock Value = D1 / (r – g),
where:
Stock Value = $17.82 / (0.16 – 0.07) ≈ $198.00
So, the estimated value of Simpkins Corporation’s stock today is approximately $198.00.
To estimate the value of Rolen Riders’ preferred stock, we can use the dividend discount model (DDM) since preferred stock pays fixed dividends.
Step 1: Calculate the annual dividend payment. The stated annual dividend rate is 10% of the $100 par value, which means a dividend of $10 per share.
Step 2: Use the current yield of 8% to estimate the value of the preferred stock. The formula for the estimated value of preferred stock is:
Preferred Stock Value = Dividend / Yield
Preferred Stock Value = $10 / 0.08 ≈ $125.00
So, the estimated value of Rolen Riders’ preferred stock when the yield is 8% is approximately $125.00.
Now, let’s consider the scenario where interest rates have risen, and the preferred stock now yields 12%.
Step 3: Recalculate the estimated value of the preferred stock using the new yield of 12%:
Preferred Stock Value (New Yield) = $10 / 0.12 ≈ $83.33
So, if interest rates rise to the point where the preferred stock yields 12%, the new estimated value of Rolen Riders’ preferred stock would be approximately $83.33.
In summary, the estimated value of Rolen Riders’ preferred stock depends on the prevailing yield. When the yield is 8%, the value is $125.00, but if the yield increases to 12%, the value decreases to $83.33. This illustrates how changes in interest rates can impact the valuation of preferred stock.
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