Staton-Smith Software is a new start-up company and will not pay dividends for the first five years of operation. It will then institute an annual cash dividend policy of $4.00
with a constant growth rate of 3%, with the first dividend at the end of year six. The company will be in business for 25 years total. What is the stock’s price if an investor wants
a. a return of 10%?
b. a return of 15%?
c. a return of 22%?
d. a return of 35%?
Calculating the stock’s price under different required returns involves using the dividend discount model (DDM). In this case, we have a company, Staton-Smith Software, which is not paying dividends for the first five years and then starts paying a constant growth dividend. Here’s how you can calculate the stock’s price for the given required returns:
a. Required Return of 10%:
To calculate the stock price at a 10% required return, we will first determine the dividends for years 6 to 25 using the constant growth rate formula:
D6 = D5 * (1 + growth rate) = $4.00 * (1 + 3%) = $4.12
Now, we can use the Gordon Growth Model to calculate the present value of these future dividends:
P6 = D6 / (required return – growth rate) = $4.12 / (10% – 3%) = $68.67
Since this is the price at the end of year 5, we need to discount it back to year 0:
P0 = P6 / (1 + required return)^5 = $68.67 / (1 + 10%)^5 = $41.34
So, at a 10% required return, the stock’s price is approximately $41.34.
b. Required Return of 15%:
Following the same method as above:
D6 = $4.00 * (1 + 3%) = $4.12
P6 = $4.12 / (15% – 3%) = $34.33
P0 = $34.33 / (1 + 15%)^5 = $18.22
At a 15% required return, the stock’s price is approximately $18.22.
c. Required Return of 22%:
Using the same approach:
D6 = $4.00 * (1 + 3%) = $4.12
P6 = $4.12 / (22% – 3%) = $24.94
P0 = $24.94 / (1 + 22%)^5 = $10.29
At a 22% required return, the stock’s price is approximately $10.29.
d. Required Return of 35%:
Similarly:
D6 = $4.00 * (1 + 3%) = $4.12
P6 = $4.12 / (35% – 3%) = $14.34
P0 = $14.34 / (1 + 35%)^5 = $4.18
At a 35% required return, the stock’s price is approximately $4.18.
In summary, the stock’s price varies significantly depending on the required return. It is highest when the required return is lowest (10%) and decreases as the required return increases. This sensitivity to the required return reflects the risk associated with the investment, with higher required returns indicating greater perceived risk and thus a lower stock price. Investors should consider their own risk tolerance and return expectations when valuing and investing in stocks.
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