Storico Co. just paid a dividend of $2.05 per share. The company will increase i
ID: 2644184 • Letter: S
Question
Storico Co. just paid a dividend of $2.05 per share. The company will increase its dividend by 24 percent next year and will then reduce its dividend growth rate by 6 percentage points per year until it reaches the industry average of 6 percent dividend growth, after which the company will keep a constant growth rate forever. If the required return on Storico stock is 10 percent, what will a share of stock sell for today? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Storico Co. just paid a dividend of $2.05 per share. The company will increase its dividend by 24 percent next year and will then reduce its dividend growth rate by 6 percentage points per year until it reaches the industry average of 6 percent dividend growth, after which the company will keep a constant growth rate forever. If the required return on Storico stock is 10 percent, what will a share of stock sell for today? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Explanation / Answer
Step 1: Calculate the Dividend for Each Year:
Since, the growth rate of dividend, will keep reducing by 6% every year till it matches the industry average growth rate. The growth rate for year 1 = 24%, for year 2 = 24% - 6% = 18%, for year 3 = 18% - 6% = 12% and for year 4 = 12% - 6% = 6%
Dividend for respective years will be calculated with the use of these growth rates.
Dividend for Year 1 = Current Dividend*(1+Growth Rate for Year 1) = 2.05*(1+24%)
Dividend for Year 2 = Current Dividend*(1+Growth Rate for Year 1)*(1+Growth Rate for Year 2) = 2.05*(1+24%)*(1+18%)
Dividend for Year 3 = Current Dividend*(1+Growth Rate for Year 1)*(1+Growth Rate for Year 2)*(1+Growth Rate for Year 3) = 2.05*(1+24%)*(1+18%)*(1+12%)
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Step 2: Calculate the Price for 3rd Year:
After 3rd year, the company will maintain a constant dividend growth rate of 6%. Here, we will use the dividend growth model to calculate the stock price. The formula would be
Stock Price (P3) = D4/(ke - g) where D4 is the dividend for Year 4, ke is the required rate of return and g is the constant growth rate.
Here D4 is 2.05*(1+24%)*(1+18%)*(1+12%)*(1+6%), ke = 10% and g = 6%
Using these values in the above formula be we get.
Stock Price (P3) = 2.05*(1+24%)*(1+18%)*(1+12%)*(1+6%)/(10%-6%) = $89.03
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Step 2: Calculate the Stock Price Today:
The current stock price will be calculated by discounting the dividend and price for 3rd year to today's value with the use of required rate of return of 10%. The formula would be:
Current Stock Price = D1/(1+Discount Rate)^1 + D2/(1+Discount Rate)^2 + D2/(1+Discount Rate)^3 + P3/(1+Discount Rate)^3
Using the values calculated in step 1 and step 2, we get,
Current Stock Price = 2.05*(1+24%)/(1+10%)^1 + 2.05*(1+24%)*(1+18%)/(1+10%)^2 + 2.05*(1+24%)*(1+18%)*(1+12%)/(1+10%)^3 + 89.03/(1+10%)^3 = $74.20