Storico Co. just paid a dividend of $1.60 per share. The company will increase i

Question

Storico Co. just paid a dividend of $1.60 per share. The company will increase its dividend by 20 percent next year and will then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend growth, after which the company will keep a constant growth rate forever. If the stock price is $34.08, what required return must investors be demanding on Storico stock? (Hint: Set up the valuation formula with all the relevant cash flows, and use trial and error to find the unknown rate of return.) (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Storico Co. just paid a dividend of $1.60 per share. The company will increase its dividend by 20 percent next year and will then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend growth, after which the company will keep a constant growth rate forever. If the stock price is $34.08, what required return must investors be demanding on Storico stock? (Hint: Set up the valuation formula with all the relevant cash flows, and use trial and error to find the unknown rate of return.) (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation / Answer

Here we have a stock with supernormal growth but the dividend growth changes every year for the first four years. We can find the price of the stock in Year 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4, divided by the required return minus the constant dividend growth rate. So, the price in Year 3 will be

P3 = $1.6 (1.20)(1.15)(1.10)(1.05) / (k – .05)

The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Year 3, therefore

$ 34.08 = $1.6(1.20)/(1+k) + $1.6(1.20)(1.15)/(1 +k)2 + $1.6(1.20)(1.15)(1.10)/(1+k)3 + {$1.6(1.20) (1.15) 91.10) (1.05) / (k - .05)}/(1+k)3

Suppose required rate of return is 10%

P3 = $51.0048

And

Stock price =1.75 + 1.82 +1.82 + 38.32 = $ 43.71 (not true)

Let’s assume another number required rate = 15%

Then

P3 = $ 25.50

And

Stock price = 1.67 + 1.67 + 1.6 +16 .77 = $ 21.77 (this is also not true)

Required rate of return is somewhere between 10% to 15% as the price at 10% is more than actual and price at 15% is less than actual

By trial and error it is coming approx 12.8%

So required rate of return is 12.8%

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