Question

Storico Co. just paid a dividend of $3.15 per share. The company will increase its dividend by 20 percent next year and 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 $54.50, what required return must investors be demanding on the company's 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.)

Answer 1

Dividend Next year = 3.15*(1+20%) = 3.78
Dividend in  year 2 = 3.15*(1+20%)*(1+15%) = 4.347
Dividend in year 3 =   3.15*(1+20%)*(1+15%)*(1+10%) = 4.7817
Dividend in year 4 = 3.15*(1+20%)*(1+15%)*(1+10%)*(1+5%) = 5.020785
Price = Dividend 1/(1+r) + Dividend 2/(1+r)² + Dividend 3/(1+r)³ + Dividend 4/((r-g)*(1+r)³ )

54.50 = 3.78/(1+r) + 4.347/(1+r)² + 4.7817/(1+r)³ + 5.020785/((r-5%)*(1+r)³)

By placing r = 10% we get price = 86.07
By placing r = 11% we get price = 71.62
By placing r = 12% we get price = 61.30
By placing r = 13% we get price = 53.36

So r lies between 12% and 13%
By placing r = 12.9% we get price = 54.24
By placing r = 12.864% or 12.86% we get price = 54.50 exactly

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