Storico Co. just paid a dividend of $2.20 per share. The company will increase i

Question

Storico Co. just paid a dividend of $2.20 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 $42.75, 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.)

Storico Co. just paid a dividend of $2.20 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 $42.75, 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.)

Explanation / Answer

Required Rate of Return =

Year dividend Growth rate 20% 5% reduction

0 2.20 - -

1 2.64 2.20*20% = 2.64 -

2 3.036 2.64*20% = 3.168 2.64*5% = 0.132

Dividend for the Year 2 = 3.168 - 0.132 = 3.036

3 3.4914 3.036*20% = 3.6432 3.036*5%= 0.1518

Dividend for the year 3 = 3.6432-0.1518 = 3.4914

formula = Stock Price = Present value of future dividend payment.

It is calculated using the Net Present Value formula as,

Summation of Co/(1+r)n + Constant dividend* reduction in growth rate/ (1+r)n

Co = Dividend payment , R= Required rate of return, n = Number of Years

Using 12% as required rate of return =

42.75 = 2.64/(1.12)1 +3.036/(1.12)2 +3.4914/(1.12)3 + (3.491*1.05/(0.12-0.05))/(1.12)3

  =45.55576

Using 13% as required rate of return =

42.75 = 2.64/(1.13)1 +3.036/(1.13)2 +3.4914/(1.13)3 + (3.491*1.05/(0.13-0.05))/(1.13)3

= 38.8924

Using Interpolation method, calculate the exact Required rate of return

R= 12+(45.55576 - 42.75)/(45.55576 - 38.8924) = 12.42107 = 12.42107

Checking the answer

42.75 = 2.64/(1.1242)1 +3.036/(1.1242)2 +3.4914/(1.1242)3 + (3.491*1.05/(0.1242-0.05))/(1.1242)3

= 42.01 approximately 42.75

The required rate of return = 12.42

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