Question

Storico Co. just paid a dividend of $1.75 per share. The company will increase its dividend by 24 percent next year and 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 stock price is $44.96, 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.)

Answer 1

Growth rate for first year will be 24% and it will reduce by 6% every year. It means, growth rate in year 1 , 2, 3, 4 will be 24% , 18%, 12% and 6%, respectively.

Let's consider, Required rate of return = r

So,

D₀ = $ 1.75

D₁ = 1.75*1.24 = $ 2.17

D₂ = 2.17*1.18 = $ 2.56

D₃ = 2.56*1.12 = $ 2.87

D₄ = 2.87*1.06 = $ 3.04

Terminal Value (TV) = D₄*(1+growth rate)/(Required rate of return - growth rate)

Terminal Value (TV) = 3.04*(1+0.06)/(r - 0.06)

Terminal Value (TV) = 3.22/(r - 0.06)

Now,

Where, r = ??

Share price = $44.96

So,

Now, We will use some trial and errors and we will find that at r = 11.62 %, share price will be $ 44.96.

So, Investor must demand required return of 11.62%.

Alternate method : we can also use interpolation method for finding r. This method will give us approximate value of r (required rate of return)

Difference of share price at r = 11%

Difference of share price at r = 12%

Interpolation method :

r = 11 + [5.63/(5.63+2.88)]

r = 11 + 0.66

r = 11.66

So, as per interpolation method, Investor must demand required return of 11.66% (Approximately).