Shore Hotels just paid an annual dividend of $1.50 per share. The company will increase its dividend by 7 percent next year and will then reduce its dividend growth rate by 2 percentage points per year until it reaches the industry average of 3 percent dividend growth, after which the company will keep a constant growth rate forever. What is the price of this stock today given a required return of 14 percent

$14.85

Explanation:

The computation of the price of the stock today is shown below

But before that following calculation need to be done

D1 i.e.next year's dividend is

= D0(1+g)

= 1.50(1.07)

= 1.605

Now growth rate is

= 7 % - 2%

= 5% or 0.05  

D2 i.e. dividend year 2 is

= D1(1+g)

= 1.605(1.05)

= 1.6853

Now

growth rate is

= 5% - 2%

= 3% or 0.03  

Terminal Cashflow; D3 is

= 1.6853 (1.03)

= 1.7359

Now the present value for each dividend would be

PV(D1) is

= 1.605 ÷ (1.14 )

= 1.4079

PV(D2) is

= 1.6853 ÷ (1.14^2 )

= 1.2968

PV of terminal cash flow (D3) is

= 1.7359 ÷ (14% - 3%) ÷ (1.14)^2

= 12.1429

And, finally the price of the stock today is

= $1.4079 + $1.2968 + $12.1429

= $14.848

= $14.85

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