Question

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?
(A) $14.85
(B) $18.99
(C) $11.83
(D) $16.54
(E) $13.02

Answer 1

Answer:

(A) $14.85

Explanation:

Annual dividend just paid (D0)= $1.50

growth rate = 7% or 0.07 as a decimal

D1 ; next year's dividend = D0(1+g) = 1.50(1.07)= 1.605

growth rate = 7-2% = 5% or 0.05 as a decimal

D2; dividend yr2 = D1(1+g) = 1.605(1.05) = 1.6853

growth rate = 5-2% = 3% or 0.03 as a decimal

Terminal Cashflow; D3 = 1.6853 (1.03) = 1.7359

Next, find the present value of each dividend at 14%;

PV(D1) = 1.605/(1.14 ) = 1.4079

PV(D2) = 1.6853/(1.14² ) = 1.2968

PV of terminal Cashflow (D3 onwards) = $\frac{\frac{1.7359}{0.14-0.03} }{1.14^{2} }$ = 12.1429

Next, sum up the PVs to find the price;

= 1.4079 + 1.2968 + 12.1429

= 14.848

Therefore the price of the stock today  is $14.85