Question

General Cereal common stock dividends have been growing at an annual rate of 7% per year over the past 10 years. The last dividend was $1.70 per share. What is the intrinsic value of a share of this stock to an investor who requires a 12% rate of return, under the following conditions: a) Dividends are expected to continue growing at the current rate indefinitely. b) The dividends are expected to decline at a constant rate of 6% per year forever.

Answer 1

Given data:- Dividend paid =d0=$1.70,growth rate=g=7%,rate of return=Ke=12%,P0=price of stock today. a)The intrinsic value of a share of this stock when the dividends are expected to grow continuously at the current growth rate indefinitely. Dividend at the end of year1 =D1 D1=D0×(1+g)= $1.70×(1+0.07)=$1.8190. now the intrinsic value of the share is given by P0=D1/Ke-g =$1.8190/12%-7% P0=$36.38.     therefore price of a share = $36.38. b)calculation of the intrinsic value of a stock when dividends are expected to decline at a constant rate of 6%. here dividend paid =D0=$1.70 , growth rate =g=6%,cost of capital =Ke=12%. so dividend at the end of year 1 =D1=$1.70×(1+0.06)=$1.8020 accordingly the price of the stock =P0=D1/Ke-g = 1.8020/12%-6% P0=$30.03. therefore price of stock =$30.03.