Question

Francis Inc.'s stock has a required rate of return of 10.25%, and it sells for $57.50 per share. The dividend is expected to grow at a constant rate of 6.00% per year. What is the expected year-end dividend, D1?

Answer 1

Using Constant Grrowth Model, we have P0=D0*(1+g)/(Ks-g)
where P0 is current Price of Stock=57.50
D1 is exp year end dividend
g = growth rate of stock = 6%
Ks = Stock's reqd rate of return = 10.25%

CUrrent Stock Price Po=D1/(Ks-g)
Exp year end dividend = P0*(Ks-g) = 57.50*(10.25%-6%) = $2.44 .....Ans

Answer 2

We have to use the dividend discounting model where

P = D/(k-g)

where

P=stock price
D=dividend
k=expected rate of return
g=expected growth rate

we plug in the numbers to get

57.5 = D / (0.1025 - 0.06)
D = 57.5 * (0.1025 - 0.06)
D = 2.44375

or $2.44 rounded off to the nearest cent

Answer 3

According to the given information,

Required rate of return (Re) = 10.25%

Price of the share (P0) = $57.50

Growth rate (g) = 6.00%

We have to calculate the year-end dividend.

According to Dividend constant growth formula,

                                              Re = (D1 / P0) + g

Substituting the values inorder to find the value of D1

                                              0.1025 = (D1 / $57.50) + 0.06

                                              0.1025 - 0.06 = (D1 / $57.50)

                                                         0.0425 = D1 / $57.50

                                                              D1 = $57.50 * 0.0425

                                                              D1= $2.44

Therefore, the year-end dividend (D1) is $2.44