Question

Briley, Inc., is expected to pay equal dividends at the end of each of the next two years. Thereafter, the dividend will grow at a constant annual rate of 4.6 percent, forever. The current stock price is $51.

  

What is next year’s dividend payment if the required rate of return is 13 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Dividend payment

Answer 1

Solution:

The current price of a stock = present value of dividends + present value of stock at year n where the firm experiences a constant growth rate

Thus the current price of the stock= P₀ = [ D₁ * ( 1 / ( 1 + r)¹ ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ P₂* ( 1 / ( 1 + r)² ) ]

Calculation of Dividend per share Years 1 to 2 :

As per the information given in the question we have

Briley, Inc., is expected to pay equal dividends at the end of each of the next two years

Let the Dividend paid each year = ‘ x ‘ . Since they are equal dividends.

Thus we have D₁ = x   ; D₂ = x ; g₂ = 4.6 % = 0.046 ;

Calculation of price of share at year 2 :

Price of the share at year 2 where the firm expects a constant growth rate of 4.6 %

The formula for calculating the price of the share at year 2

P₂ = [ D₂ * ( 1 + g ) ] / ( K_e – g )

We know that

D₂ = x ; g = 4.6 % = 0.046   ; K_e = 13 % = 0.13 ;

P₂ = [ x * ( 1 + 0.046 ) ] / ( 0.13 – 0.046 )

= ( x * 1.046 ) / ( 0.13 – 0.046 )

= ( x * 1.046 ) / 0.084

= $ 1.046x / 0.084

= $ 12.452381x

Thus the price of the share at year 2 = $ 12.452381x

Calculation of price of stock today :

Thus the current price of the stock = [ D₁ * ( 1 / ( 1 + r)¹ ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ P₂* ( 1 / ( 1 + r)² ) ]

Applying the available information in the formula we have the price of the stock as follows :

51 = [ x * ( 1 / 1.13 )¹ ] + [ x * ( 1 / 1.13 )² ] + [ 12.452381 * ( 1 / 1.13 )² ]

51 = [ x * 0.884956 ] + [ x * 0.783147 ] + [ 12.452381 * 0.783147 ]

51 = 0.884956x + 0.783147x + 9.752041

51 = 0.884956x + 0.783147x + 9.752041

51 = 1.668102x + 9.752041

51 – 9.752041 = 1.668102x

1.668102x = 51 – 9.752041

1.668102x = 41.247959

x = 41.247959 / 1.668102

x = 24.727474

x = 24.73   ( when rounded off to two decimal places )

Thus the Dividend Payment each year for two years = $ 24.73