Question

Problem 9.22

You own a company that competes with Old World DVD Company. Instead of selling DVDs, however, your company sells music downloads from a Web site. Things are going well now, but you know that it is only a matter of time before someone comes up with a better way to distribute music. Your company just paid a $1.50 per share dividend, and you expect to increase the dividend 10 percent next year. However, you then expect your dividend growth rate to begin going down—to 5 percent the following year, 2 percent the next year, and to -3 percent per year thereafter. Based upon these estimates, what is the value of a share of your company’s stock? Assume that the required rate of return is 12 percent. (Round dividends in intermediate calculations to 4 decimal places, e.g. 1.5325 and final answer to 2 decimal places, e.g. 15.25.)

Answer 1

Solution :

The current price of a share of a company is calculated as follows :

The Current price of a share = Present value of dividends + Present value of share price at year n

Thus the current price of the share with respect to the details given in the question is calculated using the formula

= [ D₁ * ( 1 / ( 1 + r) ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ D₃ * ( 1 / ( 1 + r)³) ] +   [ P₃ * ( 1 / ( 1 + r)³ ) ]

Calculation of Dividend per share Years 1 to 3 :

As per the information given in the question we have

D₀ = $ 1.50 ; g₁ = 10 %   ; g₂ = 5 %   ; g₃ = 2 % ;

Thus the Dividend per year can be calculated as follows :

D₁ = D₀ * ( 1 + g₁ ) = $ 1.50 * ( 1 + 0.10 ) = $ 1.50 * 1.10 = $ 1.6500

D₂ = D₁ * ( 1 + g₂ ) = $ 1.6500 * ( 1 + 0.05 ) = $ 1.6500 * 1.05= $ 1.7325

D₃ = D₂ * ( 1 + g₃ ) = $ 1.7325 * ( 1 + 0.02 ) = $ 1.7325 * 1.02 = $ 1.7672

Thus we have D₁ = $ 1.6500 ; D₂ = $ 1.7325   ; D₃ = $ 1.7672   ;

Calculation of price of share at year 3:

Price of the share at year 3 where the firm expects a constant growth rate of - 3 %

The formula for calculating the price of the share at year 3

P₃ = [ D₃ * ( 1 + g ) ] / ( K_e – g )

We know that

D₃ = $ 1.7672 ; g = - 3 % = - 0.03   ; K_e = 12 % = 0.12 ;

P₃ = [ $ 1.7672 * ( 1 - 0.03 ) ] / ( 0.12 – ( - 0.03 ) )

= ( $ 1.7672 * 0.97 ) / ( 0.12 + 0.03 )

= ( $ 1.7672 * 0.97 ) / 0.15

= $ 1.7142 / 0.15

= $ 11.4280

Thus the price of the share at year 3 = $ 11.4280

Calculation of price of share today :

Thus the current price of the share = [ D₁ * ( 1 / ( 1 + r) ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ D₃ * ( 1 / ( 1 + r)³) ] + [ P₃* ( 1 / ( 1 + r)³ ) ]

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

= [ $ 1.65 * ( 1 / 1.12 ) ] + [ $ 1.7325 * ( 1 / 1.12 )² ] + [ $ 1.7672 * ( 1 / 1.12 )³ ] + [ 11.4280 * ( 1 / 1.12 )³ ]

= [ $ 1.65 * 0.892857 ] + [ $ 1.7325 * 0.797194 ] + [ $ 1.7672 * 0.711780 ] + [ $ 11.4280 * 0.711780 ]

= $ 1.4732 + $ 1.3811 + $ 1.2579 + $ 8.1342

= $ 12.2464

= $ 12.25 ( when rounded off to two decimal places )

Thus the value of a share of the company’s stock = $ 12.25