Question

Biotechnica Inc. is experiencing rapid growth. Analysts forecast a growth of 10% for the next 3 years, followed by 3% growth in perpetuity thereafter. The company has just paid a dividend of $2.50, and the required return is 13%. Calculate the current value per share.

Answer 1

Solution :

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

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

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

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

n = 3 years ;

Calculation of Dividend per share Years 1 to 3 :

As per the information given in the question we have

D₀ = $ 2.50 ; g₁ = 10 %   ; g₂ = 10 %   ; g₃ = 10 % ;

Thus the Dividend per year can be calculated as follows :

D₁ = D₀ * ( 1 + g₁ ) = $ 2.50 * ( 1 + 0.10 ) = $ 2.50 * 1.10 = $ 2.75

D₂ = D₁ * ( 1 + g₂ ) = $ 2.75 * ( 1 + 0.10 ) = $ 2.75 * 1.10 = $ 3.025

D₃ = D₂ * ( 1 + g₃ ) = $ 3.025 * ( 1 + 0.10 ) = $ 3.025 * 1.10 = $ 3.3275

Thus we have D₁ = $ 2.75 ; D₂ = $ 3.025   ; D₃ = $ 3.3275   ;

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 = $ 3.3275 ; g = 3 % = 0.03   ; K_e = 13 % = 0.13 ;

P₃ = [ $ 3.3275 * ( 1 + 0.03 ) ] / ( 0.13 – 0.03 )

= ( $ 3.3275 * 1.03 ) / ( 0.13 - 0.03 )

= ( $ 3.427325 ) / ( 0.13 – 0.03 )

= $ 3.427325 / 0.10

= $ 34.273250

Thus the price of the share at year 3 = $ 34.273250

Calculation of current value per share :

Thus the current price of the share = [ D₁ * ( 1 / ( 1 + r)¹ ) ] + [ 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 current value per share as follows :

= [ $ 2.75 * ( 1 / 1.13 )¹ ] + [ $ 3.0250 * ( 1 / 1.13 )² ] + [ $ 3.3275 * ( 1 / 1.13 )³ ] + [ 34.273250 * ( 1 / 1.13 )³ ]

= [ $ 2.75 * 0.884956 ] + [ $ 3.0250 * 0.783147 ] + [ $ 3.3275 * 0.693050 ] + [ $ 34.273250 * 0.693050 ]

= $ 2.433628 + $ 2.369019 + $ 2.306124 + 23.753081

= $ 30.861853

= $ 30.86 ( when rounded off to two decimal places )

Thus the Current value per share = $ 30.86