Question

Non-constant growth model:
Do=$2.00 required return on equity= 5%

g= 9% n=1,2

g=7% n=3,4

g=3% n=5 and thereafter

No spreadsheet, worked out

Answer 1

Solution:

The Non constant growth model is used to calculate the price of a share.

The current price of a share of a company using the Non constant growth model is calculated as follows :

The Current price of a share = Present value of dividends + Present value of share 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)¹ ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ D₃ * ( 1 / ( 1 + r)³) ] + [ D₄ * ( 1 / ( 1 + r)⁴ ) ] + [ D₅ * ( 1 / ( 1 + r)⁵ ) ] + [ P₅ * ( 1 / ( 1 + r)⁵ ) ]

Calculation of Dividend per share Years 1 to 5 :

As per the information given in the question we have

D₀ = $ 2.00 ; g₁ = 9 %   ; g₂ = 9 %   ; g₃ = 7 % ; g₄ = 7 % ; g₅ = 3 % ;

Thus the Dividend per year can be calculated as follows :

D₁ = D₀ * ( 1 + g₁ ) = $ 2 * ( 1 + 0.09 ) = $ 2 * 1.09 = $ 2.18

D₂ = D₁ * ( 1 + g₂ ) = $ 2.18 * ( 1 + 0.09 ) = $ 2.18 * 1.09 = $ 2.3762

D₃ = D₂ * ( 1 + g₃ ) = $ 2.3762 * ( 1 + 0.07 ) = $ 2.3762 * 1.07 = $ 2.5425

D₄ = D₃ * ( 1 + g₄ ) = $ 2.5425 * ( 1 + 0.07 ) = $ 2.5425 * 1.07 = $ 2.7205

D₅ = D₄ * ( 1 + g₅ ) = $ 2.7205 * ( 1 + 0.03 ) = $ 2.7205 * 1.03 = $ 2.8021

Thus we have D₁ = $ 2.1800 ; D₂ = $ 2.3762   ; D₃ = $ 2.5425   ; D₄ = $ 2.7205 ; D₅ = $ 2.8021   ;

Calculation of price of share at year 5:

Price of the share at year 5 where the firm expects a constant growth rate of 3 %

The formula for calculating the price of the share at year 5

P₅ = [ D₅ * ( 1 + g ) ] / ( K_e – g )

We know that

D₅ = $ 2.8021 ; g = 3 % = 0.03   ; K_e = 5 % = 0.05 ;

P₅ = [ $ 2.8021 * ( 1 + 0.03 ) ] / ( 0.05 – 0.03 )

= ( $ 2.8021 * 1.03 ) / ( 0.05 - 0.03 )

= ( $ 2.8021 * 1.03 ) / 0.02

= $ 2.886163 / 0.02

= $ 144.308150

Thus the price of the share at year 5 = $ 144.308150

= $ 144.3082

Calculation of price of share today :

Thus the current price of the share = [ D₁ * ( 1 / ( 1 + r)¹ ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ D₃ * ( 1 / ( 1 + r)³) ] + [ D₄ * ( 1 / ( 1 + r)⁴ ) ] + [ D₅ * ( 1 / ( 1 + r)⁵) ] + [ P₅* ( 1 / ( 1 + r)⁵ ) ]

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

= [ $ 2.1800 * ( 1 / 1.05 )¹ ] + [ $ 2.3762 * ( 1 / 1.05 )² ] + [ $ 2.5425 * ( 1 / 1.05 )³ ] + [ $ 2.7205 * ( 1 / 1.05 )⁴ ] + [ $ 2.8021 * ( 1 / 1.05 )⁵ ] + [ 144.3082 * ( 1 / 1.02 )⁵ ]

= [ $ 2.1800 * 0.952381 ] + [ $ 2.3762 * 0.907029 ] + [ $ 2.5425 * 0.863838 ] + [ $ 2.7205 * 0.822702 ] + [ $ 2.8021 * 0.783526] + [ $ 144.3082 * 0.783526 ]

= $ 2.076191 + $ 2.155282 + $ 2.196308 + $ 2.238161 + $ 2.195518 + $ 113.069188

= $ 123.930648

= $ 123.93 ( when rounded off to two decimal places )

Thus the price of the share / stock as per the Non constant growth model = $ 123.93