Question

Tre-Bien, Inc., is a fast-growing technology company. The firm projects a rapid growth of 30 percent for the next two years, then a growth rate of 17 percent for the following two years. After that, the firm expects a constant growth rate of 8 percent. The firm expects to pay its first dividend of $2.45 a year from now. If the required rate of return on stocks with similar risk is 22 percent, what is the current price of the stock? Please show formulas to obtain answers on each part.

Answer 1

Solution:

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

Thus the current price of the stock = [ D₁ * ( 1 / ( 1 + r) ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ D₃ * ( 1 / ( 1 + r)³) ] + [ D₄ * ( 1 / ( 1 + r)⁴ ) ] [ P₄* ( 1 / ( 1 + r)⁴ ) ]

Calculation of Dividend per share Years 1 to 4 :

As per the information given in the question we have

D₁ = $ 2.45 ; g₁ = 30 %   ; g₂ = 30 %   ; g₃ = 17 %   ; g₄ = 17 %   ;

Thus the Dividend per year can be calculated as follows :

D₂ = D₁ * ( 1 + g₂ ) = $ 2.45 * ( 1 + 0.30 ) = $ 2.45 * 1.30 = $ 3.1850

D₃ = D₂ * ( 1 + g₃ ) = $ 3.1850 * ( 1 + 0.17 ) = $ 3.1850 * 1.17 = $ 3.7265

D₄ = D₃ * ( 1 + g₄ ) = $ 3.7265 * ( 1 + 0.17 ) = $ 3.7265 * 1.17 = $ 4.3600

Thus we have D₁ = $ 2.45 ; D₂ = $ 3.1850   ; D₃ = $ 3.7265   ; D₄ = $ 4.3600

Calculation of price of share at year 4:

Price of the share at year 4 where the firm expects a constant growth rate of 8 %

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

P₄ = [ D₄ * ( 1 + g ) ] / ( K_e – g )

We know that

D₄ = $ 4.3600 ; g = 8 % = 0.08   ; K_e = 22 % = 0.22 ;

P₄ = [ $ 4.3600 * ( 1 + 0.08 ) ] / ( 0.22 – 0.08 )

= ( $ 4.3600 * 1.08 ) / ( 0.22 – 0.08 )

= ( $ 4.3600 * 1.08 ) / 0.14

= $ 4.7088 / 0.14

= $ 33.6343

Thus the price of the share at year 4 = $ 33.6343

Calculation of price of stock today :

Thus the current price of the stock = [ D₁ * ( 1 / ( 1 + r) ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ D₃ * ( 1 / ( 1 + r)³) ] + [ D₄ * ( 1 / ( 1 + r)⁴ ) ] [ P₄* ( 1 / ( 1 + r)⁴ ) ]

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

= [ $ 2.45 * ( 1 / 1.22 ) ] + [ $ 3.1850 * ( 1 / 1.22 )² ] + [ $ 3.7265 * ( 1 / 1.22 )³ ] + [ $ 4.3600 * ( 1 / 1.22 )⁴ ] + [ 33.6343 * ( 1 / 1.22 )⁴ ]

= [ $ 2.45 * 0.819672 ] + [ $ 3.1850 * 0.671862 ] + [ $ 3.7265 * 0.550707 ] + [ $ 4.3600 * 0.451399 ] + [ $ 33.6343 * 0.451399 ]

= $ 2.008196 + $ 2.139880 + $ 2.052210 + $ 1.968100 + $ 15.182489

= $ 23.350876

= $ 23.35 ( when rounded off to two decimal places )

Thus the price of the stock = $ 23.35