Question

The Bell Weather Co. is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 20 percent a year for the next 4 years and then decreasing the growth rate to 4 percent per year. The company just paid its annual dividend in the amount of $2.70 per share. What is the current value of one share of this stock if the required rate of return is 8.20 percent?

Multiple Choice

A) $141.33

B) $101.15

C) $138.63

D) $117.93

E) $115.23

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 = [ D₁ * ( 1 / ( 1 + r)¹ ) ] + [ 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

D₀ = $ 2.70 ; g₁ = 20 %   ; g₂ = 20 %   ; g₃ = 20 %   ; g₄ = 20 %   ;

Thus the Dividend per year can be calculated as follows :

D₁ = D₀ * ( 1 + g₁ ) = $ 2.70 * ( 1 + 0.20 ) = $ 2.70 * 1.20 = $ 3.2400

D₂ = D₁ * ( 1 + g₂ ) = $ 3.2400 * ( 1 + 0.20 ) = $ 3.2400 * 1.20 = $ 3.8880

D₃ = D₂ * ( 1 + g₃ ) = $ 3.8880 * ( 1 + 0.20 ) = $ 3.8880 * 1.20 = $ 4.6656

D₄ = D₃ * ( 1 + g₄ ) = $ 4.6656 * ( 1 + 0.20 ) = $ 4.6656 * 1.20 = $ 5.5987

Thus we have D₁ = $ 3.2400 ; D₂ = $ 3.8880   ; D₃ = $ 4.6656   ; D₄ = $ 5.5987

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 4

P₄ = [ D₄ * ( 1 + g ) ] / ( K_e – g )

We know that

D₄ = $ 5.5987 ; g = 4 % = 0.04   ; K_e = 8.20 % = 0.0820 ;

P₄ = [ $ 5.5987 * ( 1 + 0.04 ) ] / ( 0.0820 – 0.04 )

= ( $ 5.5987 * 1.04 ) / ( 0.0820 – 0.04 )

= ( $ 5.5987 * 1.04 ) / 0.0420

= $ 5.822648 / 0.0420

= $ 138.634500

Thus the price of the share at year 4 = $ 138.634500

Calculation of price of stock today :

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

= [ $ 3.2400 * ( 1 / 1.082 )¹ ] + [ $ 3.8880 * ( 1 / 1.082 )² ] + [ $ 4.6656 * ( 1 / 1.082 )³ ] + [ $ 5.5987 * ( 1 / 1.082 )⁴ ] + [ $ 138.634500 * ( 1 / 1.082 )⁴ ]

= [ $ 3.2400 * 0.924214 ] + [ $ 3.8880 * 0.854172 ] + [ $ 4.6656 * 0.789438 ] + [ $ 5.5987 * 0.729610 ] + [ $ 138.634500 * 0.729610 ]

= $ 2.994453 + $ 3.321021 + $ 3.683202 + $ 4.084868 + $ 101.149118

= $ 115.232662

= $ 115.23 ( when rounded off to two decimal places )

Thus the current value of one share of this stock if the required rate of return is 8.20 percent = $ 115.23

The solution is Option E). $ 115.23