Question

Magnetic Corporation expects dividends to grow at a rate of 19.9% for the next two years. After two years, dividends are expected to grow at a constant rate of 6.4%, indefinitely. Magnetic’s required rate of return is 14.6% and they paid a $1.36 dividend today. What is the value of Magnetic Corporation’s common stock per share today? (Show your answers to the nearest cent.)

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 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 ) ] +   [ P2 * ( 1 / ( 1 + r)2 ) ]

Calculation of Dividend per share Years 1 to 2 :

As per the information given in the question we have

D0 = $ 1.36 ; g1 = 19.9 % = 0.199 ; g2 = 19.9 % = 0.199   ;

Thus the Dividend per year can be calculated as follows :

D1 = D0 * ( 1 + g1 ) = $ 1.36 * ( 1 + 0.199 ) = $ 1.36 * 1.199 = $ 1.630640

D2 = D1 * ( 1 + g2 ) = $ 1.630640 * ( 1 + 0.199 ) = $ 1.630640 * 1.199 = $ 1.955137

Thus we have D1 = $ 1.630640 ; D2 = $ 1.955137  ;

Calculation of price of share at year 2:

Price of the share at year 2 where the firm expects a constant growth rate of 6.4 %

The formula for calculating the price of the share at year 2

P2 = [ D2 * ( 1 + g ) ] / ( Ke – g )

We know that

D2 = $ 1.955137 ; g = 6.4 % = 0.064 ; Ke = 14.6 % = 0.146 ;

P3 = [ $ 1.955137 * ( 1 + 0.064 ) ] / ( 0.146 – 0.064 )

= ( $ 1.955137 * ( 1 + 0.064 ) ) / 0.082

= ( $ 1.955137 * 1.064 ) / 0.082

= $ 2.080266 / 0.082

= $ 25.369098

Thus the price of the share at year 2 = $ 25.369098

Calculation of price of share today :

Thus the current price of the share = [ D1 * ( 1 / ( 1 + r)1 ) ] + [ D2 * ( 1 / ( 1 + r)2 ) ] + [ P2* ( 1 / ( 1 + r)2 ) ]

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

= [ $ 1.630640 * ( 1 / 1.146 )1 ] + [ $ 1.955137 * ( 1 / 1.146 )2 ] + [ $ 25.369098 * ( 1 / 1.146 )2 ]

= [ $ 1.630640 * 0.872600 ] + [ $ 1.955137 * 0.761431 ] + [ $ 25.369098 * 0.761431 ]

= $ 1.422896 + $ 1.488702 + $ 19.316818

= $ 22.228416

= $22.23 ( when rounded off to the nearest cent )

Thus the value of Magnetic Corporation’s common stock per share today = $ 22.23