Question

Nu-Tek Inc. recently announced that it will pay its first annual dividend in one year in the amount of $0.50 a share. The dividend will be increased by 50% annually for the following two years, after which time the increase will be limited to 2.5% annually. How much are you willing to pay for one share of this stock today if you require a 14% rate of return?

Answer 1

Solution :

The price of a share of stock is calculated as follows :

The price of a share = Present value of dividends + Present value of share at year n

Thus the 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 = $ 0.50 ; g1 = 50 % = 0.50 ; g2 = 50 % = 0.50   ;

Thus the Dividend per year can be calculated as follows :

D1 = D0 * ( 1 + g1 ) = $ 0.50 * ( 1 + 0.50 ) = $ 0.50 * 1.50 = $ 0.75

D2 = D1 * ( 1 + g2 ) = $ 0.75 * ( 1 + 0.50 ) = $ 0.75 * 1.50 = $ 1.1250

Thus we have D1 = $ 0.75 ; D2 = $ 1.1250  ;

Calculation of price of share at year 2:

Price of the share at year 2 where the firm expects a constant growth rate of 2.5 %

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

P2 = [ D2 * ( 1 + g ) ] / ( Ke – g )

We know that

D2 = $ 1.1250 ; g = 2.5 % = 0.025 ; Ke = 14 % = 0.14 ;

P3 = [ $ 1.1250 * ( 1 + 0.025 ) ] / ( 0.14 – 0.025 )

= ( $ 1.1250 * ( 1 + 0.025 ) ) / 0.1150

= ( $ 1.1250 * 1.025 ) / 0.1150

= $ 1.153125 / 0.1150

= $ 10.027174

Thus the price of the share at year 2 = $ 10.027174

Calculation of price of share today :

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

= [ $ 0.75 * ( 1 / 1.14 )1 ] + [ $ 1.1250 * ( 1 / 1.14 )2 ] + [ $ 10.027174 * ( 1 / 1.14 )2 ]

= [ $ 0.75 * 0.877193 ] + [ $ 1.1250 * 0.769468 ] + [ $ 10.027174 * 0.769468 ]

= $ 0.657895 + $ 0.865651 + $ 7.715585

= $ 9.239130

= $ 9.24 ( when rounded off to the nearest cent )

Thus the amount that can be paid for one share of the stock today = $ 9.24