Question

Sheridan, Inc., is a fast-growth company that is expected to grow at a rate of 23 percent (per year) for the next four years. It is then expected to grow at a constant rate of 6 percent. Sheridan’s first dividend, of $3.95, will be paid in year 3. If the required rate of return is 17 percent, what is the current value of the stock if dividends are expected to grow at the same rate as the company? (Round all intermediate calculations and final answer to 2 decimal places, e.g. 15.20.)

Answer 1

Solution :

The current value of stock of a company is calculated as follows :

The Current value of stock = Present value of dividends + Present value of stock at year ‘n’

Thus the current value of the stock with respect to the details given in the question is calculated using the formula

= [ D3 * ( 1 / ( 1 + r)3 ) ] + [ D4 * ( 1 / ( 1 + r)4 ) ] +   [ P4 * ( 1 / ( 1 + r)4 ) ]

Calculation of Dividend per share Years 3 to 4 :

As per the information given in the question we have

D3 = $ 3.95 ; g4 = 23 % = 0.23 ;

Thus the Dividend for Year 4 can be calculated as follows :

D3 = $ 3.95

D4 = D3 * ( 1 + g4 ) = $ 3.95 * ( 1 + 0.23 ) = $ 3.95 * 1.23 = $ 4.8585

Thus we have D3 = $ 3.95 ; D4 = $ 4.8585  ;

Calculation of price of stock at year 4 :

Price of the stock at year 4 where the firm expects a constant growth rate of 6 %

The formula for calculating the price of the stock at year 4

P4 = [ D4 * ( 1 + g ) ] / ( Ke – g )

We know that

D4 = $ 4.8585 ; g = 6 % = 0.06 ; Ke = 17 % = 0.17 ;

P3 = [ $ 4.8585 * ( 1 + 0.06 ) ] / ( 0.17 – 0.06 )

= ( $ 4.8585 * ( 1 + 0.06 ) ) / 0.11

= ( $ 4.8585 * 1.06 ) / 0.11   

= $ 5.150010 / 0.11

= $ 46.818273

Thus the price of the stock at year 4 = $ 46.818273

Calculation of value of stock :

Thus the current value of the stock = [ 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 current value of the stock as follows :

= [ $ 3.95 * ( 1 / 1.17)3 ] + [ $ 4.8585 * ( 1 / 1.17 )4 ] + [ $ 46.818273 * ( 1 / 1.17 )4 ]

= [ $ 3.95 * 0.624371 ] + [ $ 4.8585 * 0.533650 ] + [ $ 46.818273 * 0.533650 ]

= $ 2.466264 + $ 2.592739 + $ 24.984573

= $ 30.043576

= $ 30.04 ( when rounded off to two decimal places )

Thus the current value of Sheridan Inc.’s common stock = $ 30.04