Question

Rocket Co. has just paid a dividend of $1.15 per share. The firm pays annual dividends. It is expected by analysts that the firm's earnings will grow by 8.2% per year over next six years. After that, the earnings will most likely grow at the current industry average of 5.5% per year. Analysts do not expect any changes in the payout ratio of the firm. The cost of capital is 12%. The today’s share price is closest to (nearest cents):

Select one:

a. $19.67

b. $21.30

c. $23.12

d. $20.51

Answer 1

The dividends from company are expected to grow at 8.2%p.a. (g1) for first 6 years and at 5.5%p.a. (g2) thereafter forever. Therefore,price of equity share is to be ascertained as follows:

FIRST, Calculate present value of dividends for 6 years:

Present value of future dividend = $6.12

NOW, The price of equity share at end of 6th year depends upon dividend for 7th year(D7) , cost of capital (k_e) and growth rate g2 as follows:

D₇= D₆(1+g₂)= 1.8452(1+5.5%) = $ 1.9466

The share price, P₆ = D₇ /(k_e-g₂ ) = 1.9466/(0.12- 0.055) = 1.9466/0.065 = $ 29.94

This amount of $ 29.94 is realizable after 6 years. Therefore, the present value of this amount at 12% is $ 15.18($29.94*0.507).

Now, the total expected price of share is sum total of (i) present value of future divided and (ii)present value of expected price at the end of 6th year i.e.

Expected price= 6.12 + 15.18 = $ 21.30

so, correct option is B($21.30)