Question

HCC, Inc., expects its dividends to grow at 25 percent per year for the next seven years before levelling off to a constant 3 percent growth rate. The required return is 11 percent. What is the current stock price if the annual dividend per share that was just paid was $1.05?
a. $43.21
b. $44.36
c. $38.93
d. $32.11
e. $39.96

Answer 1

Answer:

a. $43.21

Explanation:

Find dividend (D) per year;

D1 = D0(1+g)

D0= current dividend = 1.05

g= growth rate = 25% or 0.25 as a decimal

therefore;

D1 = 1.05(1.25) =1.3125

D2 = 1.3125 (1.25) = 1.6406

D3 = 1.6406(1.25) =2.0508

D4 = 2.0508 (1.25) = 2.5635

D5 = 2.5635(1.25) = 3.2044

D6 = 3.2044(1.25) =4.0055

D7 = 4.0055 (1.25) = 5.0069

Terminal dividend: D8 = 5.0069(1.03) = 5.1571

Next , find the present values of each dividend (at t=0) at 11% discount rate;

1.3125 / (1.11) = 1.1824

1.6406 / (1.11^2) = 1.3315

2.0508 / (1.11^3) = 1.4995

2.5635 / (1.11^4) = 1.6887

3.2044 / (1.11^5) = 1.9017

4.0055 / (1.11^6) = 2.1415

5.0069 / (1.11^7) =  2.4116

Price of growing perpetual at (t= 0) = $\frac{5.1571 /(0.11-0.03)}{(1.11)^{7} }  = \frac{64.46375}{2.07616} = 31.0495$

Next, sum up all the Present values to get the current stock price;

=43.2064

Therefore, the current price = $43.21