Question

Prock Petroleum's stock has a required return of 15%, and the stock sells for $60 per share. The firm just paid a dividend of $1.00, and the dividend is expected to grow by 30% per year for the next 4 years, so D 4 = $1.00(1.30) 4 = $2.8561. After Year 4, the dividend is expected to grow at a constant rate of X% per year forever. What is the stock's expected constant growth rate after Year 4, i.e., what is X? Pick the closest answer.

Answer 1

g = 0,116559243

Step-by-step explanation:

First we solve for the present value of the know dividends:

`\left[\begin{array}{ccc}#&Cashflow&Discounted\\Zero&1&\\1&1.3&1.13\\2&1.69&1.28\\3&2.197&1.44\\4&2.8561&1.63\\\end{array}\right]`

We add them and get: 5.48

as the stock sells for 60 dollar the 54.52 represent the horizon value discounted:

`(Maturity)/((1 + rate)^(time) ) = PV`

`(Maturity)/((1 + .15)^(4) ) = 54.52`

Horizon value = 95.36281912

Now, we solve for grow:

`(D_(n+1))/(r-g) = PV\\(D_0(1+g))/(r-g) = PV\\`

`(2.8561(1+g))/(0.15-g) = 95.36281912\\`

`2.8561 + 2.8561g = 0.15 x 95.36281912 - 95.36281912g`

`95.36281912g + 2.8561g = 14,304422868‬ - 2.8561`

`g =  11,448322868‬ / 98,21891912`

g = 0,116559243

Answer 2

Price =[PVF15%,1*D1]+[PVF15%,2*D2]+[PVF15%,3*D3]+[PVF15%,4*D4]+[PVF15%,4*Terminal value at year4 ]

60 = [.86957* 1.3]+[.75614*1.69]+[.65752*2.197]+[.57175*2.8561]+[.57175*TV]

= 1.1304+ 1.2779+ 1.4446+ 1.6330+ .57175TV

60 = 5.4859+.57175TV

Terminal value = [60-5.4859]/.57175

= 54.5141/.57175

= $ 95.3460

Terminal value=D4(1+g)/(Rs-g)

95.3460 =2.8561(1+g)/(.15-g)

95.3460(.15-g)= 2.8561-2.8561g

14.3019- 95.3460g = 2.8561-2.8561g

95.3460g-2.8561g = 14.3019-2.8561

92.4899 g = 11.4458

g = 11.4458/92.4899

= .1238 or 12.38%

Growth after year4 = 12.38%

**D1 =1(1+.30)=1.3

D2 =1.3(1+.3)=1.69

D3 = 1.69(1+.3)= 2.197

D4= 2.197(1+.3)= 2.8561