Question

Combined Communications is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 23 percent a year for the next 4 years and then decreasing the growth rate to 6 percent per year. The company just paid its annual dividend in the amount of $1.40 per share. What is the current value of one share of this stock if the required rate of return is 8.50 percent? a. $62.77 b. $7710 c. $73.01 d. $58.21 e. $66.50

Answer 1

Current Market value of the stock at 8.5% return: 105.88

Step-by-step explanation:

We will calculate the present value of the dividends:

`\left[\begin{array}{ccc}Year&Cash \: Flow&PV\\</p><p>1&1.722&1.59\\</p><p>2&2.12&1.8\\</p><p>3&2.61&2.04\\</p><p>4&3.21&2.32\\</p><p>5&3.40&98.13\\</p><p>&&105.88\\</p><p>\\\end{array}\right]`

We will do the following:

each dividends we multiply by the previous, by the grow rate of 23%

D1 1.40 x ( 1 + 23%) = D2 = 1.722

D2 1.722 x ( 1 + 23%) = D3 = 2.12

...

Then after the four years we calculate the gordon model for the infinite series of dividends

`(divends)/(return-growth) = Intrinsic \: Value`

3.95/(0.085-0.06) = 158

Then calculate the present of each dividends applying the present value of a lump sum

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

`(1.722)/((1 + 0.085)^(1) ) = PV_(div1)`

PV div1 = 1.59

`(2.12)/((1 + 0.085)^(2) ) = PV_(div2)`

PV div2 = 1.8

`(2.61)/((1 + 0.085)^(3) ) = PV_(div3)`

PV div3 = 2.04

...

Then we add them and get the present value of the stock