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

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TomShelby TomShelby · Answer 1 · 2019-09-10T00:28:23+02:00

Answer:

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

Explanation:

We will calculate the present value of the dividends:

[tex]\left[\begin{array}{ccc}Year&Cash \: Flow&PV\\

1&1.722&1.59\\

2&2.12&1.8\\

3&2.61&2.04\\

4&3.21&2.32\\

5&3.40&98.13\\

&&105.88\\

\\\end{array}\right][/tex]

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

[tex]\frac{divends}{return-growth} = Intrinsic \: Value[/tex]

3.95/(0.085-0.06) = 158

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

[tex]\frac{Principal}{(1 + rate)^{time} } = PV[/tex]

[tex]\frac{1.722}{(1 + 0.085)^{1} } = PV_{div1}[/tex]

PV div1 = 1.59

[tex]\frac{2.12}{(1 + 0.085)^{2} } = PV_{div2}[/tex]

PV div2 = 1.8

[tex]\frac{2.61}{(1 + 0.085)^{3} } = PV_{div3}[/tex]

PV div3 = 2.04

...

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