Shares and growth rate

[Muhammad Amir]

<b>a) GROWTH RATE-</b>

Growth rate of dividends (for above mentioned scenario) can be determined by using Historic Pattern method.

<b>Dividend Growth = [{ (Dn/Do)^(1/n) } - 1]</b>

Where,

Dn = Most recent dividend
Do = Most earliest dividend
n = Number of years
^ = sign of "power"

Dividend Growth = { (10.5/3.5)^(1/10) } - 1

Dividend Growth = 11.61%


<b>b) RATE OF RETURN-</b>

For determination of required rate of return we can use Gordon's dividend growth model. However, this model has its own limitations and assumptions that I will mention at the end of solution.

<b>Market Value of Share = [{Dividend * (1+g)}/(Re - g)]</b>

Where,

g = dividend growth rate (using above solution 11.61% or 0.1161)
Re = Rate of return

75 = [{10.5 * (1+0.1161)}/(Re - 0.1161)]

75 = [{11.719/Re - 0.1161}]

(Re - 0.1161) = {11.719/75}

(Re - 0.1161) = 0.156254

Re = 0.156254 + 0.1161

Re = 0.2723 or 27.23%

Therefore,

<b>Rate of Return = 27.23%, and;
Growth rate = 11.61%
</b>

<b>Assumptions behind Gordon's Dividend Growth model -</b>

- Complete earnings are not distributed but retained and these are retained so that growth can occur.

- Growth rate is constant

- Next dividend is paid after 1 year

- "g (i.e. growth rate)" is less than "Re (i.e. rate of return)".