Question

(a) Considering Valuation Models, what type of dividend model is useful when we are examining/valuing one with a temporary high growth rate? Fully Explain.

(b) Considering Stock Option Value, what can you say about the relationship between volatility and call option value? Fully Explain.

Answer 1

(a)The dividend model we can use the two-stage dividend discount model:

Here, we can use an example to explain, suppose Company X just paid a dividend of $2. The dividends are expected to rise at a growth rate of 14% for 3 years and then rise at a rate of 2% forever, Required return on equity is 10%

So, according to the two stage dividend growth model :

D1= 2.28 ($2*1.14)

D2 = $2.5992 ($2.28*1.14)

D3 = $2.9631 ($2.5992*1.14)

D4= 3.0224 ($2.9631*1.02)

We can calculate the share price at the end of 4 years as :

P3 =  D4/ Re - g

= 3.0223/ 0.10 - 0.02

= $37.7795

Now, discounting the dividends and the share price back 3 years , we get the present value of share today:

The present value of share is:

= 2.28/1.1 + 2.5992/1.10^2 +($3.0223+ $37.7795) /1.1^3

= $34.8758

(b) There exists a direct relationship between stock prices and volatility. The higher the volatility, the greater is the movement of the underlying stock prices, higher volatility means that the stock option value is higher as there is a greater probability that the stock prices can rise and fall thus profiting the option holder.