A stock is currently selling at 80 per share to yield an annual nominal interest rate of 10%, compounded semi-annually. The stock is expected to pay dividends at the end of each year forever. The next dividend (payable one year from now) is 2 and is expected to increase at a rate of X% per year. Calculate X.

X is 7.75%

Explanation:

The yield on a stock is determined by dividend and stock appreciation in the market.

First, we need to calculate the effective annual yield

Effective annual yield = ( 1 + Nominal interest rate/periods per year )^numbers of compounding periods annually - 1

Effective annual yield = ( 1 + 10%/2 )^2 - 1

Effective annual yield = 1.1025 - 1

Effective annual yield = 0.1025

Effective annual yield = 10.25%

Now use the following formula to calculate the X

Price of the share = Expected dividend / ( Effective annual yield - Growth rate )

Where

Price of share = 80

Expected Dividend = 2

Effective annual yield = 10.25%

Growth rate = X

Placing values in the formula

80 = 2 / ( 10.25% - X )

0.1025 - X = 2 / 80

0.1025 - X = 0.025

-X = 0.025 - 0.1025

-X = -0.0775

X = 0.0775

X = 7.75%

u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30