Question

Helen's Pottery Co.'s stock recently paid a $1.50 dividend (D0 = $1.50). This dividend is expected to grow by 15% for the next 3 years, and then grow forever at a constant rate, g. The current stock price is $40.92. If rs = 10%, at what constant rate is the stock expected to grow following Year 3? a. 5.00% b. 6.50% c. 5.67% d. 4.25% e. 3.33%

Answer 1

Answer:

e. 3.33%

Explanation:

The growth rate can be calculated as follow

Price of the stock = [ D0 x ( 1 + growth rate first 3 years )^1 / ( 1 + discount rate )^1 ] + [ D0 x ( 1 + growth rate first 3 years )^2 / ( 1 + discount rate )^2 ] + [ D0 x ( 1 + growth rate first 3 years )^3 / ( 1 + discount rate )^3 ] + [ ( D0 x ( 1 + growth rate first 3 years )^3 ) x ( 1 + growth rate forever ) / ( Discount rate - growth rate forever ) ]

Placing values in the formula

$40.92 = [ $1.50 x ( 1 + 15% )^1 / ( 1 + 10% )^1 ] + [ $1.50 x ( 1 + 15% )^2 / ( 1 + 10% )^2 ] + [ $1.50 x ( 1 + 15% )^3 / ( 1 + 10% )^3 ] + [ ( $1.50 x ( 1 + 15% )^3 ) x ( 1 + growth rate forever ) / ( 10% - growth rate forever ) ]

$40.92 = $1.57 + $1.80 + $2.07 + [2.28 x ( 1 + growth rate forever ) /  ( 10% - growth rate forever )]

$40.92 = $5.44 + [2.28 x ( 1 + growth rate forever ) /  ( 10% - growth rate forever )]

$40.92 - $5.44 = [2.28 x ( 1 + growth rate forever ) /  ( 10% - growth rate forever )]

$35.48 = 2.28 x ( 1 + growth rate forever ) /  ( 10% - growth rate forever )

$35.48 / $2.28 = ( 1 + growth rate forever ) /  ( 10% - growth rate forever )

15.56140350 = ( 1 + growth rate forever ) /  ( 10% - growth rate forever )

15.56140350 x ( 10% - growth rate forever ) = 1 + growth rate forever

1.556140350 - 15.56140350growth rate forever = 1 + growth rate forever

1.556140350 - 1 = growth rate forever + 15.56140350growth rate forever

0.556140350 = 16.56140350growth rate forever

growth rate forever = 0.556140350 / 16.56140350

growth rate forever = 3.36% ( nominal difference due to rounding effect )

Hence, the nearest option is e. 3.33%