Question

A stock just paid an annual dividend of $1.8. The dividend is expected to grow by 8% per year for the next 3 years. The growth rate of dividends will then fall steadily (linearly) from 8% after 3 years to 5% in year 6. The required rate of return is 12%.
1. What is the current stock price if the dividend growth rate will stay 0.05 (5%) forever after 6 years?
2. In 6 years, the P/E ratio is expected to be 23 and the payout ratio to be 80%. What is the current stock price when using the P/E ratio?

Answer 1

Answer:

1.

The current stock price is $28.71

2.

The current stock price is $149.15

Explanation:

1.

We need to calculate the present value of the dividends with each growth

First calculate the dividend each year

Year _________________________ Dividend

1 _____( $1.8 x ( 1 + 8% )^1__________ $1.9440

2_____( $1.8 x ( 1 + 8% )^2__________ $1.1664

3_____( $1.8 x ( 1 + 8% )^3__________ $2.2675

4_____( $2.2675 x ( 1 + 7% )________ $2.4262

5_____( $2.4262 x ( 1 + 6% )________ $2.5718

6_____( $2.5718 x ( 1 + 5% )_________ $2.7004

Calculate  the present value of each years dividend

Year _________________________ present value

1 _____( $1.9440 / ( 1 + 12% )^1 __________ $2.1773

2_____$1.1664 / ( 1 + 12% )^2___________ $0.9298

3_____$2.2675 / ( 1 + 12% )^3___________$0.7118

4_____$2.4262 / ( 1 + 12% )^4___________$1.5419

5_____$2.5718 / ( 1 + 12% )^5___________ $1.4593

6_____$2.7004 / ( 12% - 5% ) / ( 1 + 12% )^5_$21.8897

Total _____________________________ $28.7098

Hence priec of the stock is $28.71

2.

First calculate dividend of Year 6

Dividend = EPS x Payout ratio = 23 x 80% = $18.40

Present value = $18.4 / ( 12% - 5% ) / ( 1 + 12% )^5 = $149.15