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?

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

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