Question

Earnings per common share of ABC Industries for the next year are expected to be $2.25 and to grow 7.5% per year over the next 4 years. At the end of the 5 years, earnings growth rate is expected to fall to 6.25% and continue at that rate for the foreseeable future. ABC’s dividend payout ratio is 40%. If the expected return on ABC's common shares is 18.5%, calculate the current share price. (Round your answer to the nearest cent.)
Current share price $

plz show the work paper

Answer 1

The current share price will be the present value of all expected future dividends and the present value of the share price at the end of year 4, using constant growth model

The EPS is 2.25, and dividend payout ratio is 40%, so dividend will be, 40% of 2.25 = 0.9

Dividend at the end of year 1 = Present Dividend ( 1 + Growth Rate)

= 0.9 (1 + 7.5%)

= 0.9675

Dividend at the end of year 2 = Dividend at the end of year 1 ( 1 + Growth Rate)

= 0.9675 (1 + 7.5%)

= 1.04

Dividend at the end of year 3 = Dividend at the end of year 2 ( 1 + Growth Rate)

= 1.1180

Dividend at the end of year 4 = Dividend at the end of year 3 ( 1 + Growth Rate)

= 1.2019

Dividend at the end of year 5 = Dividend at the end of year 4 ( 1 + Constant Growth Rate)

= 1.277

The formula for the Constant dividend growth model is

Stock Price at the end of year 4 = Dividend for year 5 / (Required rate of Return - Constant Growth Rate)

= 1.277 / (18.5% - 6.25%)

= 10.4244

Stock Price Now = Present Value of Dividend 1 + Present Value of Dividend 2 + Present Value of Dividend 3 + Present Value of Dividend 4+ Present Value of Stock price at the end of year 4

= 0.9675 / (1 + 18.5%) + 1.04 / (1 + 18.5%)^2 + 1.1180 / (1 + 18.5%)^3 + 1.2019 / (1 + 18.5%)^4 + 10.4244 / (1 + 18.5%)^4

= 8.125

The current share price is $8.125

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