ART Inc. has come out with a new and improved product. As a result, the firm projects an ROE of 25% a year until the end of year 3 and 15% a year afterwards, and it will maintain a plowback ratio of 20%. Its earnings in the coming year, i. e., E1, will be $3 per share. Investors expect a 12% rate of return on the stock. What would be its P0/E1 ratio?

$11.43

Explanation:

In order to determine the price to earnings ratio, we need to know what the price (p0) would be

price can be determined using the constant growth dividend model

according to the constant dividend growth model

price = d1 / (r - g)

d1 = next dividend to be paid

r = cost of equity

g = growth rate

Sustainable growth rate is the rate of growth a company can afford in the long term

sustainable growth rate = plowback rate x ROE

0.25 x 0.2 = 0.05 = 5%

dividend = payout ratio x earnings

Payout ratio = 1 - retention rate

1 - 0.2 = 0.8

0.8 x 3 = $2.4

$2.4 / 0.12 - 0.05 = $34.29

P / E = $34.29 / $3 = $11.43

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