ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock.
-At what price would you expect ART to sell?

Question

Quizplus · Accepted Answer

To calculate the expected stock price, we can use the Gordon Growth Model:
P0 = (E1 / (r - g))
where
P0 = current stock price
E1 = earnings per share next year
r = required rate of return
g = growth rate of dividends

Since the question asks for stock price, we need to modify the formula slightly to account for the plowback ratio:
P0 = [(Earnings per share current year)x(1+g)] / (r - g)

Given:
- Current earnings per share = $3
- ROE = 25%, which means the growth rate of earnings = ROE x plowback ratio = 0.25 x 0.2 = 0.05
- Plowback ratio = 0.20
- Required rate of return (r) = 12%

Using these values, we can calculate the expected stock price:
P0 = [(3*(1+0.05)) / (0.12 - 0.05)]
P0 = $34.29

Therefore, the best choice is B) $34.29.

ART Has Come Out with a New and Improved Product