Final answer:
The price at which Analog stock should sell is calculated using the Gordon Growth Model, which in this case yields a stock price of $10 per share, derived from given figures like ROE, beta, earnings per share, market return, and T-bills return rates.
Step-by-step explanation:
To determine the price at which Analog stock should sell, one would typically use the Gordon Growth Model (also known as the Dividend Discount Model) which requires the dividend per share, the cost of equity (required rate of return), and the growth rate of dividends. The growth rate can be calculated using the Return on Equity (ROE) and the plowback ratio (the proportion of earnings not paid out as dividends).
The cost of equity (r) can be calculated using the Capital Asset Pricing Model (CAPM):
r = risk-free rate + beta * (market return - risk-free rate).
Given that the risk-free rate is 6%, beta is 1.25, and the market return is 14%, we can calculate r as:
r = 6% + 1.25 * (14% - 6%) = 16%.
The growth rate (g) of dividends is ROE * plowback ratio. Given ROE is 9% and the plowback ratio is two-thirds, g = 9% * 2/3 = 6%.
The Gordon Growth Model formula is P = D / (r - g), where P is the price of the stock, D is the dividend per share, r is the required rate of return, and g is the growth rate of dividends.
This year's dividend (D) is not directly given but since earnings are $3 per share and the plowback ratio is 2/3, the dividend paid out is 1/3 of the earnings, so D = $3 * 1/3 = $1.
Plugging these into the Gordon Growth Model, P = $1 / (0.16 - 0.06) = $10.
Therefore, the Analog stock should sell for $10 per share.