Question #59751

A financial analyst has been following Biostar Inc., a new high-growth company. She
estimates that the current risk-free rate is 6.25 percent, the market risk premium is 5
percent, and that Biostar Inc beta is 1.75. The current earnings per share (EPS0) isRM2.50.
The company has a 40 percent payout ratio. The analyst estimates that the company's
dividend will grow at a rate of 25 percent this year, 20 percent next year, and 15 percent
the following year. After three years the dividend is expected to grow at a constant rate of
7 percent a year. The company is expected to maintain its current payout ratio. The analyst
believes that the stock is fairly priced. What is the current price of the stock?

Expert's answer

A constant growth stock is a stock whose dividends are expected to grow at a constant rate in the forseeable future. This condition fits many established firms, which tend to grow over the long run at the same rate as the economy, fairly well. The value of a constant growth stock can be determined using the following equation:

P0 = D0*(1 + g)/(r - g) = D1/(r - g), where P0 = the stock price at time 0, D0 = the current dividend, D1 = the next dividend (i.e., at time 1), g = the growth rate in dividends, and r = the required return on the stock, and g < r.

Payout Ratio = Dividends per Share (D) / Earnings per Share (EPS), so D0/2.5 = 0.4, D0 = 2.5*0.4 = $1 per share.

D3 = D0*1.25*1.2*1.15 = 1*1.725 = $1.725 per share.

Expected market return r = rf + b*(rm - rf) = 0.0625 + 1.75*(0.0625 - 0.05) = 0.084.

The current price of the stock P0 = 1.725*(1 + 0.07)/(0.084 - 0.07) = $131.84 per share.

P0 = D0*(1 + g)/(r - g) = D1/(r - g), where P0 = the stock price at time 0, D0 = the current dividend, D1 = the next dividend (i.e., at time 1), g = the growth rate in dividends, and r = the required return on the stock, and g < r.

Payout Ratio = Dividends per Share (D) / Earnings per Share (EPS), so D0/2.5 = 0.4, D0 = 2.5*0.4 = $1 per share.

D3 = D0*1.25*1.2*1.15 = 1*1.725 = $1.725 per share.

Expected market return r = rf + b*(rm - rf) = 0.0625 + 1.75*(0.0625 - 0.05) = 0.084.

The current price of the stock P0 = 1.725*(1 + 0.07)/(0.084 - 0.07) = $131.84 per share.

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