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Nile Corp's earnings this year were $7 per share and are expected to grow by 20% each year for the next 5 years. The company expects to reinvest all the earnings for the next 5 years. 6 years from now, they expect to pay a dividend of $7 per share and to grow it by 3% every year forever after that. If the risk-free rate is 4.5%, the expected return on the market portfolio is 9% and Nile has a beta of 1.4, what price should Nile's stock be trading at right now?

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To determine the price at which Nile Corp's stock should be trading at right now, we can use the dividend discount model (DDM) and the concept of present value. The DDM calculates the intrinsic value of a stock by discounting future dividends to their present value.

Let's break down the calculation step-by-step:

Calculate the present value of dividends for the next 5 years:

PV_dividends = (Div1 / (1 + r)^1) + (Div2 / (1 + r)^2) + ... + (Div5 / (1 + r)^5)

Here, Div1 = $7, r = cost of equity = risk-free rate + beta * (expected market return - risk-free rate)

Calculate the present value of the dividend in year 6:

PV_dividend_year6 = Div6 / (r - g)

Div6 = $7 * (1 + 3%) = $7.21

g = growth rate of dividends forever = 3%

Calculate the present value of all future dividends after year 6:

PV_dividends_after_year6 = PV_dividend_year6 / (1 + r)^6

Calculate the stock price using the present value of dividends:

Stock price = PV_dividends + PV_dividends_after_year6

Note: To calculate the cost of equity (r), we will use the risk-free rate of 4.5%, the expected market return of 9%, and Nile's beta of 1.4.

Let's calculate the values:

r = 4.5% + 1.4 * (9% - 4.5%) = 11.1%

PV_dividends = (7 / (1 + 11.1%)^1) + (7 / (1 + 11.1%)^2) + ... + (7 / (1 + 11.1%)^5)

PV_dividend_year6 = 7.21 / (11.1% - 3%) = 7.21 / 8.1%

PV_dividends_after_year6 = PV_dividend_year6 / (1 + 11.1%)^6

Stock price = PV_dividends + PV_dividends_after_year6

By plugging in the values and performing the calculations, you will arrive at the current trading price of Nile Corp's stock.

User Sahat Yalkabov
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