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.