A common stock is expected to pay a dividend of $114 at the end of
each year for the first 11 years. After that, the 12th12th dividend
is $114(1.02)114(1.02), the 13th13th dividend is
$114(1.02)2114(1.02)2, and so on indefinitely. Calculate the price
P of this stock to yield an annual effective rate of 7%.
P =
Price of Stock = PV(Dividends) + PV(Horizon Value)
From Year 1 to Year 11,
Annual Dividend = $114
Interest Rate = 7%
Calculating Present Value,
Present Value of Annuity = P[(1 - (1 + r)-n)/r]
Present Value = 114[(1 - (1.07)-11)/0.07]
Present Value = $854.85
After Year 11,
Horizon Value at Year 11= D11(1 + g)/(r - g)
Horizon Value = 114(1.02)/(0.07 - 0.02)
Horizon Value = $2,325,60
Present Value of Horizon Value = 2325.60/(1.07)11
Present Value of Horizon Value = $1,104.88
Stock Value = 854.85 + 1104.88
Stock Price = $1,959.73
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