Question

# A common stock is expected to pay a dividend of \$114 at the end of each...

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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