Question

If 1) the expected return for XYZ stock is 9.5 percent; 2) the dividend is expected...

If 1) the expected return for XYZ stock is 9.5 percent; 2) the dividend is expected to be \$4.38 in one year, \$6.33 in two years, \$0 in three years, and \$2.54 in four years; and 3) after the dividend is paid in four years, the dividend is expected to begin growing by 4.5 percent a year forever, then what is the current price of one share of the stock?

The current value of the stock is computed as shown below:

= Dividend in year 1 / (1 + required rate of return)1 + Dividend in year 2 / (1 + required rate of return)2 + Dividend in year 3 / (1 + required rate of return)3 + Dividend in year 4/ (1 + required rate of return)4 + 1 / (1 + required rate of return)4[ ( Dividend in year 4 (1 + growth rate) / ( required rate of return - growth rate) ]

= \$ 4.38 / 1.095 + \$ 6.33 / 1.0952 + \$ 0 / 1.0953 + \$ 2.54 / 1.09544 + 1 / 1.09544 x [ (\$ 2.54 x 1.045) / (0.095 - 0.045) ]

= \$ 4.38 / 1.095 + \$ 6.33 / 1.0952 + \$ 0 / 1.0953 + \$ 2.54 / 1.09544 + \$ 53.086 / 1.09544

= \$ 47.97

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