# The Company dividend appears to grow smoothly at a constant rate of 5.5%. Analysts forecast that next year’s dividend should equal \$3.8. Investors require 14% return on this class of stock. What would be the price in 7 years? Use annual compounding.

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The Company dividend appears to grow smoothly at a constant rate of 5.5%. Analysts forecast that next year’s dividend should equal \$3.8. Investors require 14% return on this class of stock. What would be the price in 7 years? Use annual compounding.

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Step 1

Recall the Gordan Growth Model with constant growth. Price at any time t is given by

Pt = Dt+1 / (ke – g)

Where Dt + 1 = expected dividend in the year t + 1

ke = Cost of equity = rate of return required by the investors

g = growth rate in dividends (or earnings)

Step 2

Based on the expression in step 1, it should not take us long to realize that:

The price in 7 years = P7 = D8 / (ke – g)

ke = 14%; g = 5.5%; Expected dividend next year = D1 = \$ 3.8

Hence, D8 = D1 x (1 + g)7 = \$ 3.80 x (1 + 5.5%)7 = \$ 5.53

Step 3

Hence, P7 = D8 / (ke – g) = \$ 5.53 / (14%...

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