Question

Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 21 percent for the next 3 years, with the growth rate falling off to a constant 5 percent thereafter.

If the required return is 8 percent and the company just paid a $1.80 dividend. what is the current share price?

• $97.31

• $95.41

• $92.87

• $93.50

Answer 1

b. $95.41

The stock begins constant growth in Year 4, so we can find the price of the stock in Year 3,one year before the constant dividend growth begins as:

P3 = D0(1 + g1)^3(1 + g2) / (R − g)

P3 = $1.80(1.21)^3(1.05) / (0.08 − 0.05)

P3 = $111.61

The price of the stock today is the PV of the first three dividends, plus the PV of the Year 3 stock price. Theprice of the stock today will be:

P0 = $1.80(1.21)/1.08 + $1.80(1.21)^2/1.08^2 + $1.80(1.21)^3/1.08^3 + $111.61 / 1.08^3

P0 = $95.41