Suppose a firm's dividends are expected to grow at a rate of 15% (g1) for 3 years (t) then stabilize at 5% (g2) forever. If the firm just paid a $2.00 (D0) dividend and the discount rate is 10% (r), what is the value of a share of the firm's stock in year 3 (P3) ? (Do not round your intermediate calculation.)

The answer is: $63.88

Explanation:

First we calculate the dividends paid at year 3 will be:

- dividends year 3 = $2 x (1 + g1) ³ = $2 x 1.15³ = $2 x 1.52 = $3.04

Then we calculate the dividends paid at year 4 will be:

- dividends year 4 = $3.04 x (1 + g2) = $3.04 x 1.05 = $3.19

Finally, to calculate the value of the stock at year 3 we can use the perpetuity formula:

Price at year 3 = D4 / (r - g2)

D4 = $3.19 r = 10% g2 = 5%

P3 = $3.19 / (10% - 5%) = $3.19 / 5% = $63.88