A stock just paid an annual dividend of $1.8. The dividend is expected to grow by 9% per year for the next 4 years. The growth rate of dividends will then fall steadily by 1% per year, from 9% in year 4 to 5% in year 8 and stay at that level forever.

The required rate of return is 12%.

Part 1

What is the expected dividend in 8 years?

Growth rates: g₅ = g₄ - 1% = 0.09-0.01 = 0.08

Dividends: D_t = D_t-1 (1+g_t) D₁ = D₀ (1+g₁) = 1.8 (1+0.09) = 1.962

Table of dividends:

Year t	0	1	2	3	4	5	6	7	8
Growth rate		0.09	0.09	0.09	0.09	0.08	0.07	0.06	0.05
Dividend Dt	1.8	1.962	2.139	2.331	2.541	2.744	2.936	3.112	3.268

Attempt 1/10 for 10 pts.

Part 2

What is the expected stock price in 8 years?

P8 =D8 (1+g)rgP8 =D8 (1+g)r-g

= 3.268(1+0.05)0.120.053.268(1+0.05)0.12-0.05

= 49.02 Part 3

What should be the current stock price?