A stock just paid an annual dividend of $$2\mathrm{.}4.$ The dividend is expected to grow by $7\%$ per year for the next $4$ years. The growth rate of dividends will then fall steadily by $1\%$ per year, from $7\%$ in year $4$ to $3\%$ 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?

Part $2$

What is the intrinsic value of the stock in $8$ years?

Part $3$

What is the intrinsic value of the stock now?