The Shanghai Stock Exchange composite index on Jan $1,2010$ was at $3289\mathrm{.}75,$

and had a dividend yield of approximately $0\mathrm{.}9\%.$ For simplicity, treat the index

as a stock with P $0=3289\mathrm{.}75$ and D $1=29\mathrm{.}60775.$

The market consensus was that dividends would grow at the rate of g $=0\mathrm{.}106$

or $10\mathrm{.}6\%$ per year, which is equal to the growth rate of nominal GDP in China

in $2010.$ For simplicity, assume that Chinese GDP and dividends on the

Shanghai Stock Exchange composite index both grow at this rate in perpetuity.

a$)$ Based on the date above, what is the implied return of an investment in the

Shanghai Stock Exchange composite index? $(0\mathrm{.}5$ pts$)$

b$)$ If the expected rate of return on Chinese stocks remained at the same level

as you calculated in part a$)$ but the market$$s estimate of the dividend

growth rate decreased to $8\%$ per year $($the growth rate of GDP in $2012),$ the

Shanghai Composite Index will decline. What would be the new value of

the index? $(0\mathrm{.}5$ pts$)$