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Module $6$ questions

$1.$ The dividend yield on the S&P $500$ index is currently $1\mathrm{.}5\%$ per year. That

is$,$ if you invest $$100$ in the portfolio of stocks underlying the index,

during the next year you will receive dividends that total to $$1\mathrm{.}50.$

For simplicity, you can think of the index as being a stock with current

price of

P$0$ and dividends of

D$1=0\mathrm{.}015\backslash$times

P$0.$

You are analyzing the link between the dividend payments of the S&P and

the return on your investment. Based on historical information, you

believe that your investment in the S&P $500$ will yield annual returns of

around $11\mathrm{.}5\%.$

a$)$ How fast would dividends have to grow in perpetuity for the S&P $500$ to

give you $11\mathrm{.}5\%$ returns each year? $(1$pt$)$

Hint: What model or formula relates

P$0,$

D$1,$

r$,$ and

g$?$

$2.$ 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$)$

$3.$ Amazon$$s stock price is currently $($Jul $1,2023)$ $$127$ per share with

earnings per share over the next year estimated to be $$2\mathrm{.}57.$ What is the

net present value of its growth opportunities $($per share$)$ if the required

rate of return is $9$ percent? $(1$ pt$)$

Note, for this question, you

may find information from the live session in

Module $6$ useful.

$4.$ On May $9$th$,2023,$ Airbnb $($ABNB$)$ announced that earnings were $$0\mathrm{.}18$ per

share, beating analyst forecasts of $$0\mathrm{.}10,$ additionally actual revenue was

$$1\mathrm{.}82$ billion, beating forecasts of $$1\mathrm{.}79$billion. However, the stock price

fell from $$126\mathrm{.}60$ on May $9$ to $$109\mathrm{.}85$ on May $10.$ Does this example indicate

that markets are not efficient? Explain your answer. $(1$ pt$)$