The P$/$E ratio for the S&P $500$ describes the value of the index divided by the earnings of the

company in the index, weighted according to market capitalization. The P$/$E ratio changes over

time for two reasons:

Multiple Expansion: Investors are willing to pay a higher price for the same level of

earnings.

Earnings Growth: Firms increase their earnings by reinvesting in and growing their

business.

Find below a table of the price levels and earnings per share of the S&P $500$ index.

a$)$ For each year, compute the earnings growth rate, i$.$e$.,$ the change in EPS year over year.

EPS $\text{'}22$:

EPS $\text{'}21$: $96\mathrm{.}38$

EPS $\text{'}20$:

EPS $\text{'}19$:

b$)$ For the following years, compute the P$/$E ratio of the S&P $500$ index.

P$/$E $\text{'}22$:

P$/$E $\text{'}21$:

P$/$E $\text{'}20$: