Whatever its shortcomings, the PEG ratio is widely followed. The PEG ratio for the S&P over the last $30$ years typically has fluctuated within the range between I and $1\mathrm{.}5.$

ABC stock has an expected ROE of $12\%$ per year, expected earnings per share of $$2,$ and expected dividends of $$1\mathrm{.}50$ per share. Its market capitalization rate is $10\%$ per year.

a$.$ What are its expected growth rate, its price, and its P$/$E ratio?

b$.$ If the plowback rate were $0\mathrm{.}4,$ what would be the firm's expected dividend per share, growth rate, price, $\frac{P}{E},$ and PEG ratio?

The importance of growth opportunities is most evident in the valuation of start$-$up firms, for example, in the Internet boom of the late $1990$s$.$ Many companies that had yet to turn a profit were valued by the market at billions of dollars. The value of these companies was exclusively growth opportunities. For example, the online auction firm eBay had $1998$ profits of $$2\mathrm{.}4$ million, far less than the $$45$ million profit earned by the traditional auctioneer Sotheby's; yet eBay's market value was more than $10$ times greater: $$22$ billion versus $$1\mathrm{.}9$ billion. As it turns out, the market was quite right to value eBay so much more aggressively than Sotheby's. Its net income in $2019$ was $$2\mathrm{.}5$ billion, more than $20$ times that of Sotheby's.

Of course, when company valuation is determined primarily by growth opportunities, those yalues can be very sensitive to reassessments of such prospects. For example, when Facebook announced slower$-$than$-$expected revenue growth July $26,2018,$ its share price dropped by $19\%$ in one day. The company's market capitalization fell by $$119$ billion, the largest$-$ever one$-$day dollar decline.

As perceptions of future prospects wax and wane, share price can swing wildly, as Facebook illustrates. Growth prospects are intrinsically difficult to tie down; ultimately, however, those prospects drive the value of the most dynamic firms in the economy.

The nearby box contains a simple valuation analysis. Facebook's $2012$ IPO was among the most highly anticipated in decades, and there was widespread speculation about the price at Which it would eventually trade in the stock market. There was considerable disparity among amalysts about what the stock would be worth. The points of contention in their analysis forned on two key questions. First, what was a reasonable projection for the growth rate of Facebook's profits? Second, what multiple of earnings was appropriate to translate an carninge forecast into a price forecast? These are precisely the questions addressed by our stock valiation models.

CONCEPT

$13\mathrm{.}5$

Table $13\mathrm{.}5$ Rio National Corp. summary year$-$end balance sheets $($U$.$S$.$ $ millions$)$

$\backslash$table$[[,2021,2020],[$Cash$,$$$13\mathrm{.}00,$$$5\mathrm{.}87$