The present value of stock is given by
where P = the present value, k = discount rate, D = current dividend and is the revenue growth rate for period i.
If the growth rate is constant for to , then,
The last term corresponts to the terminal case. When the growth rate is always the same for perpetuity, the Gordon's model results:
As the Gordon's model suggests, the valuation is very sensitive to the value of g used.
It is sometimes recommended that revenue growth should be checked to ensure that earnings growth is not coming from special situations like sale of assets.
When the earnings acceleration (rate of change of earnings growth) is positive, it ensures that earnings growth is likely to continue.
According to Economics Robert Shiller, earnings per share on the S&P 500 grew at a 3.8% annualized rate between 1874 and 2004 (inflation-adjusted growth rate was 1.7%). Since 1980, the most bullish period in U.S. stock market history, real earnings growth according to Shiller, has been 2.6%.
The table below gives recent values of earnings growth for S&P 500.
|12/31/2001||1148.08||46.50||-30.8||2001 contraction resulting in P/E Peak|
|12/31/2000||1320.28||26.41||8.6||Dot-com bubble burst: March 10, 2000|
|12/31/1990||330.22||15.47||-6.9||July 1990-March 1991 contraction.|
|12/31/1988||277.72||11.69||.||Bottom (Black Monday was October 19, 1987)|
The Federal Reserve responded to decline in earnings growth by cutting the Intended federal funds rate (from 6.00 to 1.75% in 2001) and raising them when the growth rates are high(from 3.25 to 5.50 in 1994, 2.50 to 4.25 in 2005).
The growth stocks generally command a higher P/E ratio because their future earnings are expected to be greater. In Stocks for the Long Run Seigal examines the P/E ratios of growth and technology stocks. He examined Nifty Fifty stocks for the duration December 1972 to Nov 2001. He found that
|Portfolio||Annualized returns||1972 P/E||Warranted P/E||EPS Growth|
|Nifty Fifty average||11.62%||41.9||38.7||10.14%|
This suggests that the significantly P/E ratio for the Nifty Fifty as a group in 1972 was actually justified by the returns during the next three decades. However, he found that some individual stocks within the Nifty Fifty were overvalued while others were undervalued.
High growth rates cannot be sustained indefinitely. Ben McClure suggests that period for which such rates can be sustained can be estimated using the following:
|Competitive Situation||Sustainable period|
|Not very competitive||1 year|
|Solid company with recognizable brand name||5 years|
|Company with very high barriers to entry||10 years|
It has been suggested that the earnings growth depends on the nominal GDP, since the earnings from a part of the GDP. It has been argued that the earnings growth must must grow slower than GDP by approximately two percent.