## Monday, September 10, 2018

### Financial Ratio Math

How can one use forward and trailing PE ratios and PEG ratios to measure projected growth of earnings?

Question:   The table below has information on the trailing PE ratio, the forward PE ratio, and the PEG ratio for four firms.  Two of the firms AAPL and AMZN are considered growth firms.   Two of the firms GS and NEE are value firms.

 Financial Ratios for Four Firms Trailing PE Forward PE PEG APPL 20.05 16.31 1.46 AMZN 154.59 76.94 2.46 GS 18.68 9.21 0.3 NEE 9.96 20.56 2.37

Show how these three financial ratios can be used to measure expected earnings growth?

Discussion:

These financial statistics can be used to create three measures of earnings growth.

Caution: The growth measures only make sense when earnings is positive.  The PE ratio is a nonsensical statistic when earnings are negative.  Also, when earning are very close to 0 the PE ratio will be very large and earnings growth estimate will be sensitive to small changes in earnings.

The first growth measure is based on the ratio of trailing PE to forward PE.  This ratio simplifies to EF/ET where EF is forward earnings and ET trailing earnings because the same stock price is in the numerator of both PE ratios.

It follows that 100*((EF/ET) -1) is the projected growth rate in earning because EF is projected earnings next year and ET is earnings in the current year.

The second measure of projected growth is the ratio of the trailing PE ratio to the PEG ratio.  The third projected growth ratio is the ratio of the forward PE ratio to the PEG ratio.

The PEG ratio is defined as PE ratio divided by growth in earnings over some period.   The ratio of PE to PE over growth in earnings simplifies to growth in earnings.

I don’t know whether the reported PEG ratios in yahoo finance, the source of my data, use trailing or forward PE.  Also, I don’t know the time frame of the earnings growth used in the denominator of the PEG.

My approach is to present all three measures of projected growth for the four firms.

Calculations:

Here are my calculations of the three projected growth statistics for the four stocks.

 Projected Growth Rate in Earnings Trailing PE to Forward PE Trailing PE to PEG Forward PE to PEG APPL 22.9 13.7 11.2 AMZN 100.9 62.8 31.3 GS 102.8 62.3 30.7 NEE -51.6 4.2 8.7

Observations on the growth projections

On all three measures AMZN and GS are virtually tied as having the highest projected growth rates in earnings.  The rank orders of the projected growth estimates for the four companies, while not identical, are similar.

One company NEE (Nextera Energy) has projected negative growth because the forward earnings estimate is less than current earnings estimate.

The ratio of trailing to forward PE ratios lead to the higher projected growth rate for three of the four companies.   The one exception is NEE.

Concluding Remarks:

These projected growth statistics can be used to measure expectations in the market. Large projected growth in earnings could indicate that analysts are excessively optimistic.   This currently appears to be the case for several highly-traded tech firms.

Go to my finance blog for an example looking at these ratios for a comparison between PE ratios from a growth ETF and a value ETF.   The results are somewhat surprising.  Most analysts are concerned about the valuation of tech stocks but the negative PE ratio of a significant number of value firms appears to be a larger concern.

https://financememos.com/2018/09/12/valuation-of-growth-and-value-stocks-with-pe-ratios/