Questions: Price-to-Earnings Ratio and Relative Valuation

Question 1

A technology company trades at a P/E ratio of 45, while a utility company trades at a P/E of 14. An analyst concludes the tech company is severely overvalued. What critical information is missing from this comparison?

• A. The names of the companies and the year the ratio was calculated
• B. The expected earnings growth rate and required return for each company — a high P/E may be fully justified by high growth expectations or lower risk
• C. Whether the utility company pays dividends
• D. The total number of shares outstanding for each company

Answer: (B)

From the justified P/E formula (P/E = payout ratio / (r − g)), a high P/E can reflect high expected growth (large g), low required return (small r), or generous payout policy — none of which imply overvaluation. Technology companies often have high growth expectations that mathematically justify high multiples. Comparing raw P/E across sectors without examining the underlying growth and risk assumptions confuses the symptom (high multiple) with the diagnosis (overvaluation).

Question 2

According to the Gordon Growth Model derivation of the justified P/E, which of the following changes would cause a stock's P/E ratio to increase, all else equal?

• A. An increase in the required rate of return r
• B. A decrease in the expected earnings growth rate g
• C. A decrease in the payout ratio
• D. An increase in the expected earnings growth rate g

Answer: (D)

The justified P/E = payout ratio / (r − g). Increasing g reduces the denominator (r − g), which increases the ratio. This is why high-growth firms command high P/E multiples — the market is pricing in rapid future earnings growth. Conversely, increasing r (higher required return, implying more risk) raises the denominator and reduces the P/E. Understanding this formula explains most sector-level P/E differences without invoking irrationality.

Question 3

A stock with a low P/E ratio is typically a better investment than one with a high P/E ratio, because you are paying less for each dollar of earnings.

• T. True
• F. False

Answer: False

False. A low P/E may reflect low growth expectations, elevated risk, or structural industry decline — not undervaluation. From the justified P/E formula, a low P/E arises when r is high (risky company) or g is low (slow-growing or declining company). These are reasons to demand a lower price, not signals of a bargain. 'Value traps' — cheap stocks that stay cheap because fundamentals are genuinely poor — are the graveyard of investors who use P/E in isolation without examining what drives the multiple.

Question 4

The P/E ratio alone cannot determine whether a stock is overvalued or undervalued — that judgment requires understanding what growth and risk assumptions would justify the current multiple.

• T. True
• F. False

Answer: True

True. The justified P/E formula (P/E = payout ratio / (r − g)) shows that the correct P/E depends on growth expectations and required return, which differ across firms, sectors, and time periods. A P/E of 30 may be undervalued for a company with 20% annual earnings growth, and a P/E of 10 may be overvalued for a company in structural decline. Valuation requires comparing the actual P/E to what the fundamentals justify — the multiple alone conveys nothing without context.

Question 5

Why can a high P/E ratio be fully rational and not indicate overvaluation? Use the Gordon Growth Model derivation to explain.

Model answer: The justified P/E derived from the Gordon Growth Model is P/E = payout ratio / (r − g). A high P/E is rational when the expected growth rate g is high (a large g shrinks the denominator, producing a high P/E) or when the required return r is low (less risk demands less return, also shrinking the denominator). A technology company with high expected annual earnings growth will have a high justified P/E; paying 40× earnings for it may be fair value, not speculation. Overvaluation occurs when the actual P/E exceeds what growth and risk can justify — not simply when the P/E is numerically high.

The formula reveals the P/E as a compressed summary of growth and risk assumptions. The error of treating high P/E as overvaluation ignores that different companies have different growth trajectories and risk profiles. The right question is always: what growth rate and risk level would justify this P/E, and are those inputs reasonable given what I know about the company?