Equity Research puzzles, solved step by step

Puzzles
100
Traced to a firm
19
Topics
11
Hard
30
Topic
All topicsProbability and brainteasers12Expected value and decisions8Market sizing and estimation12Returns and compounding9Valuation riddles12Three statement riddles10EPS and share count9Cost of capital and rates8Growth, mix and unit economics8Mental maths6Data and reasoning traps6
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–2 of 2 · filtered from 100Clear filters
  1. 025Stock A trades at 30 times earnings and is expected to grow earnings 25% a year. Stock B trades at 15 times with 8% expected growth. Which is cheaper on a PEG basis, and what does the PEG ratio leave out?Valuation riddlesWarm upSell-side equity researchLong-only asset management

    Try it first

    Which has the lower PEG?

    Show the worked solution

    A is cheaper on PEG, 1.2 against 1.9, but PEG ignores how long the growth lasts and what it costs. PEG divides the P/E by the growth rate, so it rewards fast growth whatever its duration. If A's 25% lasts only three years, today's price is 15.4 times year-three earnings for A against 11.9 times for B, and A is the dearer stock.

    What does PEG measure?

    Think of two rented flats, one expensive in a fast-improving area and one cheap in a quiet one. Comparing rent per square foot is not enough; you would also ask how quickly each area is improving. PEG does that for stocks. It divides the P/E by the growth rate, so it expresses price per unit of growth: A pays 1.2 times per point of growth, B pays 1.88. A PEG near 1 is often used as a rough marker of fair value, which is a convention, not a law.

    PEG says A is cheaper; it cannot see how long the growth lasts0x10x20x30x40x0%10%20%30%Expected earnings growthPEG = 1 lineA: 30x, 25%, PEG 1.2B: 15x, 8%, PEG 1.9If A's 25% lasts only 3 yearsToday's price over year-3 earnings15.4xStock A11.9xStock BA is still dearer once its growth fades
    Stock A at 30x and 25% growth has a PEG of 1.2 against 1.9 for stock B at 15x and 8%, but if A's fast growth lasts only three years, today's price is 15.4 times A's year-three earnings against 11.9 times for B.

    What does PEG leave out?

    Two things. First, duration: a growth rate is a speed, and PEG ignores how long the speed lasts. If A grows 25% for three years and then slows to B's pace, you are paying 15.4 times its year-three earnings for a company then growing like B, which costs 11.9 times. Second, the cost of growth: a company that must reinvest most of its earnings to grow is worth less than one that grows with little capital, and PEG cannot see the difference.

    P/EGrowthPEGPrice / year-3 earnings
    Stock A30x25%1.215.4x
    Stock B15x8%1.8811.9x
    Year-3 earnings assume each stock grows at its stated rate for three years, with today's price held fixed.

    How a research analyst would use it: as a quick screen across a sector, then replaced by something that sees duration and reinvestment, such as a DCF or a return on capital comparison. The limitation in one line: PEG compares price to the speed of growth, not to its length or its cost.

    Where candidates lose it

    The common loss is picking B because 15x looks cheaper than 30x. The question is about price relative to growth, and on that measure A wins.

    The second, bigger loss is stopping at the PEG. The interviewer asked what it ignores; name duration and the capital growth needs, and give one number that shows duration changing the answer.

    What the interviewer asks next

    • How many years must A grow at 25% before its P/E on those earnings falls to B's current 15x?
    • Why does PEG break down for companies with very low growth?
    • How would return on capital change your view of the two stocks?
  2. 074A stock trades at Rs 400 and its EPS is Rs 20. What are its P/E and its earnings yield, and where does the price go if EPS rises 25% and the P/E stays the same?Valuation riddlesWarm upSell-side equity researchIndian brokerage research

    Try it first

    EPS rises 25% and the P/E holds at 20x. Where is the price?

    Show the worked solution

    A P/E of 20x, an earnings yield of 5%, and a price of Rs 500. P/E is price over EPS, 400 / 20 = 20. The earnings yield is the inverse, EPS over price, 20 / 400 = 5%. If EPS rises 25% to Rs 25 and the market still pays 20 times, the price is 20 x 25 = Rs 500, also 25% higher: at a constant multiple, price moves one for one with earnings.

    What does a P/E of 20 actually say?

    Buy a small shop for Rs 20 lakh that earns Rs 1 lakh a year and you have paid twenty years of today's profit, a 5% return on your price before any growth. A P/E is the number of years of today's earnings you pay for, and its inverse, the earnings yield, is those earnings as a return on the price. Neither says whether the stock is cheap; that depends on how fast the earnings grow and how risky they are.

    At a constant multiple, price moves one for one with earningsEPS 20 x P/E 20price Rs 400+25%+Rs 1002025EPS, Rs20xP/EThree readingsEarnings yield = 20 / 400= 5%, one over the P/EP/E holds at 20x:25 x 20 = Rs 500, +25%P/E falls to 16x:25 x 16 = Rs 400, flatearnings grew, price did not
    Price is the area of EPS times P/E, so a 25% rise in EPS at a constant 20 times widens the rectangle by a quarter from Rs 400 to Rs 500, while a fall in the P/E to 16x would leave the price at Rs 400.
    The relationship
    P=EPS×PE25×20=500EY=120=5%P = \text{EPS} \times \frac{P}{E} \qquad 25 \times 20 = 500 \qquad \text{EY} = \frac{1}{20} = 5\%
    Pshare price
    EPSearnings per share
    P/Ethe multiple the market pays for each rupee of earnings
    EYearnings yield, EPS over price
    What it says in wordsThe price is earnings per share times the multiple, and the earnings yield is one over the multiple.

    When does the price not follow earnings?

    When the multiple moves. If EPS rises 25% but the P/E falls from 20x to 16x, the price does not move at all: 25 x 16 = Rs 400. The price change is the earnings change and the multiple change compounded: 1.25 x 0.8 = 1.0. That is how a company can grow profit for years while its share price stands still, and why analysts separate earnings growth from rerating when they explain a move.

    Why is the earnings yield worth quoting?

    It puts the price on the same scale as other returns. A 5% earnings yield can be set beside a deposit rate or a bond yield, as long as you say what differs: earnings are not all paid out, they can grow, and they are not promised. When bond yields rise above a stock's earnings yield, the case for the stock rests more heavily on growth, which is one reason multiples tend to fall when rates rise.

    Where candidates lose it

    The slip is adding instead of multiplying: taking the extra Rs 5 of EPS, or 25 rupees, onto the Rs 400 price. The market pays twenty rupees for each rupee of earnings, so Rs 5 more of earnings is Rs 100 more of price.

    The quieter loss is saying the earnings yield is a return you receive. It is earnings on price, most of which the company keeps; say that once and the interviewer knows you understand the number.

    What the interviewer asks next

    • EPS rises 25% and the price rises only 10%. What is the new P/E? (17.6x)
    • What P/E corresponds to an earnings yield of 8%?
    • Why might two companies with the same EPS growth trade on very different P/Es?