Relative valuation and a dividend model

The case and its answers

Every question of this case, with its answer and why each other option is wrong.

An analyst compares Alpha and Beta, two fictional businesses. Alpha trades at ₹300 with current EPS ₹20 and forecast EPS growth of 10% a year. Beta trades at ₹200 with EPS ₹10 and forecast growth of 20%. For this exercise PEG equals P/E divided by the growth percentage expressed as a whole number, such as 10 rather than 0.10. A separate stable company, Gamma, is expected to pay a dividend of ₹12 next year, followed by constant 4% annual growth. Its required equity return is 10%. The forecasts are assumptions. Business quality, forecast risk and capital needs may differ among companies.

All people, firms, prices and contract terms are fictional.

Ignore taxes and transaction costs unless the case explicitly includes them.

1. Q1What is Alpha’s P/E multiple?

   • A

     Option A. 20 times

     Why it is wrong: This is Beta’s P/E.

   • B

     Option B. 10 times

     Why it is wrong: This is Alpha’s growth percentage, not P/E.

   • C

     Option C. 15 times — Correct answer

   • D

     Option D. 0.067 times

     Why it is wrong: This reverses EPS and price.

   Answer: C. ₹300 ÷ ₹20 = 15 times. Remember: A P/E multiple compares share price with earnings on the same per-share basis.

   Hint, shown before you answer in practice mode: Divide Alpha’s price by its EPS.

   XV-S2-C03-Q1easynumerical

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2. Q2What is Alpha’s PEG under the supplied convention?

   • A

     Option A. 150

     Why it is wrong: This divides by 0.10 rather than the stated whole-number growth rate.

   • B

     Option B. 1.50 — Correct answer

   • C

     Option C. 0.67

     Why it is wrong: This reverses growth and P/E.

   • D

     Option D. 1.00

     Why it is wrong: This is Beta’s PEG under these inputs.

   Answer: B. Alpha’s PEG = 15/10 = 1.50. Beta’s is (200/10)/20 = 1.00. Remember: Ratio conventions must be consistent before comparing companies.

   Hint, shown before you answer in practice mode: Use the explicit convention for the growth denominator.

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3. Q3What value does Gamma’s constant-growth dividend model produce?

   • A

     Option A. ₹200 — Correct answer

   • B

     Option B. ₹208

     Why it is wrong: This grows the already next-year dividend a second time.

   • C

     Option C. ₹300

     Why it is wrong: This uses an unsupported discount-rate spread.

   • D

     Option D. ₹120

     Why it is wrong: This ignores the growth adjustment in the denominator.

   Answer: A. ₹12 ÷ (0.10 − 0.04) = ₹200. The required return exceeds growth, as this model needs. Remember: Distinguish next-year dividend from the last dividend paid.

   Hint, shown before you answer in practice mode: Use next-year dividend divided by required return minus growth.

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4. Q4Does Beta’s lower PEG alone prove that Beta is a better investment?

   • A

     Option A. No. The growth estimate, risk and business quality also need examination. — Correct answer

   • B

     Option B. Yes, because a lower ratio removes valuation risk.

     Why it is wrong: A ratio does not remove forecast or business risks.

   • C

     Option C. No, because relative valuation can never be useful.

     Why it is wrong: It can inform analysis when its limitations are understood.

   • D

     Option D. Yes, because all forecast growth rates are certain.

     Why it is wrong: The case explicitly treats forecasts as assumptions.

   Answer: A. Beta’s ratio may justify further research, but the reliability and durability of growth and other differences must be assessed before a conclusion. Remember: A valuation multiple is evidence to interpret, not a complete investment decision.

   Hint, shown before you answer in practice mode: A ratio compresses assumptions rather than validating them.

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