Linking a required return to a dividend valuation

The case and its answers

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

A fictional company has equity beta 1.4. The analyst assumes a 5% annual risk-free rate and an 11% expected annual market return. The company is expected to pay a dividend of ₹6 per share next year, with stable 5% annual dividend growth thereafter. The current share price is ₹80. Use CAPM to estimate the required equity return and the constant-growth dividend model to value the share. For a separate return check, expected return at the quoted price is next-year dividend yield plus the assumed growth rate. Treat all forecasts as uncertain model inputs and use annual rates consistently.

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

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

1. Q1What required equity return follows CAPM?

   • A

     Option A. 20.40%

     Why it is wrong: This applies beta to the entire market return rather than its premium.

   • B

     Option B. 8.40%

     Why it is wrong: This omits the risk-free component.

   • C

     Option C. 13.40% — Correct answer

   • D

     Option D. 11.00%

     Why it is wrong: This is the market return for a beta-one exposure.

   Answer: C. 5% + 1.4 × (11% − 5%) = 13.40%. Remember: CAPM adjusts the market risk premium for beta.

   Hint, shown before you answer in practice mode: The market premium is 11% minus 5%.

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2. Q2What is the constant-growth dividend value, rounded to two decimals?

   • A

     Option A. ₹120.00

     Why it is wrong: This divides by growth rather than the required-return spread.

   • B

     Option B. ₹71.43 — Correct answer

   • C

     Option C. ₹75.00

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

   • D

     Option D. ₹44.78

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

   Answer: B. ₹6/(0.134 − 0.05) = ₹71.43 per share. Remember: Use a positive required-return-minus-growth spread in a constant-growth model.

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

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3. Q3What expected return does the quoted ₹80 price imply under the supplied yield-plus-growth formula?

   • A

     Option A. 7.50%

     Why it is wrong: This includes dividend yield but omits growth.

   • B

     Option B. 12.50% — Correct answer

   • C

     Option C. 13.40%

     Why it is wrong: This is the CAPM required return, not the return implied by ₹80.

   • D

     Option D. 10.00%

     Why it is wrong: This is not produced by the stated formula.

   Answer: B. ₹6/₹80 × 100 + 5% = 7.50% + 5% = 12.50%. Remember: An expected return implied by price can differ from the required return.

   Hint, shown before you answer in practice mode: Add next-year dividend yield to the assumed growth rate.

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4. Q4Which conclusion follows within this model?

   • A

     Option A. The share is guaranteed to fall immediately.

     Why it is wrong: A model discrepancy does not determine immediate market movement.

   • B

     Option B. At ₹80, expected return is below the required return, so price exceeds the model value. — Correct answer

   • C

     Option C. The dividend is already ₹80.

     Why it is wrong: ₹80 is the share price, not the dividend.

   • D

     Option D. The model proves beta and growth estimates cannot be wrong.

     Why it is wrong: Both are uncertain inputs.

   Answer: B. The estimated return falls short by 0.90 percentage point. The conclusion depends on the chosen forecasts and risk assumptions. Remember: A valuation conclusion is conditional on its inputs and model, not a certainty.

   Hint, shown before you answer in practice mode: Compare 12.50% with 13.40% and ₹80 with the calculated value.

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