Supernormal growth modelÂ (multi-stage) DDM

V0= [{D1/(1+ke)} +â€¦. +Â {Dn/(1+ke)n} + {Pn/(1+ke)n}]

Where Pn= Dn+1/(ke- gc)

Question:
Analyst feels that Gordon Company's earnings & dividend will grow at 25% for two years, after which growth will fall to a market-like rate of 6%. If the projected discount rate is 10% & Gordon's most recently paid dividend was $1, value Brown's stock using the supernormal growth (multistage)Â dividend discount model. Ans: (1.25/1.1) + (1.25/1.1)2 + [(1.25)2(1.06)/(0.1- 0.06)] /(1.1)2 =$36.65
Constant Growth Model

V0 = D0(1+gc) /(ke - gc)Â = D1/(ke - gc)

Question:
A firm has an constant dividend payout ratio of 60% and an expected future growth rate of 7%. What should the firm's expected price-to-earning (P/E) ratio be if the required rate of return on stocks of this type is 15%.

Ans:
Using the earning multiplier model, 0.6/ (0.15 - 0.07) = 7.5X
Critical relationship betweenÂ ke & gc
• As difference b/w ke & gc widens, value of Stock falls.
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• As difference narrows, value of stock rises.
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• Small changes in difference between ke and gc cause large changes in stock's value.
Question:
Which of the following is stock's P/E ratio based on the DDM?
• (1-RR)/[k-RR(ROE)]
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• (1+RR)/[k-RR(ROE)]
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• (1+RR)/[k+RR(ROE)]
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• (1-RR)/[k+RR(ROE)]
Ans:
(1-RR)/[k-RR(ROE)] The earnings multiplier model calculate P/E as follows: payout /( k â€“ g) Substituting term, payout = 1 â€“ RR, & g = ROE(RR)
Critical assumption of infinite period DDM
• Stock continues to pay dividends constant growth rate.
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• Constant growth rate, gc never changes.
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• ke must be greater than gc.
Question:
Holding all other factors constant, which of the following is expected to grow at the same rate as dividends in the infinite period DDM ?
• Sales
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• ROE
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• Stock price
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• All of the above
Ans:
All of the above.