**Supernormal growth modelÂ (multi-stage) DDM**

V

_{0}= [{D

_{1}/(1+k

_{e})} +â€¦. +Â {D

_{n}/(1+k

_{e})

^{n}} + {P

_{n}/(1+k

_{e})

^{n}}]

Where P

_{n}= D

_{n+1}/(k

_{e}- g

_{c})

**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**

V

_{0 }= D

_{0}(1+g

_{c}) /(k

_{e }- g

_{c})Â = D

_{1}/(k

_{e }- g

_{c})

**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 k**

_{e}& g_{c}- As difference b/w k
_{e}& g_{c}widens, value of Stock falls.

Â - As difference narrows, value of stock rises.

Â - Small changes in difference between k
_{e}and g_{c}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)]

Â - (1+RR)/[k-RR(ROE)]

Â - (1+RR)/[k+RR(ROE)]

Â - (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.

Â - Constant growth rate, g
_{c}never changes.

Â - k
_{e}must be greater than g_{c}.

**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

Â - ROE

Â - Stock price

Â - All of the above

**Ans:**

All of the above.