Question

The company has just come up with a new highly profitable product. As a result it plans to retain all earnings for the next 3 years (i.e. b=1) and invest them at a return (R) of 100% per year. After three years the company will go back to its old policy of retaining 60 percent of its earnings and investing them at 20 percent.

1. What will be the new price of the stock?
2. The new PE ratio
3. The new premium for growth?

Answer 1

DIVIDEND GROWTH MODEL

where P = price per share

g = dividend growth rate

1. The price of the stock is dependent upon the prevailing EPS in year 0.

Assuming the EPSo to be $35 and required rate of return from the business (discount rate) to be 30%

EXISTING SCENARIO

Discount rate (r)	30%
Dividend retention ratio (b)	0.6
Dividend growth rate (g)	20%

Do = EPSo*(1-b) = $35*(1-0.6) = $14

Po = Do(1+g)/(r-g) = $14*(1+20%)/(30%-20%) = $168

P/E ratio = 4.8

NEW SCENARIO

Company experiences an abnormal growth of 100% for the next three years and hence, suspends all dividend payments.

Discount rate	30%
Dividend retention ratio (b)	1
Dividend growth rate	100%

	0	1	2	3	4
EPS	35	70	140	280	336
Dividends	14	0	0	0	134
Terminal dividend value					1612.8
Price per share	612
P/E	17.5

Percentage increase in price of stock = 612/168-1 = 264.13%

Percentage increase in P/E ratio = 17.5/4.8-1 = 264.13%

These % increases are independent of the initial EPS value assumption (EPSo was assumed to be $35)

Therefore, assuming discount rate of 30%,

1) The new price of the stock will be 264.13% higher than its previous level.

2) The new P/E ratio will be 17.5

3) If a firm is likely to maintain a few years of 'above-stable' growth rates, an approximate value for the firm can be obtained by adding a premium to the stable growth rate, to reflect the above-average growth in the initial years.

i.e. we try to compute the growth level for the company had there been no other change in the company's dividend payout policy.

Po = Do(1+g)/(r-g)

Po = EPSo*(1-b)*(1+g)/(r-g)

P/E = (1-b)(1+g)/(r-g)

Substituting P/E = 17.5, b = 0.6, r = 30%, we get g = 27.1%

Therefore, premium for growth is 27.1% - 20% = 7.1%