Question

No 1. CiMob LLC is currently growing rapidly and increasing its share on the market. So, it is expected to have 4 years more of above industry growth. The growth rate during 4 years will be such that return on equity this period will be 12%. After this period of extra growth, the competition on the market from main competitors (YX LLC and Ur LLC) increases and the possibilities to increase market share will exhaust. So, the desire to continue the increase of the share and make the growth rate higher than the growth rate of the market due to large investments will lead to low return on equity. In 4 years the industry will bring on average 14% of accounting return on equity forever. Last year EPS was $12. Book equity per share at the beginning of the last year was 100. CiMob's managers have been consistently paying half of its profits to shareholders and will keep payout ratio at this level during the whole life of the company. The decision not to change payout policy after 4 years was dictated by the main priority of shareholders - not to loose and not to rise the share of the market after rapid growth during 4 years when competition was week. a) Fill in the gaps of the table below. O 100 12 0,14 Parameter Year BE per share EPS Growth rate of EPS ROE Payout Plowback Retained eps Dividend per share Plowback*ROE 0,12 0,50 0,12 0,50 0,12 0,50 0,12 0,50 0,14 0,50 0,50 | b) Find the price of the stock of CiMob LLC if required return on equity is 12%. c) Are there any differences between Growth rate of EPS and Plowback*ROE? Explain if there are any. Now assume that in 4 years the growth rate of the industry remains the same but the industry will bring on average not 14% but 12% of accounting return on equity forever. In order not to change the share of the market CiMob LLC is forced to change its dividend policy. The payout ratio after 4 years will be 41.66667% and will be kept at this level during the whole life of the company.

Answer 1

Solution:

We have following information with us:

Last year EPS = $12

Book Equity per share = $100

By putting this value in ROE formula = Net Income per share / Book Equity per share

Last year ROE is = 12/100 = 0.12\

=> Alternatively ROE is calculated as = Dividend growth rate divided by earning retention rate (Plawback ratio)

Plowback ratio = 1 - (dividend payout ratio)

Thus, Dividend growth rate from year 1 would be = ROE * Plowback ratio

For year 1-6, Dividend growth rate is = 12% * (1-0.5) = 6%

=> Dividend Payout ratio = Dividend Per Share / EPS

Thus, using this formula for year 1 EPS will be = 6.36/0.5 = 12.72

=> ROE = EPS divided by Book Equity per share

Thus, Book Equity per share = EPS divided by ROE

For year 1, value would be = 12.72 / 0.12 = 106

=> Retained EPS is = EPS minus Dividend payout

for year 1 is = 12 - 6 = 6

a) Using all these formula you can derive following missing details:

Parameters \ Year	0	1	2	3	4	5	6
Book Equity Per Share	100.00	106.00	112.36	119.10	126.25	115.79	123.89
EPS	12.00	12.72	13.48	14.29	15.15	16.21	17.34
EPS Growth rate		6.00%	6.00%	6.00%	6.00%	7.00%	7.00%
Return on Equity	0.12	0.12	0.12	0.12	0.12	0.14	0.14
Dividend Payout ratio	0.50	0.50	0.50	0.50	0.50	0.50	0.50
Dividend growth rate		6.00%	6.00%	6.00%	6.00%	7.00%	7.00%
Dividend Per Share	6.00	6.36	6.74	7.15	7.57	8.11	8.67
Share price	12.00	12.72	13.48	14.29	15.15	16.21	17.34
Plawback ratio	0.50	0.50	0.50	0.50	0.50	0.50	0.50
Retained EPS	6.00	6.36	6.74	7.15	7.57	8.11	8.67
Plawback ratio*ROE (this means Dividend per share divided by Book Equity per share)	6.00%	6.00%	6.00%	6.00%	6.00%	7.00%	7.00%

b) Stock price is mentioned above.
c) There is no difference between EPS growth rate and Plawback * ROE as dividend payout was remained 0.5b) Price of the stock is mentioned above

d) Using the above formula and changing details for EPS and dividend payout one can find following details:

Parameters \ Year	0	1	2	3	4	5	6
Book Equity Per Share	100.00	106.00	112.36	119.10	126.25	162.10	173.45
EPS	12.00	12.72	13.48	14.29	15.15	19.45	20.81
EPS Growth rate		6.00%	6.00%	6.00%	6.00%	28.40%	7.00%
Return on Equity	0.12	0.12	0.12	0.12	0.12	0.12	0.12
Dividend Payout ratio	0.50	0.50	0.50	0.50	0.50	0.42	0.42
Dividend growth rate		6.00%	6.00%	6.00%	6.00%	7.00%	7.00%
Dividend Per Share	6.00	6.36	6.74	7.15	7.57	8.11	8.67
Share price	12.00	12.72	13.48	14.29	15.15	16.21	17.34
Plawback ratio	0.50	0.50	0.50	0.50	0.50	0.58	0.58
Retained EPS	6.00	6.36	6.74	7.15	7.57	11.35	12.14
Plawback ratio*ROE (this means Dividend per share divided by Book Equity per share)	6.00%	6.00%	6.00%	6.00%	6.00%	7.00%	7.00%

f) There is no difference between EPS growth rate and Plawback * ROE

g) ROE is calculated as = Dividend growth rate divided by earning retention rate (Plawback ratio)

Plowback ratio = 1 - (dividend payout ratio)

Thus, ROE = Dividend growth rate / 1- dividend payout ratio

if dividend growth rate is constant than EPS growth rate will be constant in dividend payout ratio