Question

9.4     You’re considering buying shares of Kirk’s Information Inc. The company is still in a growth phase, so it won’t pay dividends for the next few years.                                             

Kirk’s accountant has determined that their first year’s earnings per share (EPS) is expected to be $20.

The company expects a return on equity (ROE) of 25% in each of the next five years but in year 6 they expect a ROE of 20%. In year 7 and beyond (indefinitely) it expects to earn a ROE of 15%. Assume that the required return on this investment is 15%.

Also, at the end year 6 and every year thereafter, the company expects to pay dividends at a rate of 70% of earnings, retaining the other 30% in the company.

1. Complete the following table (all values per share):              

Year	Owners’ equity, beginning	EPS	ROE	Owners’ equity, ending	Expected dividend (end of year)
1	80	20	25%	100	0
2	100	100 x 0.25 = 25	25%	125	0
3	125		25%		0
4			25%		0
5			25%		0
6			20%
7			15%
8			15%

2. What would the dividend per share be at the end of year 8 (D₈, from your table above)?      (1 mark)
3. Calculate the value of all future dividends for each share at the beginning of year 8. (Hint: P₇ depends on D₈.)   
4. What is the present value of P₇ for a single share at the beginning of year 1 (i.e., now, at time 0)?          (1 mark)
5. Recall that the value of a share is equal to the present value of all future dividends. What is the value of a single share in the company now, at time 0?                                   (1 mark)

Answer 1

(1) Calculation of owners equity and dividend paid (in $)

Year Owners Equity EPS ROE Owners Equity Dividend Paid

1 80.00 20.00 25% 100.00   0

2 100.00 25.00 25% 125.00 0

3 125.00 31.25 25% 156.25 0

4 156.25 39.06 25% 195.31 0

5 195.31 48.83 25% 244.14 0   

6 244.14 48.83 20% 258.79     34.18

(244.14 + (48.83 - 34.18)) (48.83*70%)

7 258.79 38.82 15% 270.44 27.17

8 270.44 40.57 15% 282.61 28.40

(2) Dividend for year 8 is $28.40 per share.

(3) Value of future dividends = Dividend for year 8

at beginning of year 8 Expected Return-Growth**

= 28.40

0.15-0.045

= $270 per share

**Growth

Growth= Retained earnings*ROE

=30*15%

=4.5%

(4)Present value of P7 at T0

IV0= Present Value of all dividends upto year 7

Year Dividends Present Value Factor @ 15% PV

6 34.18 0.4323 14.776

7 27.17 0.3759 10.213

24.989 ~ 25.00

(5) Present Value of a single share

Answer to (3) + (4)

= 270.00+25.00

= $ 295.00 per share.