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.                                             (10 marks)

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):              (5 marks)

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.)   (2 marks)
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

A.

Column Reference No	E	F	G	H	I	J		K
Row Reference No	Year	Owner's Equity beginning	EPS	Formula Used	ROE	Owner Equity Ending	Formula Used	Expected Dividend ( end of the year)	Formula Used	Discounting Factor @ 15%	Present Value Of Dividend (at time 0)	Formula Used
7	1	80.00	20.00		25%	100.00	F7+G7	0.00		0.870
8	2	100.00	25.00	(G7*I7)+G7	25%	125.00	F8+G8	0.00		0.756
9	3	125.00	31.25	G8*I8)+G8	25%	156.25	F9+G9	0.00		0.658
10	4	156.25	39.06	(G9*I9)+G9	25%	195.31	F10+G10	0.00		0.572
11	5	195.31	48.83	(G10*I10)+G10	25%	244.14	F11+G11	0.00		0.497
12	6	244.14	61.04	(G11*I11)+G11	20%	305.18	F12+G12	49.14	61.04*70%*(1.15)	0.432	21.24	G12*70%*(1.15)
13	7	305.18	73.24	(G12*I12)+G12	15%	378.42	F13+G13	56.51	61.04*70%*(1.15)^2	0.376	21.24	L12*1.15
14	8	378.42	84.23	(G13*I13)+G13	15%	462.65	F14+G14	64.98	61.04*70%*(1.15)^3	0.327	21.24	L13*1.15
TOTAL								170.63			63.73

What would the dividend be in year 8? 42.71 (1.15)^3 = 64.98

B.Calculate the value of all future dividends for each share at the beginning of year 8. (Hint: P7 depends on D8.

ANS :63.73 , 170.63

c. What is the present value of P7 for a single share at the beginning of year 1 (i.e., now, at time 0)?

ANS : 25