Question

Consider a firm that is not currently paying any dividends (perhaps because it has been reinvesting earnings into internal projects). The firm’s management is deciding between two plans for the future: Plan (i). Continue to pay no dividends for the next 5 years and continue reinvesting earnings into growing the company. Six years from today, pay a first annual dividend expected to be $0.50 per share. From year six onwards, dividends are expected to growth at a rate of 4% per year. Under this plan, investors’ expected rate of return over the first five years will be 12% and subsequently will be a constant 8%. Plan (ii). Pay a $0.10 dividend today, and grow that dividend at 25% per year for the following five years (note that there are six annual dividends paid including the one made today). After the sixth dividend is paid, slow down the expected dividend growth rate to 4%. Under this plan, investors’ expected rate of return over the first five years will be 10%, and subsequently will be a constant 8%.

(a). What would be the stock’s intrinsic value today if the company implements Plan (i)?

(b). What would be the stock’s intrinsic value today if the company implements Plan (ii)?

Answer 1

1-
Plan 1
Expected dividend in year 7	dividend in Year 6*(1+growth rate)	.5*(1.04)	0.52
terminal value at the end of year 6	expected dividend/(required rate of return-growth rate)	.52/(8%-4%)	13
Year	cash flow	present value of cash flow = cash flow/(1+r)^n r = 8%
6	0.5	0.315085
6	13	8.192205
present value of stock	sum of present value of cash flow	8.51
2-
Plan 2
Year		expected dividend = dividend*(1+growth rate) g = 25% and for year 7 g = 4%
1	0.1	0.1
2	0.1*1.25^1	0.125
3	0.1*1.25^2	0.15625
4	0.1*1.25^3	0.195313
5	0.1*1.25^4	0.244141
6	0.1*1.25^5	0.305176
7	0.3051*1.04	0.317304
Terminal value at year 6	expected dividend/(required rate of return-growth rate)	.3173/(8%-4%)	7.93
Year	cash flow	present value of cash flow = cash flow/(1+r)^n for year 1 to 5 r = 10%   for year 6 r = 8%
1	0.1	0.090909
2	0.125	0.103306
3	0.15625	0.117393
4	0.195313	0.133401
5	0.244141	0.151592
6	0.305176	0.28257
6	7.93	6.80084
present value of stock	sum of present value of cash flow	7.68