IBM will pay its first dividend of 1.00, two years from today. The dividends will grow...

IBM will pay its first dividend of 1.00, two years from today. The dividends will grow at a rate of 5% per annum until the 7th year. After that, the dividends will grow at a rate of 3% until the end of the 15th year.After that the dividends will grow at a rate of 2% forever. Of return of IBM stock is 10% per annual what should be the Pv of the stock?

Expert Solution

Dividend and its present value
Year	Dividend	PVF at 10%	Present value
1	0	0.909091	0
2	1	0.826446	0.826446
3	1.05	0.751315	0.788881
4	1.1025	0.683013	0.753022
5	1.157625	0.620921	0.718794
6	1.215506	0.564474	0.686122
7	1.276282	0.513158	0.654934
8	1.31457	0.466507	0.613257
9	1.354007	0.424098	0.574231
10	1.394627	0.385543	0.537689
11	1.436466	0.350494	0.503473
12	1.47956	0.318631	0.471433
13	1.523947	0.289664	0.441433
14	1.569665	0.263331	0.413342
15	1.616755	0.239392	0.387038
Present value of dividend			8.37

Expected dividend of Year-16 = 1.62 + 2% = 1.65
Horizon Value = Expected dividend /(Required rate-growth rate)
	1.65 / (10-2)% = 20.63 per share

Present value of horizon value = 20.63 *0.239392 = 4.94

Price of Stock = 8.37 +4.94 = 13.31

Answer is $ 13.31

jeff jeffy answered 1 year ago

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