Question

Assume Gillette Corporation will pay an annual dividend of

$0.62

one year from now. Analysts expect this dividend to grow at

12.7%

per year thereafter until the

44th

year.​ Thereafter, growth will level off at

2.2%

per year. According to the​ dividend-discount model, what is the value of a share of Gillette stock if the​firm's equity cost of capital is

8.6%​?

Answer 1

Price of Stock = PV of Cashflows from it.

Div Calculation:

Year	CF	Formula	Calculation
1	$      0.62	Given	Given
2	$      0.70	D1(1+g)	0.62*(1.127)
3	$      0.79	D2(1+g)	0.7*(1.127)
4	$      0.89	D3(1+g)	0.79*(1.127)
5	$      1.00	D4(1+g)	0.89*(1.127)
6	$      1.13	D5(1+g)	1*(1.127)
7	$      1.27	D6(1+g)	1.13*(1.127)
8	$      1.43	D7(1+g)	1.27*(1.127)
9	$      1.61	D8(1+g)	1.43*(1.127)
10	$      1.82	D9(1+g)	1.61*(1.127)
11	$      2.05	D10(1+g)	1.82*(1.127)
12	$      2.31	D11(1+g)	2.05*(1.127)
13	$      2.60	D12(1+g)	2.31*(1.127)
14	$      2.93	D13(1+g)	2.6*(1.127)
15	$      3.31	D14(1+g)	2.93*(1.127)
16	$      3.73	D15(1+g)	3.31*(1.127)
17	$      4.20	D16(1+g)	3.73*(1.127)
18	$      4.73	D17(1+g)	4.2*(1.127)
19	$      5.33	D18(1+g)	4.73*(1.127)
20	$      6.01	D19(1+g)	5.33*(1.127)
21	$      6.77	D20(1+g)	6.01*(1.127)
22	$      7.63	D21(1+g)	6.77*(1.127)
23	$      8.60	D22(1+g)	7.63*(1.127)
24	$      9.70	D23(1+g)	8.6*(1.127)
25	$   10.93	D24(1+g)	9.7*(1.127)
26	$   12.32	D25(1+g)	10.93*(1.127)
27	$   13.88	D26(1+g)	12.32*(1.127)
28	$   15.64	D27(1+g)	13.88*(1.127)
29	$   17.63	D28(1+g)	15.64*(1.127)
30	$   19.87	D29(1+g)	17.63*(1.127)
31	$   22.39	D30(1+g)	19.87*(1.127)
32	$   25.24	D31(1+g)	22.39*(1.127)
33	$   28.44	D32(1+g)	25.24*(1.127)
34	$   32.05	D33(1+g)	28.44*(1.127)
35	$   36.12	D34(1+g)	32.05*(1.127)
36	$   40.71	D35(1+g)	36.12*(1.127)
37	$   45.88	D36(1+g)	40.71*(1.127)
38	$   51.71	D37(1+g)	45.88*(1.127)
39	$   58.28	D38(1+g)	51.71*(1.127)
40	$   65.68	D39(1+g)	58.28*(1.127)
41	$   74.02	D40(1+g)	65.68*(1.127)
42	$   83.42	D41(1+g)	74.02*(1.127)
43	$   94.01	D42(1+g)	83.42*(1.127)
44	$ 105.95	D43(1+g)	94.01*(1.127)
45	$ 108.29	D44(1+g)	105.95*1.022

P44 = D45 / [ Ke - g ]

= 108.29 / [ 8.6% - 2.2% ]

= 108.29 / 6.4%

= 1692.03

Price Today:

Year	CF	PVF @8.6%	Disc CF
1	$        0.62	0.9208	$      0.57
2	$        0.70	0.8479	$      0.59
3	$        0.79	0.7807	$      0.62
4	$        0.89	0.7189	$      0.64
5	$        1.00	0.6620	$      0.66
6	$        1.13	0.6096	$      0.69
7	$        1.27	0.5613	$      0.71
8	$        1.43	0.5168	$      0.74
9	$        1.61	0.4759	$      0.77
10	$        1.82	0.4382	$      0.80
11	$        2.05	0.4035	$      0.83
12	$        2.31	0.3716	$      0.86
13	$        2.60	0.3421	$      0.89
14	$        2.93	0.3151	$      0.92
15	$        3.31	0.2901	$      0.96
16	$        3.73	0.2671	$      1.00
17	$        4.20	0.2460	$      1.03
18	$        4.73	0.2265	$      1.07
19	$        5.33	0.2086	$      1.11
20	$        6.01	0.1920	$      1.15
21	$        6.77	0.1768	$      1.20
22	$        7.63	0.1628	$      1.24
23	$        8.60	0.1499	$      1.29
24	$        9.70	0.1381	$      1.34
25	$      10.93	0.1271	$      1.39
26	$      12.32	0.1171	$      1.44
27	$      13.88	0.1078	$      1.50
28	$      15.64	0.0993	$      1.55
29	$      17.63	0.0914	$      1.61
30	$      19.87	0.0842	$      1.67
31	$      22.39	0.0775	$      1.74
32	$      25.24	0.0714	$      1.80
33	$      28.44	0.0657	$      1.87
34	$      32.05	0.0605	$      1.94
35	$      36.12	0.0557	$      2.01
36	$      40.71	0.0513	$      2.09
37	$      45.88	0.0472	$      2.17
38	$      51.71	0.0435	$      2.25
39	$      58.28	0.0401	$      2.33
40	$      65.68	0.0369	$      2.42
41	$      74.02	0.0340	$      2.51
42	$      83.42	0.0313	$      2.61
43	$      94.01	0.0288	$      2.71
44	$    105.95	0.0265	$      2.81
44	$ 1,692.03	0.0265	$   44.86
Price Today			$ 106.97

= $ 108.29 / [