Question

Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next nine years because the firm needs to plow back its earnings to fuel growth. The company will pay a $10 per share dividend 10 years from today and will increase the dividend by 5 percent per year thereafter. If the required return on this stock is 11.5 percent, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

For the First Nine Year growth is Zero and dividend is Capitalized.

As per dividend discount Model

D1 = the estimated value of next year's dividend
r = the company's cost of equity capital
g = the constant growth rate for dividends, in perpetuity
Using these variable, the equation for the GGM is:

Price per Share = D1 / (r - g)

Value of Stock = Dividend Per Share / (Discount Rate - Dividend Growth Rate)
= 10/(0.115-0.05)
= 153.8461538461538

However, this Price will be on 10th Year

The discounting rate for the 10th Year = 1/(1+r)^10
= 0.3367

By Discounting = 153.846*0.3367 = 51.80098

Answer is 51.80

Below explantion is for better understanding :

We can also use Bais Derivation of DDM Model:

As per which the
Price of the Stock is P = Div (1+r) + Div (1+g)/ (1+r)^2+ Div (1+g)2/ (1+r)^3 ......................Infinity

Please see the below table, which I have calculated till 50 Years, The Sum of discounted value of dividend works out at 52.8.

1	Year 1	-	0.896860987	-
2	Year 2	-	0.804359629	-
3	Year 3	-	0.721398771	-
4	Year 4	-	0.646994413	-
5	Year 5	-	0.580264048	-
6	Year 6	-	0.520416186	-
7	Year 7	-	0.466740974	-
8	Year 8	-	0.418601771	-
9	Year 9	-	0.375427597	-
10	Year 10	10.0	0.336706365	3.4
11	Year 11	10.5	0.301978803	3.2
12	Year 12	11.0	0.270833007	3.0
13	Year 13	11.6	0.242899558	2.8
14	Year 14	12.2	0.217847137	2.6
15	Year 15	12.8	0.195378598	2.5
16	Year 16	13.4	0.175227442	2.3
17	Year 17	14.1	0.157154657	2.2
18	Year 18	14.8	0.140945881	2.1
19	Year 19	15.5	0.126408861	2.0
20	Year 20	16.3	0.113371176	1.8
21	Year 21	17.1	0.101678185	1.7
22	Year 22	18.0	0.091191197	1.6
23	Year 23	18.9	0.081785827	1.5
24	Year 24	19.8	0.073350518	1.5
25	Year 25	20.8	0.065785218	1.4
26	Year 26	21.8	0.059000195	1.3
27	Year 27	22.9	0.052914973	1.2
28	Year 28	24.1	0.047457375	1.1
29	Year 29	25.3	0.042562668	1.1
30	Year 30	26.5	0.038172797	1.0
31	Year 31	27.9	0.034235692	1.0
32	Year 32	29.3	0.030704657	0.9
33	Year 33	30.7	0.027537809	0.8
34	Year 34	32.3	0.024697586	0.8
35	Year 35	33.9	0.022150301	0.8
36	Year 36	35.6	0.019865741	0.7
37	Year 37	37.3	0.017816808	0.7
38	Year 38	39.2	0.0159792	0.6
39	Year 39	41.2	0.014331121	0.6
40	Year 40	43.2	0.012853024	0.6
41	Year 41	45.4	0.011527375	0.5
42	Year 42	47.6	0.010338453	0.5
43	Year 43	50.0	0.009272155	0.5
44	Year 44	52.5	0.008315834	0.4
45	Year 45	55.2	0.007458147	0.4
46	Year 46	57.9	0.006688922	0.4
47	Year 47	60.8	0.005999033	0.4
48	Year 48	63.9	0.005380298	0.3
49	Year 49	67.0	0.00482538	0.3
50	Year 50	70.4	0.004327695	0.3