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SmartDeal Inc. has just paid dividend of $5. The dividend is expected to increase at 16%...

SmartDeal Inc. has just paid dividend of $5. The dividend is expected to increase at 16% for the first 15 years, -6% for the next 10 years and then 2% forever. The required rate of return is 12% for the first 8 years and 20% thereafter. Find its share price today. (Please show your work, and do NOT use Excel to solve)

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Expert Solution

Share price today will be the discounted value of all dividends paid in future. Here D0 = $5, g1 = 16%, g2 = -6% and g3 = 2%.

r1 = 12% and r2 = 20%

Thus dividends in future (using the above mentioned growth rates) will be:

Year Dividend
0 5.00
1 5.80
2 6.73
3 7.80
4 9.05
5 10.50
6 12.18
7 14.13
8 16.39
9 19.01
10 22.06
11 25.59
12 29.68
13 34.43
14 39.94
15 46.33
16 43.55
17 40.94
18 38.48
19 36.17
20 34.00
21 31.96
22 30.04
23 28.24
24 26.55
25 24.95
26 25.45

Now price at the end of 25th year = D26/r-g. In the 26th year r = 20% and g = 2%. Thus P25 = 25.45/(20%-2%) = $141.40

Thus price today = D1/(1.12) + D2/1.12^2....+D8/1.12^8 + D9/1.20^9 + ........D25/1.20^25 + P25/1.20^25

= 5.80/1.12 + 6.73/1.12^2 + ....16.39/1.12^8+19.01/1.20^8+......24.95/1.20^25 + 141.40/1.20^25

= $81.76

jeff jeffy answered 1 year ago
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