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XYZ company presently pays a dividend of $ 1.50 per share on its common stock. The...

XYZ company presently pays a dividend of $ 1.50 per share on its common
stock. The company expects to increase the dividend at a 20% annual rate the
first four years and at the rate of 13% at the next four years then the growth on
the dividend at a 7% thereafter. This phased growth patterns is in keeping with
the expected life cycle of earnings. You are required a 16% return to invest in
this stock. What value should you place on a share of this Stock?

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Expert Solution

Required rate= 16.00%
Year Previous year dividend Dividend growth rate Dividend current year Horizon value Total Value Discount factor Discounted value
1 1.5 20.00% 1.8 1.8 1.16 1.5517
2 1.8 20.00% 2.16 2.16 1.3456 1.60523
3 2.16 20.00% 2.592 2.592 1.560896 1.66058
4 2.592 20.00% 3.1104 3.1104 1.81063936 1.71785
5 3.1104 13.00% 3.514752 3.514752 2.100341658 1.67342
6 3.514752 13.00% 3.97166976 3.97166976 2.436396323 1.63
7 3.97166976 13.00% 4.487986829 4.487986829 2.826219735 1.58798
8 4.487986829 13.00% 5.071425117 60.294 65.36542512 3.278414892 19.93812
Long term growth rate (given)= 7.00% Value of Stock = Sum of discounted value = 31.37
Where
Current dividend =Previous year dividend*(1+growth rate)^corresponding year
Total value = Dividend + horizon value (only for last year)
Horizon value = Dividend Current year 8 *(1+long term growth rate)/( Required rate-long term growth rate)
Discount factor=(1+ Required rate)^corresponding period
Discounted value=total value/discount factor

jeff jeffy answered 2 years ago
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