Question

In: Finance

The required return for Williamson Heating's stock is 12%, and the stock sells for $40 per...

The required return for Williamson Heating's stock is 12%, and the stock sells for $40 per share. The firm just paid a dividend of $1.00, and the dividend is expected to grow by 25% per year for the next 4 years, so D4 = $1.00(1.25)4 = $2.4414. After t = 4, the dividend is expected to grow at a constant rate of X% per year forever. What is the stock's expected constant growth rate after t = 4, i.e., what is X?

a.6.02%

b.5.44%

c.7.21%

d.5.72%

e.5.17%

Solutions

Expert Solution

Required rate= 12.00%
Year Previous year dividend Dividend growth rate Dividend current year Discount factor Discounted value
1 1 25.00% 1.25 1.12 1.1161
2 1.25 25.00% 1.5625 1.2544 1.24562
3 1.5625 25.00% 1.953125 1.404928 1.3902
4 1.953125 25.00% 2.44140625 1.57351936 1.55156
Sum of discounted value = 5.3
Where
Current dividend =Previous year dividend*(1+growth rate)^corresponding year
Discount factor=(1+ Required rate)^corresponding period
Discounted value=Current year dividend/discount factor

PV of horizon value = current price of shares-Sum of discounted value = 40-5.3 = 34.7

horizon value = PV*(1+required rate)^n = 34.7*(1+0.12)^4=54.6

Horizon value = Year 4dividend* (1 + growth rate )/(cost of equity - growth rate)
54.6 = 2.4414 * (1+Growth rate) / (0.12 - Growth rate)
Growth rate% = 7.21

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