In: Finance
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%
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 |