Question

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%

Answer 1

	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