Question

The risk-free rate is 1.15% and the market risk premium is 6.74%. A stock with a β of 1.31 just paid a dividend of $1.40. The dividend is expected to grow at 22.68% for three years and then grow at 4.35% forever. What is the value of the stock?

Answer 1

Calculation of required return:
Required return= Risk free rate+beta*market risk premium
=1.15+1.31*6.74= 9.98%
Calculation of current price:
Year	Cashflows	PVF @9.98%	Present value
1	1.72	0.909	1.56
2	2.11	0.827	1.74
3	2.58	0.752	1.94
3	47.82	0.752	35.96
Total			41.21
Current price is $41.21
Working:
Calculation of dividend:
Year 1= dividend*(1+growth)= 1.40*1.2268= 1.72
Year 2= 1.72*1.2268= 2.11
Year 3= 2.11*1.2268= 2.58
Terminal value= Dividend(1+growth)/(return-growth)
=2.58*(1+0.0435)/(0.0998-0.0435)
=2.6922/0.0563= 47.82