Question

Silicon Water Company currently pays a dividend of $1 per share and has a share price of $20. If the dividend was expected to grow at 20 percent for five years and at 10 percent per year thereafter. Now what is the firm's expected or required return on equity?

Answer 1

Year	Expected Dividend
0	1.00
1	1.20
2	1.44
3	1.73
4	2.07
5	2.49
Continuing value of dividends = 2.49*1.1/(r-0.10)
The Value of the share = 20 is the PV of the expected dividends discounted at the required return
So, 20 = 1.2/(1+r)^1+1.44/(1+r)^2+1.73/(1+r)^3+2.07/(1+r)^4+2.49/(1+r)^5+2.74/((r-g)*(1+r)^5))
where r = the required return.
The value of r is to be found out by trial and error, bu sing different values of r such that
the sum of the RHS in the above equation is equal to 20.
Using a discount rate of 18%
= 1.2/(1.18)^1+1.44/(1.18)^2+1.73/(1.18)^3+2.07/(1.18)^4+2.49/(1.18)^5+2.74/((0.18-0.10)*(1.18^5)) =								$       20.23
Using a discount rate of 19%
= 1.2/(1.19)^1+1.44/(1.19)^2+1.73/(1.19)^3+2.07/(1.19)^4+2.49/(1.19)^5+2.74/((0.19-0.10)*(1.19^5)) =								$       17.89
Hence, the required rate lies between 18% and 19%. The value of r can be found out by simple interpolation as
below:
r = 18+(20.23-20.00)/(20.23-17.89) =			18.10	%
CHECK:
= 1.2/(1.181)^1+1.44/(1.181)^2+1.73/(1.181)^3+2.07/(1.181)^4+2.49/(1.181)^5+2.74/((0.181-0.10)*(1.181^5)) =									$                19.97
									Almost $20
									Difference due to approximation