Question

Silicon Wafer Company currently pays a dividend of $1 per share and has a share price of $20. a. If this dividend was expected to grow at a 12 percent rate forever, what is the firm’s expected, or required, return on equity using a dividend discount model approach? b. Instead of the situation in Part (a), suppose that the dividend was expected to grow at a 20 percent rate for five years and at 10 percent per year thereafter. Now, what is the firm’s expected, or required, return on equity?

Answer 1

Part (a) ; Calculation of required return on equity (ke) when dividend growth is 12%

ke = D1/P0 + g

= 1[1.12]/20 + .12 = .176 or 17.6 %

Part (b) ; Calculation of required return on equity (ke) when dividend growth is 20% for 5 years and 10 % thereafter

Return to the shareholders is the IRR of the future cash flows. It is calculated using trial and error method.

Step 1 ; Value of the share if the required rate is say 19%(Guess rate)

YEAR	EVENT	CASH FLOW	PVF @ 19%	DCF
1	D1	1(1.20)^1 = 1.20	.840	1.008
2	D2	1(1.20)^2 = 1.44	.706	1.017
3	D3	1(1.20)^3= 1.728	.593	1.025
4	D4	1(1.20)^4 = 2.074	.499	1.035
5	D5	1(1.20)^5 = 2.488	.419	1.042
5	P5	2.488(1.10)/19%-10% = 30.41	.419	12.74
		Price of share today		17.867

We cannot consider 19 % as IRR because the discounted cash flows does not equal the price today of $20.

Step 2 ; Value of the share if the required rate is say 18%(Guess rate)

YEAR	EVENT	CASH FLOW	PVF @ 19%	DCF
1	D1	1(1.20)^1 = 1.20	.847	1.016
2	D2	1(1.20)^2 = 1.44	..718	1.034
3	D3	1(1.20)^3= 1.728	..609	1.052
4	D4	1(1.20)^4 = 2.074	.516	1.070
5	D5	1(1.20)^5 = 2.488	..437	1.087
5	P5	2.488(1.10)/18%-10% = 34.21	.437	14.950
		Price of share today		20.209

We cannot consider 18% as IRR because the discounted cash flows does not equal the price of $ 20.

Step 3 ; Interpolating to find IRR

IRR (ke) = 18% + [20.209-20]/20.209-17.867 = 18.09 %

Investor who purchased today at $ 20 and receives dividend growing at 20% for five years from 1 and further perpetual growth of 10 5 thereafter will earn a return of 18.09% from the share.