Question

New Age Dyes (NAD), has been a successful producer of natural dye products for the last 10 years ... New Age Dyes (NAD), has been a successful producer of natural dye products for the last 10 years with 50 million shares outstanding and a beta of 1.2. At the latest 2017 AGM, the directors of NAD announced that there will be a dividend of £2.50 in 2018. The dividend is expected to grow at 6% annually for the following 3 years, until 2021, and from 2022 it is expected to remain constant.

1.2 IfNADhasaCostofDebt=6%,aCostofequity=12.1%andhasa debt/equity ratio of 40%. Calculate the after-tax weighted average cost of capital (WACC) given the current corporation tax rate is sitting at 19%.

1.3 SuzyQ, and PeterZ are producers of leather products. Both companies are in competition for all large contracts appearing in the market. The expected return on SuzyQ shares is 25.16% with a beta of 1.2, while the expected return on PeterZ is 20.4% with a beta of 0.9. If we can fully explain the differences in the share price by the Capital Asset Pricing Model (CAPM), determine the expected return of the market index and the risk-free rate of return.

Answer 1

a.

Value of equity (per share) = Present value of dividends receivable and terminal value after period of dividend growth.

Year	Dividend	Terminal value	Div+Terminal value	PVF @12.10%	PV of cash flows
2018	2.5000	0	2.5000	0.8921	2.23
2019	2.6500	0	2.6500	0.7958	2.11
2020	2.8090	0	2.8090	0.7099	1.99
2021	2.9775	=2.9775/0.121 = 24.6074	27.5850	0.6333	17.47
				TOTAL	23.80

Value of equity per share = 23.80
Total equity capital = 23.80*50 million = 1190 million

Debt/Equity ratio = 0.40 = Debt/1190
==> Value of debt = 0.40*1190 = 476 million

Using the formula for WACC:

WACC =((1190/(1190+476))*0.121)+((476/(1190+476))*(0.06*(1-0.19))) = 10.03%

b) As per CAPM: Return on risky asset = Rf +Beta*(E(Rm) - Rf), where:

• Rf = Risk free rate of return
• E(Rm) = Expected market rate of return

Thus, if CAPM holds true,

• For SuzyQ: 25.16 = Rf+1.20*(Market risk premium) ==> Rf = 25.16 -1.20Market Risk premium
• For PeterZ: 20.40 = Rf+0.90*(Market risk premium), substituing the value of Rf from SuzyQ:

20.40 = 20.40 = 25.16-1.20*(Market risk premium)+0.90*(Market risk premium)

Thus Market Risk premium = 15.87%

And Risk free rate = 25.16-(1.20*15.87) = 6.12%

And E(Rm) = 15.87-6.12 = 9.75%