Question

Q1.

(iii) Bellville Wallop (BW) Ltd operates in 2 lines of business: Electrical with an estimated value of R10 billion and Furniture with an estimated value of

R15 million. The following information is provided on average industry levered betas and debt to equity (D/E) ratios:

Line of Business	Average Industry levered Beta	Average Industry D/E ratio
Electrical	0,92	25%
Furniture	1,17	50%

Currently the firm has a D/E ratio of 1. Tax rate for the firm is 40%. Assume the current risk free rate is 6% and the market risk premium is 5.5%.

Estimate the cost of equity for BW, using the bottom up approach to estimate company's beta.

Q 2

Bellville Glassware (BG) finances its operations with debt and common share, where debt constitute 40% of the capital structure.
Analyst believe that the company will grow at an annual constant rate of 10% per annum. The annual yield on the company debt is
rd = 10% and the company’s tax rate is T = 30%. The BG’s common stock trades at P0 = R55 per share, and its current dividend of
D0 = R5 per share is expected to grow at a constant rate of g = 10% a year
Estimate BG’s weighted average cost of capital				11

Answer 1

Q1.

(iii)

beta of electrical division

Average Industry unlevered Beta =  Average Industry levered Beta / (1 + ((1 - tax rate) * DE ratio of industry))

Average Industry unlevered Beta =  0.92 / (1 + ((1 - 40%) * 25%))

Average Industry unlevered Beta = 0.80

Levered beta of electrical division = Average Industry unlevered Beta * (1 + ((1 - tax rate) * DE ratio of BW))

Levered beta of electrical division = 0.80 * (1 + ((1 - 40%) * 1))

Levered beta of electrical division = 1.28

beta of furniture division

Average Industry unlevered Beta =  Average Industry levered Beta / (1 + ((1 - tax rate) * DE ratio of industry))

Average Industry unlevered Beta =  1.17 / (1 + ((1 - 40%) * 50%))

Average Industry unlevered Beta = 0.90

Levered beta of furniture division = Average Industry unlevered Beta * (1 + ((1 - tax rate) * DE ratio of BW))

Levered beta of furniture division = 0.90 * (1 + ((1 - 40%) * 1))

Levered beta of furniture division = 1.44

beta of BW

beta of BW = (beta of electrical division * weight of electrical division) + (beta of furniture division * weight of furniture division)

weight of electrical division = value of electrical division / (value of electrical division + value of furniture division)

weight of electrical division = R10 billion / (R10 billion + R15 billion) = 0.40

weight of furniture division = value of furniture division / (value of electrical division + value of furniture division)

weight of furniture division = R15 billion / (R10 billion + R15 billion) = 0.60

beta of BW = (1.28 * 0.40) + (1.44 * 0.60)

beta of BW = 1.376

cost of equity

cost of equity = risk free rate + (beta * market risk premium)

cost of equity = 6% + (1.376 * 5.5%)

cost of equity = 13.568%