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Chapter 18

Question 5

CAPM and gearing risk

Eleven Co is a manufacturer of wooden shelving whose equity:debt ratio (by
market value) is 3:2. The corporate debt, which is assumed to be risk free, has
a gross redemption yield of 8%. The beta value of the company’s equity is 0.9.
The average return on the stock market is 15% and the rate of corporation tax is
30%.

The company is considering a project in which it will make and sell wooden
sculptures.

Dustin Co is a compamy that is in the wooden sculpture market. It has an
equity beta of 1.4 and an equity:debt ratio of 4:1.

If Eleven Co takes on the new project it expects to maintain its existing capital
structure.

Calculate a suitable risk-adjusted cost of equity for use in evaluating the
sculpture project.

Use proxy beta from Dustin Co – de-gear it find an asset beta (assume the debt
beta is zero):

V e
β a = ––––––––––––– β e
V e + V d(1 – T)

β a = 4/(4 + (1 × 0.7)) × 1.4

β a = 4/4.7 × 1.4 = 1.191

Re-gear the asset beta to Eleven Co’s gearing levels:

1.191 = 3/(3 + (2 × 0.7)) × β e

1.191 = 3/4.4 × β e

β e = 1.191/0.6818 = 1.747

Use the risk-adjusted equity beta figure in the CAPM to find an appropriate
equity cost:

Ke = 8 + 1.747 × (15 – 8) = 20.2%

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