Question

Aiolos plc. is a small firm that produces and sells industrial machinery. The
following figures of the company are from the most recent financial period:
- Sales €20,000,000
- Earnings before interest and taxes €2,000,000
- Debt €10,000,000
- Interest expenses before tax €1,000,000
- Capital Expenditures €1,000,000
- Depreciation expenses are 50% of capital expenditures
- Book value of equity € 10,000,000
Also, you have collected financial information concerning the industrial
machinery sector of listed companies (all figures are on an average basis):
- Beta coefficient of listed companies of the sector 1.30
- Financial leverage in terms of debt to market value of equity 20%
- Firms in the sector trade three times (3x) their book value of equity.
- Effective tax rate 20% tax rate.
The management of Aiolos plc. expects that the company will experience a twostage
growth pattern. Specifically, during the first period which will last for the
next 5 years, net income, capital expenditures and depreciation will have a 25%
growth rate per annum, whereas during the second period (i.e. steady state),
net income will have a 7% growth rate to infinity and capital expenditures and
depreciation will offset each other.
Working capital requirements are estimated to remain stable during both growth
periods, while the proportion of net capital expenditure changes with debt will
remain to 0.3 for the next five years. The yield-to-maturity of the 10 year
government bond is 3%, while the market risk premium is 5%.

Required:
A. Estimate the cost of equity for this Aiolos plc. (5 points)
B. Estimate the value of the owner's stake in Aiolos plc., using the free cash
flow to equity approach. (15 points)
C. Identify and briefly describe any qualitative aspects of growth. (5 points)

Answer 1

A. Calculation of Interest Rate on Debt:

Debt = $10,000,000

Interest Expense = $1,000,000

Therefore,

Ineterest on Debt = $1,000,000/$10,000,000 * 100%

=10%

B. Book value of Equity (Given) = $10,000,000

It is given that firms in the sector trade three times (3x) their book value of equity.

Therefore, market value of equity = $10,000,000 * 3

= $30,000,000

C. Calculation of unlevered beta :

Unlevered Beta = Levered Beta/ 1+[(1-Tax)(Debt/Equity)]

Unlevered Beta = 1.3/ 1+[(1-0.2)(0.2/1)]

Unlevered Beta = 1.3/1.16

Unlevered Beta = 1.12069

D.Calculation of Levered Beta:

Financial leverage in terms of debt to market value of equity for Aiolos plc. is = $10,000,000/$30,000,000

= 0.3333 i.e., 33.3333 %

Levered Beta = Unlevered Beta * [1+(1-Tax Rate)*(Debt/Equity)]

Levered Beta = 1.12069*[1+(1-0.2)*(0.3333/1)]

Levered Beta = 1.12069*1.26664

Levered Beta = 1.41951

E. Calculation of cost of equity for Aiolos plc. ;

Given:

Market risk premium = 5%

Yield-to-maturity of the 10 year government bond i.e., risk-free rate = 3%

Beta of the company = 1.41951

Therefore, cost of equity as per CAPM = Risk-free rate + Beta*(Market risk premium)

= 3% + 1.41951*(5)

=3% + 7.1%

=10.1 %