Perfetta operates without taxes. Equity beta is 1.2, debt beta 0.8 and market D/E is 0.6.
- A.Find asset beta.
Asset and Equity Beta
A.
1.05.
Asset and Equity Beta
There are no taxes. Asset volatility is 45%, correlation with the market 0.7, market volatility 30%, market expected return 12% and risk-free return 6%. The firm initially has no debt. It then targets debt equal to 40% of total value; debt beta is 0.2.
- A.Calculate asset beta and required return.
- B.Find equity beta and return before borrowing.
- C.Find equity beta and return after borrowing.
A.
B.
With no debt, beta(E) = beta(A) = 1.05 and r(E) = 12.3%.
C.
Debt return = 7.2%; equity return = 15.7%.
D/E = 2/3; keeping full precision avoids understating the relevered return.
Asset and Equity Beta
- A.Must debt beta always be below asset beta and asset beta below equity beta?
A.
For a normally levered firm with positive market-value weights and equity risk greater than debt risk, asset beta is their weighted average and lies between them. Strict inequalities require positive debt and equity and distinct betas. They are not universal mathematical identities for every conceivable claim or asset portfolio.
Asset and Equity Beta
- A.In perfect markets without taxes, a firm issues equity to repay debt. What happens to equity beta?
A.
With operating risk fixed and asset beta above debt beta, reducing D/E reduces equity beta. The asset beta and total enterprise value remain unchanged; the financing mix reallocates operating risk among claimholders.
Asset and Equity Beta
Bookland buys the children’s books division of Il bello di leggere for €8 billion. Before the sale, the seller has the following unlevered operating values and asset betas. All amounts are in € billions.
| Division | Unlevered value | Asset beta |
|---|---|---|
| Children’s books | 8 | 1.20 |
| Novels | 6 | 1.40 |
| Noir | 11 | 0.90 |
The risk-free rate is 4.5%, the market risk premium is 6%, and corporate tax is 45%. Ignore transaction taxes and costs. Consider two independent financing scenarios. In the levered scenario, use permanent risk-free debt, fully usable tax shields and the MM corporate-tax model; the division values exclude financing tax shields.
- A.Assume the seller initially has no debt. Reinvest 40% of the sale proceeds in financial assets with beta 0.6 and 60% in risk-free assets. Find equity beta and WACC before and after the sale.
- B.Independently, assume initial debt of €8 billion and use the entire sale proceeds to retire it. Find equity beta and WACC before and after the sale.
A.
The proceeds remain inside the firm: €3.2 billion goes into assets with beta 0.6 and €4.8 billion into risk-free assets. Total value remains €25 billion.
WACC falls from 11.196% to 9.3528%.
B.
The initial after-tax WACC is 9.786713%. After the sale, all €8 billion of proceeds repays debt. The remaining operating value is €17 billion, debt is zero and the debt tax shield disappears.
WACC after repayment = 10.958824%.
The loss of the debt tax shield raises WACC even though the operating beta falls slightly. Do not substitute the pretax weighted return on debt and equity for the after-tax WACC.