How does leverage affect shareholders

1
How does leverage affect shareholders risk?

• In a CAPM context

Assume bond beta 0 (i.e., assume debt is
riskfree), then
In words, leverage increases the equity beta by
the degree of leverage.
Example A firms operating assets has a beta of
1. If the firm has a debt ratio (B/V) of 25,
what is its equity beta? (Assume its debt is
riskfree.) Answer 1 0.75 beta(equity) ? beta
equity is 1.33.
2
Review question Homemade leverage

• Refer to Example 2 in the lecture notes for
  Chapter 16. On slide 17 we showed that if the
  firm stayed with the original all-equity capital
  structure, investors who preferred the
  alternative with 50 debt financing could
  effectively do this themselves by purchasing
  shares and borrowing. (homemade leverage).
  Suppose instead that the firm does switch to the
  capital structure with 50 debt. Show that
  investors who prefer the original all-equity
  capital structure can effectively do this
  themselves.
• (i.e. to replicate the cashflows of the
  unlevered firm with levered firm and
  borrowing/lending. homemade unlever a firm)

3
Solution

• Step 1 Find out the payoffs of the target
• Unlevered ROE 15, B/S 0
• Step 2 Find out the payoffs of things on your
  menu
• levered ROE 20, B/S1, bond, r10
• Step 3 Decide your homemade leverage (or
  unleverage)
• The trick is that your personal portfolios
  leverage leverage of target, in this case 0.
• If you buy levered equity, you are buying sth.
  with a leverage of 1. To reduce this leverage to
  0 (the target), you need to lend out an amount
  equal to (your implicit) borrowing (your firm is
  borrowing but you are lending so cancel out
  leverage). Solution
• Buy 1 levered equity, lend 1 to bank, total
  investment 2.
• Return 1 (20) 1 (10) 0.3,
• Return 0.3/2 15 unlevered firm.