Chapter 15: Debt Policy

1
Topic Financial Leverage/Capital Structure Policy
Objectives

• Examine the effect of financial leverage on EPS
  and ROE
• Introduce the concept of homemade leverage
• Demonstrate the Capital Structure Irrelevance
  Proposition in a world with no taxes and perfect
  capital markets

2
The Effect of Financial Leverage An Example

• Goal show how financial leverage works through
  EPS and ROE. Currently no debt. Proposal to issue
  debt and use the proceeds to buy back equity (a
  restructuring). Assume no depreciation and no
  taxes. Keep share price fixed for now.
• Current Proposed
• Assets 1,000,000 1,000,000
• Debt 0 500,000
• Equity 1,000,000 500,000
• Debt/equity ratio 0 1
• Share Price 20 20
• Shares outstanding 50,000
  25,000
• Interest rate 10 10

3

• Recession Expected Expansion
• Current capital structure No debt
• EBIT 20,000 60,000 120,000
• Interest 0 0 0
• Net income 20,000 60,000
  120,000
• ROE 2 6 12
• EPS .4 1.2 2.4
• Proposed capital structure D/E 1
• EBIT 20,000 60,000 120,000
• Interest 50,000 50,000
  50,000
• Net income -30,000 10,000
  70,000
• ROE -6 2 14
• EPS -1.2 .4 2.8

4
The Effect of Financial Leverage

• We conclude that
• The effect of financial leverage depends upon
  EBIT
• When EBIT is high, financial leverage raised ROE
  and EPS
• The variability of ROE and EPS is increasing with
  financial leverage
• Overall higher financial leverage magnifies the
  effect of changes in EBIT on ROE and EPS. Using
  more debt makes ROE and EPS more risky.

5
Corporate Borrowing and Homemade Leverage

• Homemade leverage the use of personal
  borrowing/lending to change the overall amount of
  financial leverage to which the individual is
  exposed.
• Example Suppose the firm did not change its
  capital structure. We will show that investors
  can replicate the returns from the proposed
  capital structure by borrowing on their own.
• Suppose a shareholder wants to invest 100 in
  the firm, and prefers the proposed rather than
  the current capital structure.
• If the proposed capital structure is not
  adopted, he buys 5 shares with her own money, and
  5 shares by borrowing 100 at 10 interest. So he
  replicates the returns under the proposed capital
  structure while the cost of the investment is the
  same.

6
Homemade Leverage An Example

• Recession Expected Expansion
• Proposed capital structure D/E 1
• EPS -1.2 .4
  2.8
• Earnings for 5 shares -6 2
  14
• Net cost 5 shares at 20 100
• Original capital structure and homemade
  leverage
• EPS .4 1.2
  2.4
• Earnings for 10 shares 4 12
  24
• Less Interest on 100 at 10 10 10
  10
• Net earnings -6 2
  14
• Net cost 10 shares at 20 Amount borrowed
• 200 - 100 100

7
Homemade Leverage Main conceptual point

• Suppose that investors can borrow or lend at the
  same rate as the corporation (perfect capital
  markets).
• Then they can always use homemade leverage to
  undo in their own portfolios any change in a
  firms capital structure choice.
• Thus, they can attain the same cash flows that
  they would have attained without the firms
  leverage change.
• Therefore, investors are indifferent to changes
  in the firms capital structure, and so share
  prices should be the same regardless of capital
  structure.

8
Modigliani and Millers Proposition I

• Assumptions
• A1. No taxes
• A2. No capital market imperfections
• A3. The firms cash flows are independent of how
  it is financed
• Then the value of the firm is independent of its
  capital structure
• Understanding MM Prop. I
• Consider 2 firms with the same operating income
  X every year. However, firm L is levered and
  firm U is not.
• Value of L VL EL DL , Value
  of U VU EU
• MM Proposition I VL VU

9
Proof by the Non-arbitrage Argument

• Consider 2 firms that exist for one year, and
  have the same operating income X at the end of
  that year, and then liquidate. However, firm L is
  levered and firm U is not.
• Notation
• EL equity of levered firm
• DL debt of levered firm
• EU equity of unlevered firm
• X net cash flows, is the same for both levered
  and unlevered firm
• I payment of interest and principal. It is the
  same for borrowing at the corporate or individual
  level

10
Proof by the Non-arbitrage Argument

• Prove MM Proposition I by contradiction
• Logic of proof suppose that VL gt VU.. Then,
  according to MM, firm L is overpriced relative to
  U. Thus, show that there is an arbitrage
  opportunity (smart investors can obtain a profit
  from this situation). Since arbitrage
  opportunities cannot persist in perfect capital
  markets, then our assumption of VL gt VU. is
  false. In a similar way, we can show that VL lt
  VU. cannot be true either. Thus we can conclude
  that VL VU. , which completes the proof.
• For brevity, we will only show that VL gt VU.
  cannot be true

11
The Arbitrage Opportunity
Suppose VL gt VU , that is EL DL gt
EU Current action CF Today CF Tomorrow Sell
short 1 of EL .01xEL -.01x(X-I) Borrow
amount to 1 of DL .01xDL -.01xI Use
proceeds to buy 1 of EU -.01xVU
.01xX Net Cash Flow .01xELDL-VUgt0
0 Remember that from the terminal cashflow X,
bondholders receive interest I, and shareholders
get what is left, X-I. Thus VL VU.
12
Aside short-selling

• An investor who sells stock short borrows shares
  from a brokerage house and sells them to another
  buyer. Proceeds from the sale go into the
  shorter's account. He must buy those shares back
  (cover) at some point in time and return them to
  the lender.

13
Aside short-selling

• Thus, if you sell short 1000 shares of Gardner's
  Gondolas at 20 a share, your account gets
  credited with 20,000. If the boats start
  sinking---since David Gardner, founder and CEO of
  VENI, knows nothing about their design---and the
  stock follows suit, tumbling to new lows, then
  you will start thinking about "covering" your
  short there for a very nice profit. Here's the
  record of transactions if the stock falls to 8.
• Borrowed and Sold Short 1000 shares at 20
  20,000 Bought back and returned 1000 shares at
  8 -8,000
• Profit 12,000

14
Aside Short-selling

• But what happens if as the stock is falling, Tom
  Gardner, boatsmen extraordinaire, takes over the
  company at his brother's behest, and the holes
  and leaks are covered. As the stock begins to
  takes off, from 14 to 19 to 26 to 37, you
  finally decide that you'd better swallow hard and
  close out the transaction. You do so, buying back
  shares of TOMY (new ticker symbol) at 37.
• Here's the record of transaction
• Borrowed and sold short 1000 shares at 20
  20,000 Bought back and returned 1000 shares at
  37 -37,000
• Loss -17,000

15
Aside short-selling

• Ouch. So you see, in the second scenario, when I,
  your nemesis, took over the company, you lost
  17,000...which you'll have to come up with.
  There's the danger....you have to be able to buy
  back the shares that you initially borrowed and
  sold. Whether the price is higher or lower,
  you're going to need to buy back the shares at
  some point in time.

16
ExampleEBIT and Leverage

• Probit Inc. has no debt outstanding and total
  market value of 80,000. Earnings before interest
  and taxes, EBIT, are projected to be 4000, if
  economic conditions are normal. If there is a
  strong expansion in the economy, then EBIT will
  be 30 higher. If there is a recession, then EBIT
  will be 60 lower. Probit is considering a
  35,000 debt issue with a 5 interest rate. The
  proceeds will be used to repurchase shares of
  stock. There are currently 2,000 shares
  outstanding. Ignore taxes.
• A. Calculate EPS for all economic conditions
  before any debt is issued. Calculate the
  changes in EPS when the economy expands or enters
  a recession.
• B. Repeat part A assuming the probit goes through
  with recapitalization. What do you observe?

17
ExampleEBIT and Leverage

• A. Normal conditions EBIT4000, EPS4000/20002
• Expansion EBIT5200, EPS5200/20002.6
• Recession EBIT1600, EPS1600/2000.8
• Normal to Expansion, change in EPS30
• Normal to Recession, change in EPS-60
• B. Interest paid to debtholders,I535,0001750
• NIEBIT-I, no shares left(.45/.8)20001125
• Normal conditions EBIT2250, EPS2250/11252
• Expansion EBIT3450, EPS3450/11253.07
• Recession EBIT-150, EPS-150/1125-0.13
• Normal to Expansion, change in EPS53.5
• Normal to Recession, change in EPS-106.5

18
Degree of Financial Leverage

• Degree of Financial Leverage change in EPS/
  change in EBIT

19
Topic Financial Leverage/Capital Structure Policy
Objectives

• Develop Modigliani and Millers Proposition II
• Analyze the effect of debt financing on the risk
  and required return of shareholders
• Understand the concepts of RA and ?A
• Determine the effect of a change in capital
  structure on
• - RA and ?A
• - RE, ?E and RD, ?D

20
Example A

• No corporate tax, U-firm has 100 shares
  outstanding at 10/share.VU 1,000 EU. Future
  cash flow will depend on the state of the
  economy
• Boom Recession
• Probability 1/2 1/2
• CFs to equity 1,400 900
• Return on equity
• Expected return on equity
• Standard deviation of return on equity 25

21
Example A

• Introduce leverage L-firm has 300 face value of
  1-period riskless bonds outstanding (rate is
  10). VL 1,000, EL 700, DL 300.
• Boom Recession
• Probability 1/2 1/2
• Total future CFs 1,400 900
• CFs to debt 330 330
• CFs to equity 1,070 570
• Return on equity
• Expected return on equity
• Standard deviation of return to equity 35.8
• Expected return to debt 10
• Leverage increases both the risk and expected
  return on equity

22
Introducing Debt on WACC (RA)

• Unlevered firm
• Levered firm
• Conclusion

23
MM Proposition II

• Assuming no corporate taxes and zero probability
  of bankruptcy,
• As leverage (D/E) ?, RE ?
• MM proposition II the expected rate of return on
  equity of a levered firm increases in proportion
  to the debt to equity ratio

24
MM I II with No Taxes
RE
Cost of capital
WACCRA
RD
D/E
25
Understanding the diagram

• MM Proposition I (VU VL) is reflected in the
  fact that WACC does not depend on D/E. So capital
  structure is irrelevant!
• Intuition given that cash flows do not depend on
  D/E, the market value of the firm is independent
  of D/E only if the cost of capital (WACC) used to
  discount those cash flows is also independent of
  D/E.
• MM Proposition II is reflected in the positive
  slope of RE.
• Intuition the expected return on equity
  increases linearly with the D/E ratio (with
  riskless debt). RE business risk financial
  risk
• Even though RE increases with D/E, WACC stays the
  same because we assign a lower weight to RE and a
  higher weight to RD.

26
What if debt becomes risky?

• At high levels of leverage, debt can become
  risky, in the sense that there is a positive
  probability of bankruptcy.
• If leverage increases the risk of the debt,
  debtholders demand a higher return on the debt.
  This causes the rate of increase in RE to slow
  down.
• Holders of risky debt begin to bear part of the
  firms operating risk. As the firm borrows more,
  the more this risk is shifted form stockholders
  to bondholders.

27
MM III with No Taxes and Risky Debt

28
Change in Capital Structure when TC0

• Note

29
Change in Capital Structure when TC0

• Suppose more debt is issued
• RE, ?E both go up
• RD, ?D stay the same (assuming probability of
  bankruptcy0 at the original D/E)

30
Example B

• Nodebt, Inc. is a firm with all-equity financing.
  Its equity beta is .80. The t-bill rate is 5
  and the market risk premium is expected to be
  10. What is the Nodebts asset beta? What is
  Nodebts WACC? The firm is exempt from paying
  taxes.
• If D0, then

31
Example C

• Now suppose that Nodebt issues a little debt so
  little debt, in fact, that investors perceive the
  bonds to be risk-free. After the issue, the debt
  comprises 10 of the firms capital structure and
  the equity comprises 90.
• a) What is the beta and required rate of return
  on the debt?
• b) What must be the new beta of and required rate
  of return on the firms equity?
• c) Calculate the WACC of the firm under the new
  financing mix. Has WACC changed?
• d) Interpret your result. Calculate the
  weighted-average asset beta given the new
  financing mix. Has weighted-average beta changed?

32

• Since debt is riskless, the ßD0, and RD5
  (risk-free rate).
• ßE ßA x (1D/E) .8x(11/9) .8889
• RE RA(RA-RD)x(D/E) 13 (13-5)x(1/9)
  13.8889
• WACC .9 x 13.8889 .1 x 5 13 (no
  change)
• When debt is issued, the risk of equity
  increases and so does the required return on
  equity. But the weight on the cost of equity in
  the WACC calculation falls from 1 to .9, and the
  remaining weight is placed on the cost of debt,
  which is lower. Since changes in D/E do not
  affect firm value (MM Prop. I), and cash flows
  are not affected, then the WACC used to discount
  those cash flows is not affected either.
• d) ßA D/V x ßD E/V x ßE .1 x 0 .9 x .8889
  .8 (no change)

33
Topic Financial Leverage/Capital Structure Policy
Objectives

• Introduce taxes in the MM analysis
• Optimal capital structure is determined by the
  tradeoff between
• - Taxes savings
• - Bankruptcy costs
• Describe Go-for-Broke behavior
• Explain the Underinvestment Problem

34
Does Capital Structure Policy Matter?

• MM propositions suggest that capital structure
  does not matter in perfectly functioning capital
  markets with no taxes, and no bankruptcy costs.
  No matter how much the firm borrows, the value of
  the firm remains the same, and so does the WACC.
• In reality, however, managers do worry about a
  firms capital structure. They try to find the
  right mix to optimize firm value and to reduce
  its cost of capital. What is going on?

35
Introducing Corporate Taxes

• Interest tax shield The tax saving attained by a
  firm from interest expenses
• This saving is usually valued by discounting at
  RD (the tax shield has the same risk as D). In
  the case of perpetual debt,
• MM I with Taxes

36
MM I with Taxes
Value of the firm, VL

TC
TC ?D
VU

VU
Total debt, D
37
Implications of MM I with taxes

• 1. Debt financing always increases firm value, so
  using debt is very attractive. Capital structure
  matters a lot!
• 2. The value of the corporate tax shield is
  represented in the lower after-tax cost of debt
• This means that WACC decreases in leverage. Value
  increases because we are discounting the cash
  flows with a lower WACC.

38
MM II with taxes

• Note that now WACC decreases with D/E
• So formula for MM II with taxes cannot be derived
  from previous equation of WACC.
• Define RU to be the WACC when D0, so RU is the
  unleveraged cost of capital
• MM II with taxes
• Implications are similar to the case without
  taxes

39
Corporate Taxes and WACC

• With taxes capital structure matters a lot!
• Now we know that the value of the tax shield
  increases as D/E ratio increases.
• Thus, with taxes firm value increases and the
  cost of capital decreases with leverage
• Big question why dont all business borrow as
  much as they can? It seems that the optimal
  capital structure is 100 debt! Having lots of
  debt is always good?

40
Optimal Capital Structure

• As D/E increases, the prob. of financial distress
  also increases. One cost of having debt is
  expected bankruptcy costs (legal and adm.
  expenses difficulty of running a distressed
  firm)
• As the D/E ratio ?, the costs of financial
  distress ?
• The optimum capital structure is the D/E level at
  which the PV of the tax shield from borrowing an
  additional dollar is just offset by the increase
  in the PV of financial distress costs
• - This is the Static Theory of Capital Structure

41
The Static Theory of Capital Structure
Firm Value, VL

PV(financial distress costs)
VL
PV(tax shields on debt)
Value of firm with no debt VU
VU
D
D
42
Bankruptcy Costs

• Direct bankruptcy costs The costs that are
  directly associated with bankruptcy, such as
  legal and administrative expenses
• Indirect bankruptcy costs The difficulties of
  running a business that is experiencing financial
  distress
• Agency cost of equity can result from shirking by
  owner-managers due to their diluted equity stake
  at the firm. If the entrepreneur issues debt
  rather than equity, then she has an incentive to
  work harder (opposite direction as bankruptcy
  costs).

43
Examples of Bankruptcy Costs

• Go-for Broke behavior Shareholders of
  financially distressed firms have the tendency to
  invest in high risk, negative NPV projects (also
  called risk-shifting)
• Intuition if project succeeds, then shareholders
  keep the benefit. If it fails, shareholders dont
  lose anything due to limited liability.
• Example
• Suppose a firm has 1,000 cash. The face value
  due at the end of this year on the firms bonds
  is 5,000. So if nothing happens the firm goes
  bankrupt and is liquidated, bondholders get the
  cash, and shareholders get nothing.

44
Go-for-Broke Behavior Example

• Strategy A (safe) Firm could invest 1,000 in
  government securities at 15. A the end of the
  year the firms cash will be 1,150, the firm is
  liquidated, bondholders get the cash,
  shareholders still get nothing (but bondholders
  get more).
• Strategy B (very risky) Invest the 1,000 in a
  project that will pay 20,000 with 2
  probability, and zero otherwise.
• But shareholders will typically prefer strategy B!

45
Examples of Bankruptcy Costs

• Underinvestment Problem Shareholders of levered
  firms forego investment in positive NPV projects
  because debtholders will capture most of the
  benefit (Debt overhang problem)
• Suppose a firm has a very attractive project.
  If it invests 2,000 now it will get back 11,000
  for sure next year. The face value of debt due
  next year is 10,000, R10
• NPV -2,000 11,000/1.1 8,000

46
Underinvestment Problem

• A Suppose the firm has no cash and it cant
  borrow via issuing debt due to its poor financial
  condition and has to depend on the shareholders
  for funding the project.
• If shareholders fund the project, it will cost
  them 2,000 now, and they will get 11,000 at the
  end of the year. Since they have to pay 10,000
  to bondholders, they will be able to recover only
  1,000 of their original investment. So they will
  not undertake the project even though it has a
  positive NPV.
• B Suppose the firm has 2,000 cash
• If they dont undertake the project,
  shareholders lose the cash in liquidation. By
  undertaking the project shareholders generate
  11,000, of which 10,000 go to bondholders, so
  they will keep 1,000, which is better than
  nothing.

47
Optimal Capital Structure A Recap

• Case I No taxes, no bankruptcy costs the total
  value of the firm and its WACC are not affected
  by capital structures - capital structure does
  not matter.
• Case II With corporate taxes and no bankruptcy
  costs the value of the firm increases and the
  WACC decreases as the amount of debt goes up
  maximize borrowing
• Case III With corporate taxes and bankruptcy
  costs the value of the firm reaches a maximum
  (WACC reaches a minimum) when the tax benefit
  from an extra dollar in debt is exactly equal to
  the increase in expected bankruptcy costs there
  exists an optimal capital structure

48
Examples

• Fordebtful Industries has a debt-equity ratio of
  2.5. Its WACC is 12 and its cost of debt is 12.
  The corporate tax rate is 35.
• A) What is Fordebtfuls cost of equity capital?
• B) What is Fordebtfuls unlevered cost of equity
  capital?
• C) What would the cost of equity be if the
  debt-equity ratio were 1.5gt
• What if it were 1.0? What if it were 0?

49
Examples

• QC corporation expects an EBIT of 7500 every
  year forever. QC currently has no debt , and its
  cost of equity is 17. The firm can borrow at
  14. If the corporate tax rate is 38, what is
  the value of the firm? What will the value be if
  QC converts to 50 debt? To 100 debt?