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Capital structure and the cost of capital

Capital structure and the cost of capital 

Risk, Return, and Capital Budgeting (Chapter 12) 

  1. estimating beta
  • market model – regression  Ri =  +  Rm +  
  • industry beta
  • time variation
  1. Business risk and financial risk 

Income statement 

                                          10% increase in sales revenue

Sales Revenue   1000  1100  


VC (20% of sales)  200  220  

Depreciation   100  100

EBIT (Operating income) 200  280 

                                          40% INCREASE IN EBIT 

Interest    100  100  FINANCIAL LEVERAGE

EBT    100  180

Tax (40%)   40  72

EAT    60  108

EPS (100 Shares)  . 6  1.08 

                                          80% INCREASE IN EPS 

  1. weighted average – pure arithmetic

Assume constant Rb, Ra, and Rb<Ra 


Ra = (B/A) Rb + (S/A) Rs 

As B/A , will Rs  or  or remain constant?

Assume Ra and Rb constant. 
Capital structure and the cost of capital (Chapter 15,16,17) 

  1. Value of a firm = value of equity + value of interest bearing debt
  1. Principle of additivity (Divide and conquer or all court press) 

   PV(A+B) = PV(A) + PV(b) 

A, B:  two cash flow streams 

i.e. discounting combined CF by appropriate risk-adjusted discount rate (WACC)

is equivalent to

discounting each CF by its appropriate risk-adjusted discount rate and add them. 


A has payoff $100 in one year and a =1

B has payoff $150 in one year and b=2

Market risk premium =8%


Using CAPM,

PV(A) = 100/1.14 = 87.72,  where 14%  = 6 + 1 x 8

PV(B) = 150/1.22 = 122.95 

p = 1 x 87.72/210.67 + 2 x 122.95/210.67 = 1.58

PV(A+B) = 250/1.1864 = 210.72


Big Picture (Forest or tree) or Summary 

  • Assumptions of  the Modigliani-Miller (MM) Model

   Homogeneous Expectations

   Homogeneous Business Risk Classes

   Perpetual Cash Flows

   Perfect Capital Markets:

    • Perfect competition
    • Firms and investors can borrow/lend at the same rate
    • Equal access to all relevant information
    • No transaction costs
    • No taxes
  • MM'S PROPOSITION I (Debt Policy doesn’t matter)  

When there are no taxes and capital markets function well, it makes no difference whether the firm borrows or individual shareholders borrow.  Therefore, the market value of a company does not depend on its capital structure. 

    Capital structure does not affect cash flows

    • No taxes
    • No bankruptcy costs
    • No effect on management incentives


   It should cost no more to buy pieces of a chicken (or pizza) than to buy one whole. 

  • The MM Propositions I & II  (No Taxes)

Proposition I

Firm value is not affected by leverage


V is independent of the debt ratio. 

Proposition II

Leverage increases the risk and return to stockholders

      rs = r0 + (B / SL) (r0 - rB

      rB is the interest rate (cost of debt)

      rs is the return on (levered) equity (cost of equity)

      r0 is the return on unlevered equity (cost of capital)

      B is the value of debt

      SL is the value of levered equity


  • The MM Propositions I & II  (with Corporate Taxes)

Proposition I (with Corporate Taxes)

Firm value increases with leverage

VL = VU  + Tc B

Proposition II (with Corporate Taxes)

Some of the increase in equity risk and return is offset by interest tax shield 

       rs  = r0 + (B/ SL ) (1- Tc ) (r0 - rB )  

      rB is the interest rate (cost of debt)

       rs is the return on equity (cost of equity)

       r0 is the return on unlevered equity (cost of capital)

       B is the value of debt

      SL is the value of levered equity 

  • Cost of Financial distress, information asymmetry


  1. Money machine


M&M world (Um um sweet M&M ..) 

Proceeds from short sales are fully obtained.


Two firms are in the exactly same business with possible EBIT with equal probability as follows:

            Recession Normal Boom

EBIT  400  1200  2000 

Firm U has 400 shares with the price of $20 per share

Firm L has 200 shares with the price of $22 per share and debt of $4,000.

In this perfect market, P/E multiple remains constant for both firms, and equals to 10.

Interest rate for both unlimited borrowing and lending by an individual as well as firms is 10%. Can you create money machine with zero cost today, and how?  


Unlevered     Levered

EPS 1 3 5  0 4 8 

                        R N B

Short sell 1L  +22 0 -40 -80

Borrow   +18 -19.8 -19.8 -19.8

Buy 2U  -40 +20 +60 +100

CF   0 0.2 

If levered price is $18,

                        R N B

Buy 1L -18 +0  +40 +80

Sell 2U +40 -20  -60 -100

Lend   -22 +22.2  +22.2 +22.2

CF  0 2.2 

Q: Show EBIT-EPS relationship? 

  1. Whoops!

M&M world without any taxes, again


All-equity (unlevered) firm: Ro=20% 

  1. Vu = 100/0.2=500
  2. VL =?

Sell bond $250 to repurchase stock at Rb=10% 

EBIT  =100

I = 25

EBT = 75

Tax = 0

EAT =75 

S = 75/0.2 = 375

B = 250

VL = S + B = 625 (?) 

Q: Is this the correct value of VL? 

  1. In M&M world, what is the value of a firm of unlevered and levered firm by theory?


  1. What is Rs and WACC of levered firm?

   Correct procedure 

  1. First, find VL   500
  2. S by VL –B   250
  3. Rs = EAT/S  75/250 = 30%
  4. Check if WACC of both firms are the same


      In M&M, Ro remains the same  

WACC (Ro) = B/V rb + S/V rs

Rs = Ro + (B/S) ( ro – rb) 

Ro = � Rb + � Rs = 20 

  1. M&M irrelevance - Law of conservation of value

Sure, the value of a pie is NOT independent of how it is sliced, if slicer is also a nibbler. 

  1. Maximizing firm value = minimizing cost of capital, if operating income is fixed.
  1. Comment on the following: Shareholders demand – and deserve – higher expected rates of return than bondholders do. Therefore, debt is cheaper capital source. We can reduce the WACC by borrowing more. 
  1. A perfect capital market in which M&M theory holds. – Financial manager’s job is to find market imperfection and utilize it. 

    e.g. Czar of junk bond, Michael Milken


  1. Effect of taxes on levered firm (Death and Taxes, Oh no!, it is Debt and Taxes)

Two equivalent approaches

  1. VL = after-corporate tax UCF / (1+WACC)
  2. VL = after-corporate tax UCF / (1 + Ro)  + PV of net interest tax shields

      – APV approach 

Ro = Cost of unlevered equity


Tc  = 35%

EBIT  = $100

Plan U – No debt, Ro =20%

Plan L - $400 permanent debt with Rb =10% 

What are the VL and WACC?

            Vu VL

EBIT  100 100

Interest   0 40

EBT  100 60

Taxes  35 21 tax savings = 14

EAT  65 39 

Note: Quirk in tax on interest income and interest expense

  1. After-tax cost of interest to a firm(?):   rb(1-tc) = 6.5%
  2. return to bondholder(?):    rb  = 10%

TS is tax savings or tax shield, not tax refund from IRS.

  • TS is tax reduction from overall tax bills, and requires positive taxable income  (earnings) for some time.
  • IRS total tax bill is reduced
  1. Norwegian quirk on person loan 

Tax on interest income (lender) – tax deduction on all personal loans (borrower)

 IRS total tax billl remains the same 

  1. Vu = 65 / 0.2 =325
  2. VL =?

APV approach

VL = Vu + PVTS = 325 +140 = 465

PVTS = 14 /0.10 =140 OR 0.35*400=140  


  1. Vu is discounted by unlevered (all-equity) discount rate
  2. TS is discounted by interest rate. What is the risk of TS cash flow?
  1. B = 400, S = 65,  B/S identity 
  1. Rs = 39/65=60% 
  1. WACC 

PV(B+S) =PV(B) +PV(S) 

After-tax UCF from Asset + TS

= after-tax CF to bondholders + after-tax CF to stockholders 

After-tax CF to bondholders = 40

After-tax CF to stockholders = 39 

      B/S     CF

--------------------------  --------------------------------------

Vu=325 B=400  UCF 65 CF to bond 40

PVTS=140 S=65  TS 14 CF to stock 39

--------------------------  ----------------------------------------

Total 465    Total 79  

Why not WACC = 79/465 = 16.99% 

  1. Do UCF and TS have the same risk?

   UCF/ro + TS/rb = rb B/ rb + rsS/rs 

  1. Do bondholders care about financial risk? Who bears financial risk? What risk do bondholders care?
  2. What risks do stockholders bear?

   business risk + financial risks 

Note: WACC is the discount rate for CF from assets (UCF)! 

Ro = only business risks 

Risk  – only beta risk can be averaged by using weights of each part. (!) 

Value additivity applies only when risk can be combined linearly or only when return and risk are linearly related as in CAPM. 

WACC =UCF / VL, where UCF =EBIT(1-tc) 

WACC = 65 /465 =13.98%

Note that WACC is smaller than Ro of unlevered firm? Is that what you have expected? 

  1. Verify with WACC formula

WACC = rs S/V + rb ( 1-tc) B/V, V=S+B 

WACC = rs S/V + rb (1-tc) B/V 

= 60*(65/465)+10*(1-0.35) *(400/465) = 13.98% 

rs = 60 = 20 +(400/65)*(1-.35)*(20-10) 

WACC = rb (1-tc) B/V  / 1 + rs S/V 

  1. MM II

      B/S     CF

--------------------------  --------------------------------------

Vu  B  Vu ro  CF to bond B rb

TcB  S  TcB rb  CF to stock S rs

--------------------------  ---------------------------------------- 

from this identity of B/S and CF statement 

rs= ro + (B/S) (1-tc) (r0-rb) 


  1. Will stockholders accept the bond issue when total equity value declines?

    Suppose 100 shares for unlevered firm, and issue bond and repruchase stocks. 

      Unlevered      Levered

    A 325 S 325   A 465 B 400

                                              S 65

    Stock price = 3.25    ? 


    A stock price of levered firm = 4.65

    Number of shares repurchased = 400/4.65 = 86.02 shares

        Px =65 and  (100-x) P =400

    1. Miller’s personal taxes
    1. tax advantages of debt – tax deductibility of debt interest at the corporate level 
    2. tax disadvantage of debt

       – personal tax levied on interest income > personal tax on income derived from equity 

    for each dollar paid by a firm, the payoff net of all taxes to 

    1. shareholders:  (1-tc) (1-ts)
    2. debt holders:  (1-tb)

    Relative tax advantage of paying a dollar to the debtholders instead of paying to the shareholders 

    If RA>1, net-of-all taxes, return to shareholders > return to bondholders 

    PV of net tax advantage of one dollar of perpetual debt 


    Classic M&M with corporate taxes Miller equilibrium

    with corporate and personal taxes

    Corporate income is taxed at tc

    No taxes on personal income

    Corporate income is taxed at tc

    Personal tax rate on equity income: ts

    Personal tax rate on debt income : tb

    Debt adds value by reducing corporate tax payments Trade-off:

    Net after-all taxes equity income:  (1-tc)(1-ts)                                    

    Net after-all taxes debt income: (1-tb)

    Capitalized tax advantage of one $1 of debt: tc  
    VL = Vu +Btc VL = Vu +BT

    Why should shareholders care about personal taxes that are paid by debt holders?

     Relative taxation of debt and equity income affects the relative price (and required return) of bonds and stock. 


    Assume riskless bond and riskless stock.

    after-tax risk-free return: 6%



    For investors,

          Before-tax return on bond =10%

            - gross-up from before-tax return of 6% = 6/(1-.4)

          Before-tax return on stock =7.5% (= 6/(1-.2) 

    A manager of a firm (tc=34%) faces

      1. After-corporate tax cost of debt = 6.6% =10 x (1-.34)
      2. Cost of equity =7.5%

          and switches to debt 

    net advantage of redirection of $1 from equity holders to bondholders 

          (1-tb) - (1-tc)(1-ts)

              e.g. (1-.4)-(1-.34)(1-.2) = .6-.528=.072 or 7.2% 

    PV of net advantage of perpetual debt   


    Note: discount rate is after-personal tax rerurn, (1-tb) rb 

    In equilibrium, (1-tc)(1-ts) = (1-tb) or T=0


    1. Unlevered cost of capital and equity

    (graph of modified MM II) 


    assume current leverage is 40% debt and 60% equity.

    equity beta = 1.5

    market risk premium =8.5%

    risk-free rate = 8%


    Tc =40% 

    1. cost of equity and WACC with current leverage?

    Rs =20.75% for a firm with 40% debt and 60% equity. (CAPM) 

    WACC with 40% debt = (2/5)*12*(1-.4) + (3/5)*20.75 = 15.33% 


    1. all equity (unlevered)  cost of capital?

          = (20.75+12*(1-.4)*2/3)/(1+(1-.4)*2/3) 

          =18.25% (unlevered cost of equity) 

    1. cost of equity with 25% of B and 75% of S?

       apply the formula again with  

       rs= 18.25 + (1/3) *0.60* (18.25-12) = 19.5% 

    1. WACC with  25% of B and 75% of S?

       � *12 *0.6 + � *19.5 = 16.425% 


    1. and Leverage

    asset = weighted average beta of bond and stock 

    (graph of CAPM) 

    1. Why b is adjusted by (1-tc)?

      graph of CAPM 

    1. In practice, it is simplified by assuming that the beta of bond is zero.

       asset = (S/V) s  


    assume current leverage is 40% debt and 60% equity.

    equity beta = 1.5

    risk-free rate = 8%

    Tc =40% 

    1. assume beta of debt = 0

       then asset = 1.5*0.6 =0.9 

       ro using SML = 8+0.9*8.5= 15.65%, approximately 

    1. if debt = 0.47

       asset = 0.47*(1-.4)*(2/5)+1.5*(3/5)=1.0128 

       Ro  = 8+1.0128*8.5=16.61%

    1. Conflicts of interest  and Agency problem (Digression)

    It is important to understand the agency problem in the context of "conflicts of interest". Bigger issue in financial economics is the conflicts of interest among participants. Agency problem deals with the conflicts of interest between principal and agent. 

    1. between manager and stockholder

    Fractional ownership of owner cum manager  


          Firms run by the founder or by professional managers

          Stock options



    Control of the firm 

          Corporate governance issues e.g. board of directors, proxy fight

          Dual class common stock 

    Free cash flow

          Good to have financial slack (Myers & Majluf)

          Bad when manager have opportunity to waste or take negative NPV project

                Debt reduces FCF




          Is bank loan or credit line beneficial to stockholders?

          Underwriting of new stock issues 

    1. between stockholder and bondholder

    In near bankruptcy, a firm has an incentive to take risky project, to not take positive NPV project, and to milk the firm. 

    Bond covenants 

    1. Describe conflicts of interest in a firm where the fraction of ownership by government is significant.
    1. What are participants in the resource allocation process in Japan Inc. and what conflicts of interest might occur? 

    1. Costs of financial distress
    1. direct costs of financial distress 
    • legal and administrative costs
    1. Costs of Financial Distress - Costs arising from bankruptcy or distorted business decisions before bankruptcy. 
    1. impaired ability to conduct business (e.g. lost sales, no supplies, etc.) 
    1. risk shifting 


    • A firm holds cash of 10 and bond of 20 due next period


      B/S in market value

       cash   =10 bond = 9

                         equity = 1 

       Why does the equity have any value ? 

    • New project
      • initial investment = 10
      • CF $120 with 10% probability
      • CF $0 with 90 % probability
    • NPV  = -2 

    Will stockholdes take this project? 

            If stockholders takes the project

    do nothing  Win   Lose 

    B = 10  20   0 

    S = 0  100   0 


    1. refusing to contribute equity capital

    bond due = 20

    cash   = 10

    cost of project = 15

    safe project with NPV = 5 

    Will stockholdes take this project? 

    do nothing issue stock ($5) and take project

    B=10  15

    S =0  0 

    1. cash in and run, leaving empty shell
    • nature of business 
      • low debt for intangible assets
      • growth opportunity (Internet firms) or stable revenue stream
    • benefit of low debt
      • unused debt capacity and financial slack
      • control of managerial agency costs
    • opportunity cost of low debt (or benefit of high debt)
      • tax deduction
    1. Asymmetric information 

    To the outside world Smith & Co. and Jones, Inc. are identical. Each runs a successful business with good growth opportunities. The two businesses are risky, however, and investors have learned from experience that current expectations are frequently bettered or disappointed. Current stock prices each firm is $100 per share, but true values can be higher at $120 or lower at $80.

          Both firms need to raise new money to fund capital investment. They can do this either by issuing bonds or by issuing new stocks.  

    One manages (lets’ call her A) reason as follows:

          Sell stock for $100 per share? Ridiculous! It’s worth at least $120. A stock issue would hand a free gift to new investors. I just wish those stupid, skeptical shareholders would appreciate the true value of this company. Our new factories will make us the world’s lowest-cost producer. We’ve painted a rosy picture for the press and security analyst’, but it just doesn’t seem to be working. Oh, well, the decision is obvious: we’ll issue debt, not underpriced equity. A debt issue will save underwriting fees too. 

    The other manager (let’s call him B) is in a different mood:

          Beefalo burgers were a hit for a while, but it looks like the fad is a fad. Our company gotta find some good new product or it’s all downhill from here. Fortunately the stock price has held up pretty well and we had some good short-run news for the press and security analysts. Now’s the time to issue stock. We have major investments under way, and why add increased debt service to my other worries? 

    Q. Why can’t the optimistic financial manager simply educate investors?


    Suppose there are two press releases.

    Jones, Inc, announced plans to issue $120 million of five-year senior notes.

    Smith & Co announced plans to issue 1.2 million new shares to raise $120 million. 

    Q. As a rational investor, what would you learn from this press release?

    1. Who is likely to be the manager of Smith & Co and Jones, Inc., i.e. A or B?
    2. What is likely to happen to the stock price as a result of the press release?

    A1. Jones is optimistic.

    A2. Smith cannot sell stock at $100 per share. 

    Q. Under what circumstances, does it make sense to issue equity?


      • Too much leverage already
      • High-tech firms
      • Pecking order follows.
    1. Financial choices (I am dead tired now.) 

      Trade-off Theory - Theory that capital structure is based on a trade-off between tax savings and distress costs and benefits of debt. 

      Pecking Order Theory - Theory stating that firms prefer to issue debt rather than equity if internal finance is insufficient. 

        Consider the following story: 

              The announcement of a stock issue drives down the stock price because investors believe managers are more likely to issue when shares are overpriced. 

              Therefore firms prefer internal finance since funds can be raised without sending adverse signals. 

             If external finance is required, firms issue debt first and equity as a last resort. 

              The most profitable firms borrow less not because they have lower target debt ratios but because they don't need external finance. 

        Some Implications:

           Internal equity may be better than external equity.

        • Financial slack is valuable.
        • If external capital is required, debt is better.  (There is less room for difference in opinions about how much debt is worth).

      1. Value of a firm with financial leverage (Hue! At last.)
      1. The Adjusted-Present-Value (APV) Approach 

      APV = NPV + NPVF 

      NPV: NPV of unlevered firm

        • NPV = PVUCF - Initial investment for entire project
        • PVUCF: PV of Unlevered Cash Flows (UCF)
        • UCF=CF from operations - Capital Spending - Added NWC
        • Discount rate: r0

      NPVF: NPV of financing side effects

      • PV of Tax Subsidy to Debt
      • Costs of Issuing New Securities
      • The Costs of Financial Distress
      • Subsidies to Debt Financing
      1. WACC approach 
      • UCF discounted by WACC 

        WACC has to be adjusted to incorporate side effects 

      1. Estimating discount rate
      1. Calculate the firm’s cost of capital and not the cost of equity 
      2. Be consistent in your treatment of inflation - Use industry data to estimate the cost of capital for the firm, not just the firm’s own data. The cost of capital cannot be calculated, but only be estimated.
      1. Quiz

      A manager Q of so-so company is campaigning for a pet project knows WACC formula. And think. Aha! My firm has good credit rating. It could borrow, say, 90 percent of the projects’ cost if it likes. That means B/V = .9 and S/V =.1. My firm’s borrowing rate is 8 percent, and the required return on equity is 15 percent. Therefore the WACC is

      .08 *(1-.35)(.9) +.15(.1)=.062 or 6.2 percent. When I discount at that rate, my project looks great. 

      What are logical errors? 

      1. debt ratio of 90%
      2. project’s overall contribution to the firm’s borrowing capacity
      3. both rs and rb 
      1. Financial Distress 

      Financial Asset

      Distress restructuring 

                  Financial  Private workout


                  Legal bankruptcy Reorganization (Chapter11)

                                                      * prepackaged bankruptcy 

                        Liquidation (Chapter 7) 


      Responses to Financial Distress

      • Asset Restructuring
        • Merging with another firm
        • Selling major assets
        • Reducing capital spending and R&D spending
      • Financial Restructuring
        • Issuing new securities
        • Negotiating with banks and other creditors
        • Exchanging debt for equity
        • Filing for bankruptcy


      Bankruptcy versus Private Workout

      • Advantages
      • Available new credit - "debtor in possession" or "DIP" debt
      • Discontinued accrual of interest on pre-bankruptcy unsecured debt
      • An automatic stay provision
      • Tax advantages
      • Requires only approval by 1/2 of creditors owning 2/3 of outstanding debt


      • Disadvantages
      • A long and expensive process
      • Judges are required to approve major business decisions
      • Distraction to management
      • ’Hold out' by stockholders

      Note: Absolute priority rules (APR) is sometimes violated 



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