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					   Finance and the Financial Manager




                            Chapter 1
1.1 What is a Corporation?

1.2 The Role of the Financial Manager

   Two Basic Questions
      1   Investment Decision
      2   Financing Decision
1.3 Who is the Financial Manager

              (2)                      (1)


  Firm's            Financial                Financial
                                (4a)
 Operations         Manager                  Markets

              (3)                  (4b)
1.4 Goal of the Firm ?
1.5 Agency Problem
   A. Separation between Ownership and Management

   B. How to solve agency problem?
      1   Monitoring by board of directors
      2   Compensation package
      3   Monitoring by outside large blockholders
          (Bank, insurance Co., pension, mutual fund)
      4   Efficient outside managerial labor market
      5   Active outside takeover market
   Present Value and The Opportunity
    Cost of Capital



                            Chapter 2
2.1 Introduction
   A. Present Value
      PV = C / (1+r)
      r:



      NPV = PV - C0

   B. Risk and Present Value

   C. PV and Rate of Return
D. The Opportunity Cost of Capital

   1   From your Investment
         C0 : $ 100,000
         C1 : Slump : $ 80,000
              Normal : $ 110,000
              Boom : $ 140,000

       E(C1)
2   From Stock Market
    Find stock X which has same risk as your project :
    P0 : $ 95.65
    P1 : Slump : $ 80
         Normal : $ 110
         Boom : $ 140
    E(P1) = 1/3 (80 + 110 + 140) = 110
    E(R) = 110 - 95.65 = 0.15  15%  k
                95.65

Q : What is the Present Value of your project?


 PV of project =




      NPV =
   How to Calculate Present Values




                            Chapter 3
3.1 Cash Flows in Several Periods (*)

3.2 Perpetuities and Annuities (*)

3.3 Growing Perpetuities (*)

3.4 Compounding Interest (*)
3.5 Nominal and Real Interest
                 Nominal CF
  A. Real CF = (1+inflation rate)
                     (1+ Nominal rate)
  B. (1+Real Rate) = (1+inflation rate)

3.6 Bond Valuation
               C        C      … ... + C+F
   PVbond =         +      2 +
              1+r     (1+r)            (1+r)n
         =    C  PVAF + F  PVF
   (Ex) Coupon rate: 10%, r=5%,
        face value=$1,000 N=7years
   PVbond = 100  5.786 + 1100  0.711 = $1360.7
   The Value of Common Stocks




                          Chapter 4
4.1 How Common Stocks are Traded?

    A. Primary Market

    B. Secondary Market

       • NYSE
       • AMEX
       • OTC (NASDAQ)
4.2 Stock Valuation
 A. Today‟s Price
    E(R) = (P1 - P0 + DIV) / P0 = r
      r: market capitalization rate
              P1 - P0        DIV
          =             +
                P0            P0

          = Holding Period Return = E(R)

 (Ex) P0 = $100 , P1 = $110 , DIV = $5
   r=
P0 = (P1 + DIV) / (1+r)
   = (110 + 5 ) / 1.15 = 100

$ 100 ;
equilibrium price if 15% is an appropriate discount rate



Q: What happen if P0 is different from $100 ?
B. What determines next year‟s price ?
   Valuation Model
    P0 = (P1 + D1) / (1 + r), P1 = (P2 + D2) / (1 + r)
    P0 = D1 / (1 + r) + (P2 + D2) / (1 + r)2
       = D1 / (1 + r ) + D2 / (1+r)2
               + D3 / (1 + r)3 + ………
           
       =    Dt / (1 + r)t
           t=1

    Assume: Dividend grows at a constant rate; g
        P0 = [D0 • (1 + g)] / (r - g) = D1 / (r - g)
4.3 Simple Way to Estimate r

    r = D1 / P0 + g
         D1 / P0 : Dividend Yield
         g : Dividend Growth

   EX : Pinacle West Corp (p 69)
       P0 = $41, Div1 = $1.27, g = 5.7%

    r=
Alternative Approach:

Payout ratio = DIV1 / EPS = 0.47

Plowback Ratio = 1- Payout ratio = 0.53

ROE = EPS / Book Equity per Share = 0.1

g = Plowback ratio * ROE =
r = 0.031 + 0.053 = 0.084 or 8.4%
Some Warnings about Constant-Growth Formulas
1. Individual stock‟s r is subject to estimation errors
        Portfolio approach
2. Growth rate can rarely sustained indefinitely
  Ex. Growth-tech
   DIV1=$0.05, P0=$50, Plowback Ratio=80%, ROE=25%
      g=
      r=
Ex: at t=3 and thereafter      ROE =16%
Firm responds by plowing back 50% of earnings
   g =
Table 4.2
                 YEAR1   YEAR2      YEAR3       YEAR4

Book equity      10.00     12.00    14.40        15.50
Earning per
share, EPS        2.50      3.00     2.30         2.49
Return
on Equity, ROE     .25        .25      .16         .16
Payout ratio       .20       .20      .50          .50
Dividends per
share, DIV         .50       .60     1.15         1.24
Growth rate
of dividends        -        .20      .92          .08
• General DCF formula to find the capitalization rate r:

       DIV1 DIV2      DIV3 + P3
P0 =   1+r
           +
             (1+r)2 +
                        (1+r)3

P3 =

P0 =

50 =
4.4 The link between stock price and
    earning per Share
           Growth stock vs Income stock
   A. Income Stock
       No Growth                   Perpetuity Model
             EPS1       DIV1
    P0 =            =
              r          r
  (EX)
   Expected Return = Dividend Yield = 10/100 =.10 = r
   Price = DIV1 / r = EPS1 / r =
B. Growth Stock (r=10%)
  at t = 1: (once & for all)

  Invest $10 into project with permanent return of 10%
  $ 1 (each year)
   NPV =

  This investment contributes “0” to value.

  (EX) Return on project is higher or lower than 10%;
       NPV?      (go to table 4-3)
Table 4-3
Effect on stock price investing an additional $10 in year 1 at different rates of return.
Notice that the earnings-price ratio overestimates r when the project has negative NPV
and underestimates it when the project has positive NPV.


                                                   Project's impact
      Project Rate   Incremental    Project NPV     on Share Price    Share Price     EPS1
       of Return                               a                      in Year 0, P0
                     Cash Flow, C    in Year 1         in Year 0 b                     P0    r

        .05           $ .50         - $ 5.00         - $ 4.55         $ 95.45         .105   .10
        .10           1.00             0               0              100.00           .10   .10
        .15           1.50          + 5.00           + 4.55           104.55          .096   .10
        .20           2.00          + 10.00          + 9.09           109.09          .092   .10
        .25           2.50          + 15.00          + 13.64          113.64          .088   .10

a
     Project costs $ 10.00 (EPS1). NPV = - 10 + C / r, where r = .10
 b
     NPV is calculated at year 1. To find the impact on P0, discount for 1 year at r = .10
In general :
        EPS1
P0 =     r      +    PVGO

PVGO : Present Value of Grow Opportunity
       Sum of all NPVs (per share)


 EPS1
         : Capitalized value of average earning
  r          under a no-growth policy
Determinants of P/E Ratio
        EPS1
P0 =             + PVGO
         r
Divide each side by EPS

             1     PVGO
P/E =            +
             r       E
1. Cost of Capital(r): “-”
2. Conservative accounting procedure(EPS): “-”
3. Growth opportunities(PVGO): “+”
Q : Japanese firm : P/E  50
    U.S. firm     : P/E  17
    Is Japanese firm growing fast?
EX : Fledgling Electronics Case (p73)
   r = 15 % , D1 = $ 5
   P0 = D1 / (r - g) =

   If EPS1 = $ 8.33, Payout ratio = D1 / EPS1 = 5 / 8.33 = 0.6
   If ROE = .25, g =


   P0 =
Analyze:      $ 44.44
Plowback Ratio = .4, 8.33 * .4 = $ 3.33
    Invest: $ 3.33 at 25% (ROE)
    .25 * 3.33 = $ .83
    at t = 1; NPV1 = -3.33 + .83 / .15 = 2.22
    at t = 2;
    Invest 3.33 * 1.1 = 3.69 (g = 10%)
    NPV2 = -3.33 * 1.1 + (.83 * 1.1) / .15 = 2.44
    PVGO = NPV1 / (r - g) = 2.22 / (.15 - .1) = $ 44.44

This is growth stock, not because g = 10%,
but because
C. Some Example of Growth Opportunities
Table 4-4 Estimated PVGOs (p.76)
                                                   Market                        PVGO,
                        Stock                   Capitalization     PVGO        Percent of
      Stock            Price, P0     EPS*         Rate, r**      =P0 - EPS/r   Stock Price      P/ E
Income Stocks:
  AT & T                $52.00       $2.85           .094           $21.70           41.7        18.2
 Conagra                26.00         1.33           .106            13.50           51.7        19.5
 Duke Power             60.00         3.58           .094            21.90           36.5        16.8
 Exxon                  64.00         2.89           .099            34.70           54.3        22.1

Growth Stocks:
 Compaq                 30.00         0.69           .123            24.40           81.3        43.5
 Merck                  120.00        4.43           .118            82.50           68.7        27.1
 Microsoft              101.00        2.08           .165            85.10           84.2        48.6
 Wal-Mart                 60.00       0.73           .094            52.20           87.1        82.2

* EPS defined as the average earnings under a no-growth policy. As an estimate of EPS, we use the forecasted
  earnings per share for the 12 months ending March31, 1999. Source: Value Line.
* The market capitalization rate was estimated using the capital asset pricing model.
   We describe this model and how to use it in Section 8.2 and 9.2. EX: market risk premium = 6%

      Why NPV leads to better
    Why Net Present Value Leads to
         Investment Decisions
    Better Investment Decisions than
    Other Criteria
          than Other Criteria

                           Chapter 5
5.1 Review of Basics

   1   Forecast Cash Flow

   2   Determine appropriate Cost of Capital

   3   Discount with Cost of Capital
Q : Why NPV ?

 • All cash flows are considered

 • Time Value of Money

 • NPV is not affected by manager‟s taste,
   accounting method, profitability of existing
   business, and profitability of other
   independent business
 5.2 Payback Period

   • Number of years it takes before cumulative
     cash flow recovers initial investment

             CASH FLOWS, DOLLARS
                                           Payback          NPV at
Project     C0      C1     C2     C3      Period, Years   10 Percent
  B       - 2,000 + 500 + 500 + 5,000          3             2,642
  C       - 2,000    500 +1,800 + 5,000        2               -58
  D       - 2,000 + 1,800 + 500 +     0        2               +50
5.3 Book Rate of Return

  Book Rate of Return =   Book income
                          Book assets


       Cash flow vs. Book Income

  Problems :
Example
Computing the average book rate of return on an investment of $9000 in project A
                                     CASH FLOWS, DOLLARS

            Project A            Year 1               Year 2              Year 3
Revenue                          12,000                10,000                 8,000
Out-of-Pocket cost               6,000                 5,000                  4,000
Cash flow                        6,000                 5,000                  4,000
Depreciation                     3,000                 3,000                  3,000
Net income                       3,000                 2,000                  1,000

                             average annual income              2,000
Average book rate of return =                        =                          = .44
                             average annual investment          4,500


                                 Year 0                Year 1                 Year 2    Year 3
Gross book value of investment   $ 9,000              $ 9,000                 $ 9,000   $ 9,000
Accumulated depreciation              0                 3,000                  6,000        9,000
Net book value of investment     $ 9,000              $ 6,000                 $ 3,000   $      0
                                           Average net book value = $ 4,500
5-3 Internal Rate of Return: IRR
     Discount rate that makes NPV = 0

    C0 = - 4,000     k: cost of capital
    C1 = 2,000
    C2 = 4,000

                    2,000          4,000
    NPV = -4,000 +           +             =0
                   (1+IRR)       (1+IRR) 2




   (Rule)    Accept IRR>k  NPV>0
             Reject IRR<k  NPV<0
Net Present Value, dollars
     2500
     2000
     1500
     1000                              IRR=28%
      500
         0
      -500       10    20    30   40   50   60   70     80  90    100
                                                      Discount rate (%)
    -1000
    -1500
    -2000
Pitfall 1. Lending vs. Borrowing?

                    CASH FLOWS,
                     DOLLARS
                                                      NPV at
          Project     C0        C1      IRR, Percent 10 Percent
            A       - 1,000   + 1,500     + 50
            B       + 1,000   - 1,500     + 50



             CASH FLOWS, DOLLARS
                                                                 NPV at
 Project    C0         C1        C2         C3     IRR, Percent 10 Percent
  C      + 1,000    - 3,600   + 4,320    - 1,728      + 20        - .75
Net Present Value, dollars
      60



      40



      20



       0
               10    20      30   40   50   60   70    80    90   100
                                                      Discount rate (%)
     -20
Pitfall 2. Multiple Rates or Return

           0         1      2         3          4        5        6
  Pretax -1,000     300   300        300        300      300     300
  Tax              +500   -150       -150       -150     -150    -150
  Net   -1,000      800    150       150        150       150    -150


                   CASH FLOWS, DOLLARS
                                                               NPV at
         Project     C0         C1         C2    IRR, Percent 10 Percent

            D       + 1,000 - 3,000 + 2,500            none     + 339
  NPV
1000

                   IRR=15.2%
500


  0                            Discount
                               Rate


-500    IRR=-50%


-1000
Pitfall 3. Mutually Exclusive Projects
     3.1 Different scale
                CASH FLOWS,
                 DOLLARS
                                                    NPV at
     Project     C0        C1      IRR, Percent   10 Percent
       E       - 10,000 + 20,000      100
       F       - 20,000 + 35,000       75


                CASH FLOWS,
                 DOLLARS
                                                    NPV at
     Project     C0        C1      IRR, Percent   10 Percent
       F-E     - 10,000 + 15,000      50           + 3,636
3.2 Different pattern of cash flow over time
                    CASH FLOWS, DOLLARS
                                                                      IRR,    NPV at
Project     C0        C1      C2      C3      C4       C5       Etc. Percent 10 Percent

  G       - 9,000   +6,000 +5,000 +4,000           0        0    …     33     3,592


  H       - 9,000   +1,800 +1,800 +1,800 +1,800 +1,800           …     20     9,000


  I                 -6,000   +1,200 +1,200   +1,200 +1,200 …           20     6,000
  NPV, dollars
10,000

+6,000
+5,000                          33.3

                                            Discount Rate,
     0                                      percent
                 10   20   30   40     50
                                            Project G
           15.6

                                             Project H
  -5000
Pitfall 4. What happens if term structure is not flat?


        (generally)
         NPV = - C0 + C1 / (1+r1) + C2 / (1+r2)2 + …


         IRR vs.        r1
                        r2         ?
                        r3
5.5 Limited Resource (Capital Rationing)

    <$10> t=0
              CASH FLOWS, MILLIONS OF DOLLARS    NPV at
    Project       C0        C1         C2       10 Percent
      A          - 10      + 30       +5           21
      B           -5        +5        + 20         16
      C           -5        +5        + 15         12
<$10> t=0, t=1


             CASH FLOWS, MILLIONS OF DOLLARS    NPV at      Profitability
 Project         C0        C1          C2      10 Percent      Index
   A             - 10     + 30         +5         21            2.1
    B            -5        +5         + 20        16            3.2
    C            -5        +5         + 15        12            2.4
   D               0      - 40        + 60        13            0.4
• More Elaborate Capital Rationing Models
 We accept proportion A of project A.

 NPV of accepting A of A 



 Previous Example

 NPV =
Constraint: (Costs)
at t = 0, 10 A + 5 B + 5 C + 0 D  10
at t = 1, 40 D  30A + 5 B + 5 C + 10

       0  A , B , C , D  1

 Maximize: 21 A + 16 B + 12 C + 13 D

   Subject to : 10 A + 5 B + 5 C + 0 D  10
                -30 A - 5 B - 5 C + 40 D  10
                     0  A ,  B , C , D  1
   Making Investment Decisions with
    the Net Present Value Rule



                           Chapter 6
• How to apply the rule to practical investment problems?
• Question
   What should be discounted?
      CF: relevance, completeness, consistency, accuracy
    How NPV rule should be used when there are
     project interactions?
• Estimate Cash Flow on an Incremental Basis

  Average vs. incremental
  Include all incidental effects
  Do not forget NWC requirement
  Forget sunk cost
  Include opportunity costs
  Beware of allocated overhead costs
  Consider spillover effect “erosion”
• Treat Inflation consistently.
   – Real CF     : discount with real rate
   – Nominal CF: discount with nominal rate
  (Ex)              C0    C1   C2    C3
         Real CF -100 + 35     +50   +30
         rN = 15%, I = 10%
   NPV =

   NPV =
6.2 Example - IMFC Project


• Initial investment: $ 10 mil
• Salvage value at year 7: $ 1 mil (sold)
• Depreciation: 6 year straight line with arbitrary
  salvage of : $ 500,000
                            9.5 mil
      annual depreciation =             = $ 1.583 mil
                               6
Table 6 - 1 Nominal Cashflow
Ex: forecast of inflation: 10%
IM&C's guano project - revised projections reflecting (figures in thousands of dollars)
                                                                   PERIOD
                                 0           1            2            3            4            5        6        7
1. Capital investment        10,000                                                                              -1,949*
2. Accumulated
   depreciation                            1,583        3,167        4,750        6,333        7,917    9,500      0
3. Year-end book value       10,000        8,417        6,833        5,250        3,667        2,083     500       0
4. Working capital                          550         1,289        3,261        4,890        3,583    2,002      0
5. Total book value
     (3 + 4)                 10,000        8,967       8,122        8,511        8,557         5,666    2,502      0
6. Sales                                    523        12,877       32,610       48,901        35,834   19,717
7. Cost of goods sold                       837        7,729        19,552       29,345        21,492   11,830
8. Other costs **             4,000        2,200       1,210        1,331        1,464         1,611    1,772
9. Depreciation                            1,583       1,583        1,583        1,583         1,583    1,583
10. Pretax profit
    (6 - 7 - 8 - 9)          -4,000       -4,097        2,365       10,144       16,509        11,148   4,532    1,449**
11. Tax at 35%               -1,400       -1,434         828        3,550        5,778         3,902    1,586      507
12. Profit after tax         -2,600       -2,663        1,537       6,594        10,731        7,246    2,946      942
*   Salvage value.
** The difference between the salvage value and the ending book value of $ 500 is a taxable profit
  IM&G‟s guano project-cash-flow analysis
                                                                                (thousand)
  Period
                               0        1        2        3      4      5         6         7
1. Sales                               523     12,887   32,610 48,901 35,834 19,717
2. Cost of goods and sold              837      7,729   19,552 29,345 21,492 11,830
3. Other costs               4,000    2,200     1,210    1,331 1,464 1,611 1,772
4. Tax on operations        -1,400 -1,434         828    3,550 5,778    3,902    1,586
5. Cash flow from           -2,600 -1,080       3,120    8,177 12,314   8,829    4,529
   operation
6. Change in working                   -550      -739   -1,972 -1,629   1,307    1,581   2,002
   capital
7. Capital investment and   -10,000                                                      1,442
   Disposal
8. Net cash flow            -12,600   -1,630    2,381    6,205 10,685 10,136     6,110   3,444
9. Present value at 20%     -12,600   -1,358    1,654    3,591 5,153 4,074       2,046     961


Net present value = +3,519(sum of 9)
• Cash flow = Sales - CGS - Other costs - Taxes
• Net cash flow = Cash flow from operation 
                   Networking capital
 [- Initial Investment + Recovery of Salvage Value]

• NPV =
6.3 Project Interacting

Choosing between Long & Short Equipment

       C0     C1   C2     C3     PV
                                at 6%
 A    +15    +5    +5     +5    28.37
 B    +10    +6    +6           21.00
Equivalent Annual Cost

            C0    C1     C2   C3    PV
                                   at 6%
Machine A   +15   +5     +5   +5   28.37
 EACA             x      x    x    28.37
Machine B   +10   +6     +6        21.00
 EACB             y      y         21.00
   Risk and Return & opportunity
    Risk, Return & Opportunity
    Cost of Capital
            Cost of Capital


                       Chapter 7&8
7.1 Seventy-Two year of Capital Market
 Dollars
                                                                       5,520 Small Cap
                                                                       1,828 S&P
1000


                                                                   55.38 Corporate Bonds
                                                                    39.07Government Bonds
 10                                                                    14.25 Treasury Bills




 0.1
   1925    1933   1941   1949   1957   1965   1973   1981   1989   1997
 Dollars


1000
                                                                   613.5 Small firms
                                                                   203.2 S&P 500



 10                                                                6.16 Corporate bonds
                                                                   4.34 Government bonds
                                                                   1.58 Treasury bills


 0.1
   1925    1933   1941   1949   1957   1965   1973   1981   1989   1997
Average rate of return on Treasury bills, Government bonds,
Corporate bonds, and common stocks, 1926-1997

                                                   (Percent per year)
                   AVERAGE ANNUAL        AVERAGE RISK PREMIUM
                    RATE OR RETURN
                                           (EXTRA RETURN VS.
PORTFOLIO          NOMINAL       REAL        TRESURY BILLS)

Treasury bills        3.8          .7                 0
Government bonds      5.6         2.6                 1.8
Corporate bonds       6.1         3.0                 2.3
Common stocks        13.0         9.7                 9.2
(S&P 500)
Small firm           17.7        14.2                13.9
common stock
7.2 Measuring Portfolio Risk
   • Variance (Standard Deviation)
   • Expected =  Ri * Pi = E (R) = R
   • Variance =  (Ri - R)2 * Pi = 2 = V

   • Risk
     Systematic Risk: market risk
         macro-economic variables
     Unsystematic Risk: firm unique or specific risk
                         STANDARD
   PORTFOLIO             DEVIATION()       VARIANCE(2)
Treasury bills                3.2               10.2
Long-term government bonds    9.2               84.6
Corporate bonds               8.7               75.7
Common stock (S&P 500)       20.3              412.1
Small-firm common stocks     33.9             1149.2

       PERIOD                           MARKET SD()
      1926-1929                            23.9%
      1930-1939                            41.6
      1940-1949                            17.5
      1950-1959                            14.1
      1960-1969                            13.1
      1970-1979                            17.1
      1980-1989                            19.4
      1990-1997                            14.3
                   STANDARD                                      STANDARD
    STOCK          DEVIATION()                 STOCK            DEVIATION()
AT&T                           22.6           General Electric           18.8
Bristol-Myers Squibb           17.1           McDonald‟s                 20.8
Coca-Cola                      19.7           Microsoft                  29.4
Compaq                         42.0           Reebok                     35.4
Exxon                          13.7           Xerox                      24.3


Stock      SD()       MARKET         SD()   Stock    SD() MARKET SD()

BP          16.3       UK              12.2   LVMH      25.8     France      16.6
Deutsche    23.2       Germany         11.3   Nestle    18.9     Switzerland 14.6
Bank
Fiat        35.2       Italy           24.5   Sony      27.5     Japan          17.4
Hudson
Bay         26.3       Canada      11.7       Telefonia          Argentina      28.6
                                              de        52.2
KLM         30.1       Netherlands 14.2
                                              Argentina
Portfolio standard deviation




                                   Unique
                                   risk

                                                        Market risk
                               0
                                            5          10             15
                                            Number of Securities
7.3 Calculating Portfolio Risk

 n=2


                                       


              A                  B

                        


         Between A, B    Covariance; 2(,)
         Itself          Variance; 2(,)
    A   B
A

B
  Weights; A , B ,     A + B
               =1
            A            B
     A          2
                 A
                             AB
     B             BA      2
                             B



Portfolio Risk =
     Example;
                           
Bristol-Myers :     0.55   0.171
 McDonald‟s :       0.45   0.208

 BM =       0.15

    2
     p   =
n=3
Variance:
Covariance:

n=4
Variance:
Covariance:
Limits to Diversification

     VP = 2P = N * (1/N)2 2 + (N2 - N) * (1/N2) cov

     2 : average variance
     cov : average covariance

     2P = VP = (1/N) 2 + (1 - 1/N) cov
     lim VP 
      N


     (Ex) mutual fund
Special Cases
=1
  2P = X12 12 + X22 22 + 2X1X2 1 2 * 1
      = (X1 1 + X2 2 )2
                     ( a  b)2  a2 + b2  2ab

  P = X1 1 + X2 2 , when  = 1

     There is:
     • no diversification
     • no risk reduction

  * Portfolio risk is simply weighted average of
    individual risk; linear combination !
    =-1
    2P = X12 12 + X22 22 - 2X1X2 1 2
        = (X1 1 - X2 2 )2
    P = X1 1 - X2 2 , when  = -1

• Risk may be completely eliminated by combining
  X1, X2  (Ex)

• Portfolio Risk is (again) a linear combination of
  individual risks.
Example
                A          B
    E(R)        10%       12%
    2           9%       16%
    AB = -1
  Find the weights, A, B for Minimum
   Variance Portfolio. ( p = 0)
  What is the risk & return of that portfolio?

    * General case :   -1
       We need Calculus.
• Efficient Frontier
         Ep                   • B


                             AB = 1
                 A•
                                       P


        Ep          = -1      • B


               = -1   A•
                                       P
Generally   1

   Ep                   • B




                   A•


                              P
E(RP)

 22

 20
 18

 16

 14

 12

 10

  0
        09   11   13   15   17   19   21
                                           
                                           P
Efficient Portfolio
   E(RP)


                          
                      
                        
                        
                       
                  
               


                              P
We Introduce Borrowing & Lending (p193)
 2P = X12 12 + X22 22 + 2X1X2 1 2 12
 (risk-free asset : 2 = 0 )
 - Lending
   2P = X12 12  P = X1 1 (linear combination)
   EP = X1R1 + X2Rf

 - Borrowing
   2P = ( X* + 1 )2 12 + ( -X* )2 22 + 2( 1+X* )( -X* ) 12
   P = (1+X*) 1
   EP = (1+X*) R1 - X* Rf
 Portfolio Risk : Linear combination of individual risk
Combination of Risky(A) and Risk Free Asset




                      •
                          A

     Rf
New Efficient Portfolio



                                      C
                                  •
                                  •
                          •           D   Old Efficient
                                          Portfolio
            A                 T
              •
    Rf       B•
EP


                  T
EM                 •
Rf



                 M               P
 T is a market portfolio; M
 Capital Market Line  CML

     • Risk-return relationship for efficient portfolios
     • Intercept: Rf  price of time
     • slope: (EM - Rf) / M  price of risk
             Ep = Rf + [ (EM - Rf) / M ] x P
• Capital Asset Pricing Model: CAPM
   Apply Portfolio Theory to evaluate all risky assets

      Systematic Risk vs. Unsystematic Risk
 We can eliminate unsystematic risk by combining
 securities. (it cancels each other)

 We can not eliminate systematic risk since it moves
 with market as a whole

    Therefore,
• Systematic Risk = Market risk = Covariance(iM)
     Required        Risk-free
  Rate of Return                   +        Risk
                   =
  on Risky Asset     Rate(Rf)             Premium

  = Rf + amount of risk  Price of risk

  = Rf +


  = Rf +


  = Rf +
   STOCK               BETA     STOCK            BETA
AT&T                    .65   General Electric   1.29
Bristol-Myers Squibb    .95   McDonald‟s          .95
Coca-Cola               .98   Microsoft          1.26
Compaq                 1.13   Reebok              .87
Exxon                   .73   Xerox              1.25


STOCK                  BETA   STOCK              BETA
BP                      .74   LVMH               1.00
Deutsche               1.05   Nestle             1.01
Bank
                              Sony               1.03
Fiat                   1.11
Hudson                        Telefonia de
Bay                     .51   Argentina          1.31
KLM                    1.13
                              EXPECTED RETURN
  STOCK                BETA       rf+(rm - rf)
AT&T                    .65          10.7%
Bristol-Myers Squibb    .95          13.1
Coca-Cola               .98          13.3
Compaq                 1.13          14.5
Exxon                   .73          11.3
General Electric       1.29          15.8
McDonald‟s              .95          13.1
Microsoft              1.26          15.6
Reebok                  .87          12.5
Xerox                  1.25          13.9
Summary

 “”
 1) Covariance risk (normalized)
         iM
         2M

 2) Sensitivity of stock i‟s return with respect to
    market
Ex:
Security Market Line: SML
          E(Ri)
                                          ?
             ?
             Rf

              0        1                      i
  1) CAPM Line
  2) Equilibrium Line;
    If asset is correctly priced (in its equilibrium),
    in terms of CAPM, it falls on this line.
    Below this line :
    Above this line :
E(R)
                •   C
                        •   B

rm

           •A
 rf


      0   0.5   1.0     1.5     
              Beta vs. Average Risk Premium

Avg Risk Premium 1931-91
                                                   Market line
   30
                                                          10
   20                                                9
                                              8
                                      6   7
        Investors           5
                        3
   10               2
               1            4                     Market Portfolio

    0

                                                      Portfolio Beta
                                1.0
Avg Risk Premium 1931-65                                     Market Line
    30
                                                              10
             Investors                                  9
     20                                     7     8
                                 45     6
                             3
                         2
                 1                                    Market Portfolio
     10

      0
Avg Risk Premium 1966-91          1.0                    Portfolio Beta
     30

                                                             Market Line
     20

          Investor       2   3   4 5                     9
                     1                  6   7     8
     10                                                      10
                                                Market Portfolio

      0
                                  1.0                       Portfolio Beta
8.4 Some Alternative Theories

   Arbitrary Pricing Theory
         Assumes that each stock‟s return
         depends partly on macroeconomic
         factors or noise
         (event that are unique to company)

          R = a + b1rf1 + b2rf2 + b3rf3 + … … noise
   Expected
   Premium = r - rf = b1 (r1- rf ) + b2 (r2 - rf )
                      + b (r - r ) + … …
                            3   3   f
APT example
 1. Identify the Macroecnomic Factors
   •   Yield Spread
   •   Interest Rate
   •   Exchange Rate
   •   Real GNP
   •   Inflation
 2. Estimate the Risk Premium for Each Factor
    Factor                  Estimated risk premium
                                  (rfactor - rf)
   Yield spread                      5.10%
   Interest rate                      -.61
   Exchange rate                      -.59
   Real GNP                            .49
   Inflation                          -.83
   Market                             6.63
3. Estimate the Factor Sensitivity
 Factor         Factor risk   Estimated risk      Factor risk
                                premium            premium
                   (b)          (rfactor - rf)   [b(rfactor - rf)]

Yield spread      1.04             5.10%             5.30%
Interest rate    -2.25             -.61              1.37
Exchange rate      .70             -.59               -.41
Real GNP           .17              .49                .08
Inflation         -.18             -.83                .15
Market             .32             6.63              2.04
Total                                                8.53%
   Capital Budgeting and Risk




                            Chapter 9
Are the New Projects More Risky or Less Risky
than its Existing Business?

         Each project should be evaluated
             at its own Cost of Capital
     (implication of Value Additivity Principle)

Firm Value = PV(AB) = PV(A) + PV(B)
            = sum of separate assets

PV(A), PV(B) are valued as if they were mini-firms
in which stockholders invest directly.
r


             •   B

     A•   Cost of Capital

rf


                        
• True Cost of Capital
  - depends on the use to which the capital is put
  - Project beta ()
    Expected Return = r = rf + (project beta)  (rm - rf)

• “” of project or division
   - Look at an average of similar companies
     (or industry beta)
  - Firm‟s borrowing policy (leverage) affects its stock
     beta
  - Project beta shifts over time.
Industry Beta and Divisional Cost of Capital
   Individual   measurement error
   Portfolio   error cancelled out


If you consider across-the-board expansion,
such as new division,
What is the “” for new division?

Answer:
• Measuring Betas
  – Using monthly stock return on IBM
  – Using monthly market return
  (Ex) 60 months

           R1IBM         R1M
           R2IBM         R2M
             ……



                        ……

           R60IBM       R60M
 ( = alpha)
  Average rate of price appreciation or depreciation,
  born by stock-holders when investors in the market
  as a whole earn nothing.


R-squared  R2
  The proportion of variance of stock price change
  that can be explained by market movement.
   means  systematic risk / total risk
          Change in prices
       of DEC common stock

                    Beta = 1.30




                                  Change in
   Alpha = -.65                   market index




 = -0.65% ; -0.65  12  -7.8%
9.2 Capital Structure & Company Cost of Capital(COC)
   Cost of Capital; hurdle rate
    minimum return required to make firm value unchanged.
    Depends on


    also depends on


   * Financial leverage does not affect the risk or the
     expected return on the firm‟s assets.
     But,
How Changing Capital Structure Affects Expected Return?

Company         = r Asset = r portfolio
Cost of Capital
                          D                 E
     (WACC) =                      rd +          re
                      D+E                  E+D

(EX)         B/S (market value)
             A 100          D 40
                            E 60
                   100         100
       r d = 8% r e = 15%
       r Asset =
 • (Now) : Issue 10 equity, Retire 10 debt
                    B/S (market value)
                    A 100          D 30
                                   E 70
                        100            100
* The change in financial structure does not affect

   does affect

 (Ex) lower leverage: rD  7.3% (Given)
  rAssets =
How does Changing Capital Structure Affect Beta?

                          D   + E 
 Assets = Portfolio   = V    D
                                  V    E


 V=D+E                   D = 0.2   E = 1.2

 A =

 After refinancing; D  0.1(Given)
  Expected 20                                Before Refinancing
  return (%)

       requity=15
     rassets=12.2

         rdebt=8



                                                                   Beta
               0       debt= .2   assets= .8       equity=1.2
Expected
return (%)   20                                 After Refinancing

     requity=14.3
     rassets=12.2

        rdebt=7.3


                                                                   Beta
                0   debt=.1       assets=.8     equity=1.1
9.3 How to Estimate the company Cost of Capital

   • Pinnacle West‟s Common Stock
                                      Beta   Standard. Error
         Boston Electric             .60              .19
         Central Hudson              .30              .18
         Consolidated Edison         .65              .20
         DTE Energy                  .56              .17
         Eastern Utilities Associate .66              .19
         GPU Inc.                    .65              .18
         NE Electric System          .35              .19
         OGE Energy                  .39              .15
         PECO Energy                 .70              .23
         Pinnacle West Corp.         .43              .21
         PP & LResources             .37              .21
         Portfolio Average           .51              .15
requity = rf + equity  [ rm - rf]
        = 0.045 + 0.51  0.08 = 0.0858
           8.6%

                       D        E
rd = 6.9%, re = 8.6%, V = 0.43, V = 0.57
WACC = Company Cost of Capital
        = D  rd + E  re
           V         V
9.4 Discount Rates for International Projects

 • Foreign investments are not always riskier.
                           Correlation
                 Ratio                  Beta
                           coefficient
   Argentina      3.52         .416      1.46
     Brazil       3.80         .160       .62
   Kazakhstan     2.36         .147       .35
    Taiwan        3.80         .120       .47


 • Foreign Investment in the US
E(RP)

 22

 20                                 Taiwan Index
 18

 16

 14

 12

 10                              US Index

  0
        09   11   13   15   17     19       21
                                                 
                                                 P
9-4 Setting Discount Rate when you can‟t calculate 

    Avoid fudge factors
      Do not add fudge factors to the discount rate
       instead adjust cash flow forecasts
      (Ex) dry hole, FDA approval,
           politica1 unstability in foreign country etc


    Think about the determinant of asset beta
(Ex)
Q: What are industries which are risky,
   but have low  ?
• Determinants of Asset Beta:
   Cyclicality:
    Firms whose revenue depend on business cycle
     high 
   Operating Leverage
    Commitment to fixed production charges
    • High fixed cost ratio
     High operating leverage
     High Asset Beta
    Why ?
Break Even Point Analysis

$



                            Total
                            Cost
         Unit Variable
         Cost
                                    Fixed
                                    Cost
                                        Q
                         TR

                                  TC

                Profit




  Loss

                                  FC

          BEF

Low Fixed Cost
(high Variable Cost)     Low OL
                      TR

                             TC




                             FC


High Fixed Cost
(Low Variable Cost)    High OL
9-6 Another Look at Risk and Discounted Cash flow
    Risk-adjusted:
           n
    PV =  [Ct / (1+r)t],
         t=1
                               r = rf +  (rM - rf)
  (Ex)   r = 6 + 0.75  8 = 12%
            Year       CF       PV
              1       100       89.3
              2       100       79.7
              3       100      71.2
                               240.2
          100
          1.12
          x = 94.658 (x = certainty equivalent cash flow)
          100 = 89.3 = x
         (1.12)2          (1.06)2
          x = 100  (1.06/1.12)2 = 89.57
• General Solution
                                 Risky        1+rf  t
                                 Cash Flow        
  Certainly equivalent
  Cash Flow at time t =                       1+r 
                                                   
                                 at time t
                    1+rf   t
                           
  We call  t =            
                    1+r    
   Certainty equivalent coefficient
    1 = (1.06 / 1.12) = 0.946
    2 = (1.06 / 1.12)2 = 0.896
    3 = (1.06 / 1.12)3 = 0.848

  Valuing CE cash flow
          CE(CF)        CF
  PV =              =
          (1 + rf)     1+r
(Example)
 E(C) = -1,000,000  0.5 = -500,000
  r = 25%
                              
   NPV = -125 -    500 +  125
                   1.25       t=2
                                  (1.25)t
         = -125 or -$125,000?
  Convert into Certainty Equivalent cash flow:
  Success
    NPV = -1000 + (250/0.1) = +1500 (50% chance)
  Failure
     NPV = 0 (50% chance)
   E(NPV) = 1500  0.5 = 750 (if  = 0.5)
                 (750  0.5)
   NPV = -125 +      1.07    = 225.5 or $225,000
   Making Sure Managers Maximize NPV




                        Chapter 12
12.1 Incentives
A. Agency Problems in Capital Budgeting
   • Reduced Effort
   • Perquisites
   • Empire Building
   • Entrenchment
   • Avoiding Risk
B. Monitoring

C. Compensation
                                Capital     Return on   Cost of
                        EVA
                                Invested    Capital     Capital
        Coca Cola     $2,442    $10,814        36.0%      9.7%
    Dow Chemical        6,81     23,024       12.2         9 .0
       Ford Motor      1,719     58,272        12.1        9 .1
  General Electric     2,515     53,567        17.7      12 . 7
   General Motors     - 3,527    82,887         5.9        9 .7
   Hewlett- Packard     - 99     24,185        15.2      15 . 7
             IBM      - 2,743    67,431         7.8      11 . 8
Johnson & Johnson      1,327     18 ,138       21.8      13 . 3
            Merck      1,688     22 , 219      23.0      14 . 5
         Microsoft     1,727      5 , 680      47 . 1    11 . 8
     Philip Morris     3,119     42 ,885       20 . 1    12 . 5
          Safeway        335      4 , 963     15 . 7       8 .5
              UAL        298     13 , 420       9 .8       7 .2
       Walt Disney      - 347    30 , 702     11 . 0     12 . 6
   Corporate Financing and
    Market Efficiency



                              Chapter 13
                      B/S
                                ?
       How to spend $? How to raise $?

• So far, we assume „all equity‟ financing.
   Stockholders supply all the firm‟s capital, bear all
  the business risks, and receive all the rewards.
<Questions>
13.1 We always come back to NPV
  (ex) Government offer: $100,000, 10yrs at 3%
                           Market fair rate: 10%
  NPV = Amount borrowed - PV of interest payments
        - PV of loan payment
                      10 3,000
      = +100,000 -               - 100,000 = $43,200
                      t=1 (1.10)t    (1.10)10

  Difference between Investment & Financing Decisions
   Easy reverse  Abandonment value is O.K.
   Lose or make money is not easy
        180
Level


        130




         80
              Month
        230
Level




        180



        130



         80
               Month
13.2 Efficient Market Hypothesis
   • Definition
     Stock price reflects information
     immediately and completely

   • Level of Efficiency
     - Weak Form
       Stock price reflects previous price movement
       immediately and completely
     - Semi-Strong Form
       all publicly available information
     - Strong Form
       all information (public, private, and insider)
• Test of Market Efficiency
 - Weak form
 - Semi-Strong form
 - Strong form

• Market Anomaly
 - Small firm Effect
 - January Effect
 - Weekend Effect

Q: Is market inefficient?
   The Dividend Controversy




                          Chapter 16
Q1 : How company set dividend?
Q2 : How dividend affect stock price?

- So far:   Investment           Financing
                      independent
If dividend affects firm value, attractiveness of
new project depends on where the money is coming from.

Dividend                         Financing decision
Decision       Mixed with        Investment

Given capital budgeting & financing decision,
what is the effect of change in dividend?
16.1 How dividends are paid?
  Board of directors
  Record date

  Legal Limitation
  Companies are allowed to pay a dividend out of surplus
  but they may not distribute legal capital
  (par value of all outstanding shares)
  Share Repurchase
  ‟80: Ford: $1.2 bil, Exxon: $15 bil, IBM, COCA etc.
   Just after 1987 Crash: Citi Corp  $6.2 bil
  How to Repurchase?
  1. Open market repurchase
  2. Tender Offer
  3. Direct negotiation
Greenmail
Target of a takeover attempt buys off the hostile bidder
by repurchasing any shares that it has acquired with
premium at the expense of existing shareholders.


16.2 Information content of Dividend


 Signaling Model

 Other Signaling Tools
16.3 Dividend Controversy
 MM(1961)
 - Dividend irrelevance
 In a world without taxes and transaction costs
 (efficient and perfect capital market)
 (Ex)             B/S (Market Value)
          Cash 1,000       0         D
          FA 9,000      10,000+NPV E
         10,000 + NPV       10,000 + NPV
        Pay dividend by issuing new shares($1,000)
        We want to continue project w/t cash($1,000)
• Value of original shareholders‟ shares (Ex Post)
  = Value of company - Value of new shares
  = (10,000 + NPV) - 1,000 = $ 9,000 + NPV
      $1,000 cash dividend = $1,000 capital loss

Investment and borrowing policies are unaffected by dividend
[overall value 10,000 + NPV, is unchanged]

* Crucial Assumption
  New stock holders pay fair-price

Old stockholders have received $1,000 dividend
and $1,000 capital loss
Dividend policy doesn‟t matter.
(Ex)
       N = 1,000 shares
       NPV = $2,000

       Vold =

       Vold* =


       Number of
       new shares   =
       sold
16.4 The Rightist
  Trade a safe receipt with an uncertain future gain?
   Sell it!
   – Market Imperfection
      • Transaction costs
      • Temporarily depressed price
      • Information asymmetry about future Earning

16.4 The Leftist
   Tax Argument
    Weakened after 1986 „Tax Reform Act‟
16.6 Middle of the Roaders
• Without tax and transaction cost (perfect & efficient market),
  company‟s value is not affected by dividend policy (irrelevant):
  MM (1961)

• Even if with tax and other imperfections,
  Q: If company increase stock price by paying more or less
  dividend, why have not they already done so?
   (perhaps)



   – “Supply Effect”
   Does Debt Policy Matter?




                           Chapter 17
                 B/S
    Asset              Capital       Mix of different
    Structure          Structure     securities


       “Maximize V”

MM Proposition I
Firm can not change the total value of securities just by
splitting its cash flows into different streams. (RHS)
Firm value is determined by its real assets. (LHS)
17.1 The Effect of Leverage in a Tax Free Economy


     VU: Value of unlevered firm
     EL = VL - DL


     1) 1% of unlevered firm
     $ investment      $ return (NOI)
     .01  VU         .01  profit
2) 1% of equity & debt of levered firm (I: interest)

            $ invest          $ return
   Debt        .01 DL           .01 I         NI
   Equity      .01 EL       .01 (profit -I)
            .01(DL + EL)      .01  profit
               = .01 VL

  same profit (NOI)  same cost (same investment)
                 VU = VL
3) Buy 1% of equity of levered firm
               $ investment            $ return
                .01 EL              .01 (profit -I)
                = .01 (VL - DL)

4) Alternative way: Borrow .01 DL on your account
                    Buy 1% of equity of unlevered firm
                 $ investment              $ return
   Borrowing      -.01 DL              -.01 I
   Equity          .01 VU               .01 profit
                   .01(VU - DL)         .01  (profit - I)

      Same profit
                         same cost (same investment)
       VU = VL
Example of Proposition I (p.477)
A All Equity
   E(EPS) = $1.5, P = $10, E(R) = 1.5/10 = 15%

   N = 1,000
   P = $10
   VU = $10,000

    NOI($) 500 1,000 1,500 2,000
    EPS($) .5 1.0    1.5   2.0
    ROE(%) 5    10    15    20
B   Issue:
    debt $5000, k = 10%, repurchase: 500 shares

    N = 500
    P = $10, k = 10%
    Market value of stock: $5,000
    Market value of debt : $5,000
    NOI($) 500 1,000 1,500 2,000
    Interest 500 500   500   500
    NI($)      0    500   1,000   1,500
    EPS($)     0      1      2        3
    ROE(%)     0     10     20      30
3.00
                Equal proportions
                debt and equity
2.50
       Expected EPS with
       debt and equity
2.00
       Expected EPS with               All equity
       all equity
1.50


1.00

 .50                                Expected
                                    operating
                                    income

          500     1000     1500         2000
C   Personal Leverage
    Borrow $10, then invest $20 in two unlevered shares
    (Initially, I have $10)
                                          NOI($)
                                 500    1,000 1,500 2,000
    Earnings on two shares($)      1       2       3      4
    Interest($) at 10%            -1       -1      -1     -1

    Net Earnings($)                0       1       2      3
    Return on
                                   0%     10%    20%      30%
    $10 investment
17.2 How Leverage Affects Return

          Current structure   Proposed
             all equity       structure
 E(EPS)       $1.5             $2.0       NOI = $1,500 V=10,000
 P            $10              $10          N =1,000 D=5,000
E(ROE)          15%             20%         Kd = 10%   E=5,000


Leverage increases EPS, but not P.

 The change in EPS is exactly offset by a change in the
  rate at which the earning are capitalized.
  15%  20%
Expected return                   NOI
on asset(rA)    =       Market value of all security

Assumption:
• In a perfect market, borrowing decision does not affect
  operating income or total market value of its securities.

• Borrowing decision does not affect expected return
  on firm‟s assets(rA).
             D          E
  rA =           rD + D+E          rE
            D+E

  rE =      rA + D (rA - rD)
                    E

Expected Expected Debt/          Expected Expected
return on = return on + Equity  return on - return on
equity      assets      Ratio    assets      debt
• Proposition II (MM)
 The expected return on equity (rE) of a levered firm
 increases in proportion to debt to equity ratio (D/E)
 & the rate depends on the spread between rA and rD.

 (Ex)
               rA = 15%   D = 5,000
               rD = 10%   E = 5,000


        rE =
                                   r
• Figure 17-2
  MM‟s proposition II.                         rE =Expected Return on Equity
  The expected return on
  equity rE increases
  linearly with the debt-
  equity ratio so long as
  debt is risk-free. But if
  leverage increases the
  risk of the debt,                            rA =Expected Return on Assets
  debtholders demand a
  higher return on the
  debt. This causes the       rD
  rate of increase in rE to
  slow down.                                   rD=Expected Return on Debt
                                                                        D
                                   Risk free       Risky                E
                                   debt            debt
The Risk-Return Trade-off

       D        E
 A =     D +     E
      D+E      D+E
               D
 E = A +           (A- D)
               E

 Investors (stock-holders) require higher returns
  on levered equity
17.3 The Traditional Position

   A Moderate degree of financial leverage
     may increase rE although not to the degree
     predicted by MM proposition II

     Excessive debt raise rE faster
      rA (=WACC) decline & later rise.
     r                                             rE = (MM)


                                                  rE = (traditional)
                                                        rA = (MM)
                                                  rA = (traditional)



rD                                                           rD

                                                       D = debt
     Traditionalist believe there is an optimal        E   equity
     debt-equity ratio that minimizes rA
B Transaction Costs
  Imperfections may allow firms that borrow
  to provide valuable service.
  (Ex. Economies of scale in borrowing)

   Levered Shares might trade at premium
   compared to their theoretical value
   in perfect market
  Smart financial engineer already recognize this
  and shift capital structure to satisfy this client.
   How Much Should a Firm Borrow?




                         Chapter 18
Question: Why do we worry about debt policy?

Evidence:
1. D/E ratio are different across the industry.
2. Imperfections:
    • Tax
    • Bankruptcy Costs (T.C.)
    • Cost associated with financial distress
    • Potential conflicts of interests between security holders
    • Interactions of investment and financing decision
18.1 Corporate Taxes

                               Income statement Income statement
                                   of Firm U        of Firm L
Earnings before
         interest and taxes        $1,000           $1,000
Interest paid to bondholders            0               80
Pretax income                       1,000              920
Tax at 35%                            350              322
Net income to stockholders           $650             $598
Total income to both             $0 + 650 = $650 $80 + 598 = $678
bondholders and stockholders
Interest tax shield (.35interest)        0             28
Interest Payment =   rD  D

PV(Tax shield) =
                     TC   (rD• D)
                           rD
                =    TC D

PV(Tax shield) = 0.35  0.08  1000
                           0.08
                = $350
      Normal Balance Sheet(Market Values)
Asset value (present value            Debt
 of after-tax cash flows)            Equity
      Total assets               Total value

      Expanded Balance Sheet(Market Values)

Pretax asset value (present           Debt
value of pretax cash flows)   Government „s claim
                              (present value of future
                              taxes)
                                     Equity
   Total pretax assets             Total value
Table 18.3(a)
                          Book Values
  Net working capital    $2,644     $1,347    Long-term debt
  Long-term assets       17,599      6,282    Other long-term
                                                 liabilities
                                    12,614    Equity
  Total assets           $20,243   $20,243


                          Market Values
  Net working capital    $2,644     $1,347    Long-term debt
  Market value of                             Other long-term
  long-term assets       131,512     6,282
                                                 liabilities
                                   126,527    Equity
  Total assets          $134,156   $134,156       Total value
Table 18.3(b)
                             Book Values
  Net working capital      $2,644              Long-term debt
  Long-term assets                     6,282   Other long-term
                           17,599                 liabilities
                                      11,614   Equity
  Total assets             $20,243   $20,243


                            Market Values
  Net working capital      $2,644              Long-term debt
  Market value of                              Other long-term
  long-term assets         131,512     6,282
                                                  liabilities
  Additional tax shields                       Equity
  Total assets                                    Total value
MM & Taxes: MM Prop I with corporate tax.

VL = VU + PV (Tax Shield)

100% debt?
18.2 Corporate and Personal Taxes
                           Operating income
                                $1.00




   Corporate tax

   Income after
   corporate tax

    Personal tax

   Income after
     all taxes
Corporate Borrowing is better
  If (1 - TP) > (1- TPE) * (1 - Tc)
                                            (1 - TP)
  Relative Tax Advantage of Debt =
                                      (1 - TPE) • (1 - Tc)

Special Cases:
  1. TPE = TP,    RTAD =        1
                             (1 - TC)
     MM‟s original
  2. (1 - TP) = (1 - TPE) * (1 - Tc)
     RTAD = 1.0
     Debt policy is irrelevant!
     This case happen when Tc < TP & TPE is small.
(Ex) Tc = 35%, TP = 39.6%
     What TPE makes debt policy irrelevant?
18.3 Cost of Financial Distress
  Value of firm   Value of all + PV(tax shield)
  (levered)     = equity
                             - PV (costs of financial distress)
  Market Value of The Firm




                                                          Debt
Bankruptcy Costs
               ACE LIMITED                               ACE LIMITED
Payoff to     (limited liability)            Payoff to (unlimited liability)
bondholders                                  bondholders



                            Payoff                                    Payoff
  1,000                                        1,000
    500                                          500

                                     Asset                                     Asset
Payoff to 500 1,000                  value             500 1,000               value
stockholders                                 Payoff to
                            Payoff           stockholders
                                                                     Payoff
  1,000                                        1,000


     0                               Asset         0                           Asset
          500 1,000                  value             500 1,000               value

 -1,000                                       -1,000
Direct: legal fee, court fee, etc.
Indirect: difficult to measure




                            Table 18.4
                     SHARE PRICE             NUMBER OF CHANGE
           FRIDAY      MONDAY                  SHARES    IN VALUE
         APR 10, 1987 APR 13, 1987 CHANGE    (MILLIONS) (MILLIONS)

Texaco     $31.875        $28.50   -$3.375      242       -$ 817
Pennzoil    92.125         77.00   -15.125       41.5       -628
Total                                                     -$1,445
• Financial Distress without Bankruptcy
When firms get into trouble,
stockholders‟ & bondholders‟ interests conflict.
 reduce value of firm

           Circular File company (Book Values)
Net working capital    $ 20     $ 50    Bonds outstanding
Fixed assets             80       50    Common stock
Total assets           $100     $100    Total value

           Circular File company (Market Values)
Net working capital     $20      $25    Bonds outstanding
Fixed assets             10        5    Common stock
Total assets            $30      $30    Total value
 Risk Shift: The First Game
 (Ex1) C0                               C1
                                       $120 (p=10%)
        -$10
                                       $ 0 (p=90%)

         If r=50%,
                     1200.1+0
         NPV = -10 +           = -$2
                        1.5
           Circular File company (Market Values)
Net working capital     $10      $20    Bonds outstanding
Fixed assets             18        8    Common stock
Total assets            $28      $28    Total value
(Ex2): Amount of Debt = $600

              High Risk Project
        Good (p=0.5)       Bad (p=0.5)

  V         2,000                 300
  D
  S


  V=
  D=
  S=
           Low Risk Project
     Good (p=0.5)    Bad (p=0.5)

V       1,400            1,000
D
S


V=
D=
S=
Refusing to contribute equity capital: The second game

Good project with NPV= + $5 by investing $10

Net working capital   $20     $33   Bonds
Fixed assets           25      12   Common stock
Total assets          $45     $45   Total value

Firm value increase by $15
Bond value increase by $8
Stock value increase by $7
Cost of Distress Vary with Type of Asset

Firms with intangibles having value only as a part of
going concern, high technology, investment
opportunities, human capital, lose more in the financial
distress.
Trade off Theory of Capital Structure
Trade-off between interest tax shield and the costs
of financial distress

  • Company with safe, tangible asset and plenty of
    taxable income       High debt ratio
  • Unprofitable company with risky, intangible assets
          Equity finance
  • Trade-off theory explains what kinds of companies
   “go private in LBO”
  • Trade-off theory cannot explain why some most
    successful companies thrive with little debt.
18.4 The Pecking Order of Financing Choice,
     Information Asymmetry

     Asymmetric information affects the choice
     between internal and external financing and
     between new issues of debt and equity securities
        Pecking order: internal fund, new issue of debt,
        finally new issue of equity

     (Exception)
       Firm with already excessive debt
       High-tech, high-growth company
Implication of Pecking Order
1. Firms prefer internal financing
2. Firms adopt target payout ratio &
   try to avoid sudden changes in dividend
3. Sticky dividend policy
4. If external finance is required,
   debt, convertible bond, then equity

Financial Slack: Cash, marketable securities, readily
saleable real assets, & ready access to the debt market
or to bank financing
    More valuable to firm with plenty of positive-NPV
    growth opportunity
   Interactions of Investment and
    Financing Decisions



                            Chapter 19
 Introduction


• So far, all equity financing
           All financing decisions are irrelevant

• In this chapter,we consider capital budgeting decision
  when investment and financing decision interact
  and can not be separated
                  NPV of
APV = Base +      financing decisions
      NPV         caused by
                  project acceptance


   (value additivity principle)
19.1 After-tax WACC


 WACC =   rD D + rE E
             V      V

 WACC =   rD (1-Tc) D + rE E
                    V      V
Sangria Corporation

               (Book Values, millions)
Asset             $100       $50    Debt
                              50    Equity
Total assets      $100      $100    Total value


               (Market Values, millions)
Asset             $125       $50    Debt
                              75    Equity
Total assets      $125      $125    Total value
WACC =?
rD =0.08   rE =0.146     TC=0.35

 D =                   E =
 V                     V


WACC =
Invest: $12.5 million
        $ 7.5 million (Equity)
        $ 5 million (Debt)
Pretax cashflow: $2.085 (perpetual)
Tax: 35%
After-tax cashflow: $1.355 million


NPV =

Return on Investment =
Return on Equity:

NOI                  2.085
I                   -0.4     (=0.085)
Earning
After tax           1.685
-Tax                -0.59    (=1.6850.35)
                     1.095

Expected return on Equity = 1.095 = 0.146
                            7.5
E(RE) = rE          NPV=0
19.2 Using WACC - Some tricks of the trade

Current Assets,                Current liabilities,
  including cash, inventory,     including accounts payable
  and accounts receivable        and short-term debt
Plant and equipment            Long-term debt (D)
                               Preferred stock (P)
Growth opportunities           Equity (E)
                                Firm value (V)




                               Total capitalization (V)
Industry Cost of Capital

Cost of capital of new subsidiary
   Company‟s WACC vs. a weighted-average cost
   of capital of for a portfolio of industry
An Application of the Railroad Industry
Aggregate industry capital structure in 1979
Debt            $24,383 bil   29.7%
Equity          $57,651 bil   70.3%
rd=7.2%, g=11.5%, D/P= 2.3%, TC = 35%
rE =
WACC =
Valuing Companies:
WACC vs. Flow-to-Equity Method

 WACC
 • Debt ratio is expected to be constant
 • Calculate tax as if firm is all equity-financed
 • Usually forecast to a median-time horizon and add
   a terminal value to the cashflow in the horizon year
 • Discount at WACC        evaluation of the assets and
   operation of the firm
 Flow-to Equity Method
  • Evaluation of equity
  • Discount the cashflow to equity, after interest
    and taxes, at the cost of equity
  • Leverage change       cost of equity change
       two methods give different answer

   rE=rA +   D (r -r )(1-T )
             E A D        C
19.3 Adjusting WACC when debt ratios or
     business risks change
   Rate of         Cost of Equity(rE)
    return




                   Opportunity cost of capital (r)
    r
                                        WACC


                              Cost of
                              Debt(rD)
                                                     Debt-Equity
                                                     Ratio
(Ex) D                        D
     V = 0.4                  V = 0.2
    Step1: unlevering the WACC

          Calculate opportunity cost of capital
           r = rD D + r E E
                     V           V
        * If taxes are left out, WACC equals the r and
          is independent of leverage

    Step2: Estimate rD at 20% debt ratio, &
           Calculate new rE
          rE   =   rA + (rA- rD)
                              D
                              E
    Step3: Recalculate the WACC at the new financing
           weight
                  D
Step1: current    V = 0.4
      r=

                            D
Step2: rd = 8%,    when     V= 0.2
       rE=

Step3:
 WACC=
    Rate of
return, percent
                                 14.6          Cost of Equity(rE)
    14            13.0

                               Opportunity cost of capital (r)
    12
                  11.4
                                 10.84
                                                      WACC
    10



                                  8.0           Cost of
    8
                                                Debt(rD)
                                                                    Debt-Equity
                    .25             .67                             Ratio(D/E)
                  (D/V = .2)      (D/V = .4)
Unlevering and Relevering 

- Unlevering 
  asset = debt ( D ) +  equity( E
                    V                 V
  )
- Relevering 
  equity = asset + (asset - debt) D
                                     E
  or (1+ D ) asset , if debt = “0”
           E
  *. Underlying assumption: Rebalancing
     Maintain the same market-value debt ratio
19.4 The Adjusted Present Value Rule
   Base-NPV
                10
   NPV = -10 +  [1.8 / (1.12)t ] = $0.17 mil
               t=1

   • Issue costs.
     5% of gross proceeds of issue
     
    APV = base NPV - issue cost
        = .17 mil - 526,000 = -356,000  Reject it!
   • Additions to the Firm‟s debt capacity
    APV = base NPV + PV tax-shield
Table 19-1
Calculating the present value of interest tax shields on debt supported by
the solar heater project (dollar figures in thousands)
                      Debt Outstanding                     Interest   Present Value
  Year                  at Start of Year      Interest   Tax Shield    of Tax Shield
    1                      $ 5,000            $400           $140             $129.6
    2                        4,500             360            126             108.0
    3                        4,000             320            112              88.9
    4                        3,500             280             98              72.0
    5                        3,000             240             84              57.2

    6                        2,500              200            70             44.1
    7                        2,000              160            56             32.6
    8                        1,500              120            42             22.7
    9                        1,000               80            28             14.0
    10                         500               40            14              6.5
                                                                          Total: $576
Assumptions:
1. Marginal tax rate = Tc = .35; tax shield = .35 x interest.
2. Debt principal repaid at end of year in ten $500,000 installments.
3. Interest rate on debt is 8 percent.
4. Present value calculated at the 8 percent borrowing rate. The assumption here is
   that the tax shields are just as risky as the interest payments generating them.
• APV = 170,000 + 576,000 = $746,000
• The value of interest Tax Shield (ITS).
   – We treat the interest tax shield as safe cash-inflow
     & discount at 8%.
   – We assume firm can capture interest tax shields of
     35cents on every dollar of interest.

• You can‟t use interest tax shield unless you pay taxes.

• Corporate tax favors debt.
  Personal tax favors equity.
• A project‟s debt capacity depends on how well it does.
APV for the Perpetual Crusher project
Base case NPV = - 10 + 1.355/0.12 = $1.29 mil
Financing Rule 1: Debt fixed
Financing Rule 2: Debt rebalanced
    Under rule 1
    PV (tax shield) = [0.350.08 5] ÷ 0.08 = $1.75 mil
    APV = 1.29 + 1.75 = $3.04 mil
    Under rule 2
    Debt is rebalanced to 40% of actual project value.
     debt levels are not known & depend on the
      project‟s actual performance.  cost if capital is
    12%
    PV(tax shield) = (0.35 0.08 5)  0.12 = $1.17 mil
    APV = 1.29 + 1.17 = $2.36 mil
A. Technical Point on Financing Rule 2

   • Discount at opportunity cost of capital

   • Multiply the resulting PV by (1+r) and
     divide by (1+rD)

                    0.14
     PV(approx) =         = 1.17
                    0.12
     PV(exact) = 1.17  1.12 = 1.21
                         1.08

     APV = 1.29 + 1.21 = $2.5 mil
APV and hurdle Rates
APV tells whether a project makes a net contribution
to the value of the firm
        It tells break-even cashflow
         CF                       Tax
APV =           - Investment + PV Shield
          r
                CF
(Ex) APV =            - 10 + PV Tax
               0.12             Shield
            CF
     APV =            - 10 + 0.97 = 0
           0.12
        CF = 1.084               IRR = 10.84%
General Definition of
                Adjusted Cost of Capital

 • The Opportunity Cost of Capital (r)
   The expected rate of return offered in capital markets
   by equivalent-risk assets.
   This depends on the risk of the project‟s cash flows.

 • The Adjusted Cost of Capital (r*)
   Adjusted opportunity cost or hurdle rate that reflects
   the financing side effects of an investment project
   Spotting and Valuing Options




                           Chapter 20
20.1 Call vs. Put
Call: Right to buy underlying asset at a specified price
Put: Right to sell underlying asset at a specified price
American: Exercise anytime
European: Exercise only at an expiration date

Exercise Date     Exercise      Price of        Price of
                   Price       Call Options    Put Options

October 1998        $80           $8.875          $3.25
January 1999         80           11.375            4.75
January 1999         85            8.625            6.875
Value                         Value
of Call                       of Put

                                 85
   85




                85    Share                  85   Share
          (a)         Price            (b)        Price

           Value
           of Share

                 85




                                       Share
                                       Price
                              (c) 85
    Selling Calls, Puts, and Shares
                           85                                   85
  0                                     Share      0                    Share
                                        Price                           Price




-85
                                                  -85

Value of Call                               Value of Put
Seller‟s Position       (a)                 Seller‟s Position    (a)
                                            85                  Share
                                0                               Price




                              -85

                    Value of Stock
                    Seller‟s Position       (c)
Value
of Share                    Your Payoff                     Your Payoff

      Buy Share                           Sell call


                           +                                =


           $85    Future Stock              $85       Future Stock        $85 Future Stock
                  Price                               Price                   Price
Value
of Share                    Your Payoff                     Your Payoff

      Buy Share                           Buy Put


                           +                                =


           $85    Future Stock             $85      Future Stock          $85 Future Stock
                  Price                             Price                     Price
Value                              Your                         Your
of Share                           Payoff                       Payoff

                                            Buy Call
      Bank deposit paying $85

$85                             +                          =


               $85        Future             $85       Future            $85   Future
                          Stock                        Stock                   Stock
                          Price                        Price                   Price
Put - Call Parity

C + PV (Ex) = P + S

                        Expiration Date
   Today
                    S*  EX          S* < EX

V1=C+PV(EX)

V2=P+S
The Difference between Safe & Risky Bonds

Bond holder: Effectively acquire a firm
Stock holder: Effectively purchase a call option
               on the assets of firm
              (PB=promised payment to bondholders)

               Circular File Co. (MV)
Asset value        $30       $25   Bond: Asset - Call
                              5    Stock: Call
                   $30      $30    Firm: Asset
Stockholders‟ Position
       V<50         S=
       V50         S=

    S




     0             Ex= $50              V
                   (Promised Payment to Bondholders)
Bondholders‟ Position
      V<50         B=
      V50         B=

    B




     0            Ex= $50              V
                  (Promised Payment to Bondholders)
PB: Promised Payment to Bondholders (safe)
V : Firm value (asset)
S : Stock value
B : Risky bond value
C+ PV(EX) = P + S
              ?
S+ PV(PB) = P + V
S+ B = V
B = V - S = PV(PB) - P

Value of = Value of - “p”
risky debt riskless
           debt
          Circular File Co. (Market Value)
Asset value $30   $25 Bond value = present value of promised
                                   payment - value of put


                    5 Stock value = asset value - present value
                                    of promised payment +
                                    value of put



           $30    $30
  Spotting the Option
  (Ex) Incentive program:
       Paid bonus of $50,000 for every $ that
       price of stock exceeds $120. Maximum
       bonus is set at $2 million
Pay
off

$40




  0
                 120        160           Stock Price
Pay
off




  0                                        Stock Price
                   120         160



      Buy call with exercise price of $120 and
      Sell call with exercise price of $160

      * Any set of contingent payoffs can be valued
        as a mixture of simple options on that assets
20.3 What determines option values?
 Value
 of call

           Upper bound:
           Value of call                    B
           equals share
           price




                                            Lower bound:
                                            Value of call
                                            equals payoff
                                            if exercised
                                  C         immediately

 A                         Exercise price              Share Price
Payoff to call
option on firm
  X‟s shares
                   Probability
                   distribution of
                   future price of                    Payoff to
                   firm X‟s shares                    option on X




Payoff to call                       Exercise price
option on firm
  Y‟s shares

                 Probability
                 distribution of
                 future price of                      Payoff to
                 firm Y‟s shares                      option on Y




                                     Exercise price
Value of calls
on shares of
firms X and Y
                                  Upper bound




                         Y
                                  Lower bound

                         X


                 Exercise price             Share Price
   What the price of a call options depends on
1. Increase in variables:
   If there is an                     The changes in the call
   increase in:                       option price are:
      Stock price (P)                 Positive
      Exercise price(EX)              Negative
      Interest rate (rf)              Positive
      Time to expiration(t)           Positive
      Volatility of stock price ()   Positive
2. Other properties:
   a. Upper bound. The option price is less than the stock price
   b. Lower bound. The option price never falls below the payoff
      to immediate exercise (P-EX or zero, whichever is larger)
   c. If the stock is worthless, the option is worthless
   d. As the stock price becomes very large, the option price approaches
      the stock price less the present value of the exercise price
20.4 An Option-Valuation Model
 Constructing Option Equivalents from
 common stocks & borrowing

 Stock Price      Stock Price
   Today         6 months later         Call
                        $68
    $85
                    $106.25

 rf =2.5%
 Exercise price = $85
• Hedge ratio (Option delta):
 Number of shares that are needed to replicate on call
 Option    Spread of option prices
 delta = Spread of share prices

         =

• How much to borrow?
  Present value of the different between the payoff from
  the option and the payoff from the option delta number
  of shares

 PV(37.78) = $36.86             Amount of borrowing
Option Equivalents:
Buy 5 shares and borrow $36.86 today
     9
                        6 month later
   Today          S* = $68         S* = $106.25
Buy 5 shares
     9
Borrow $36.36


Value of call today
= value of shares - $36.86 bank loan
=
Arbitrage Opportunity
EX 1: If call is priced at $12 : overpriced

Strategy: Sell a call option
          Buy 5/9 share & borrow 36.86 today
                         6 month later
  Today
                   S* = $68         S* = $106.25
  +12
   -47.22
  +36.86
 + $ 1.64
EX 2: If call is priced at $9 : underpriced

Strategy: Buy a call option
          Sell 5/9 share of stock short
          & lend(deposit) $36.86 today
                         6 month later
  Today
                   S* = $68         S* = $106.25
    -9
  +47.22
  -36.86
 + $ 1.36
Risk-Neutral Valuation: All investors are indifferent about risk
Expected Return on any risky assets = rf =
E(R) = Pu  Ru + Pd  Rd
Ru = 106.25-85 =
         85
         68-85
Rd =               =
           85
E(R) = Pu  (      ) + Pd  (      )=
where, Pu + Pd = 1      Pu = probability of stock price
                             increase in the hypothetical
Pu =        Pd =             risk-neutral world

at t=1 E(C1) =
at t=0   C0 =
Valuing the Intel Put Option
   t=0                  S                 P   EX=$85

                       $68
   $85
                      $106.25
  Option        Spread of option prices
  delta =       Spread of share prices

          =                  =

              shares Intel share &
 Lend $46.07           How is it computed?
                            6 month later
   Today              S* = $68         S* = $106.25
Sell 4 shares
    9
Lend $46.07



Value of put = - 4 of share + $46.07 bank loan
                  9
              =
20.5 The Black -Scholes Formula
  Construct a situation where the stock price is
  changing continuously and generate a continuum
  of possible six month prices
       Replicate a call option by a levered
       investment in the stock by adjusting
       the degree of leverage continuously


  Value of call = (delta  Share price) - (bank loan)

                  [N(d1)       P]    [N(d2)  PV(EX)]
Value of call=[N(d1)  P] + [N(d2)  PV(EX)]
 where
      Log[P/PV(EX)]           t
d1 =                     +
           t                 2
d2 = d1 -  t
N(d) = cumulative normal probability density function
EX = exercise price of option; PV(EX) is calculated
    by discounting at the risk-free interest rate, rf
  t = number of periods to exercise date
  P = price of stock now
   = standard deviation per period of
     (continuously compounded) rate of return on stock
   Real Options




                   Chapter 21
Real Option

 Option to make follow-on investment if
 the immediate investment project succeeds.
 Option to abandon a project
 Option to wait before investing
 Option to vary the firm‟s output or its
 production methods
21.1 The value of follow-on investment
Table 21-1
Summary of cash flows and financial analysis of
the Mark I microcomputer
                                                (millions of dollars)

                                           Year
                         1982   1983   1984 1985      1986      1987
After-tax operating
  cash flow (1) *        -200   +110   +159   +295    +185         0
Capital Investment (2)   250      0      0       0         0       0
Increase in working
                           0     50    100     100    -125     -125
  capital (3)
Net Cash Flow            -450   +60    +59    +195   +310 +125
  (1) - (2) - (3)
NPV at 20% = - $46.45, or about -$46 million
• Table 21-2.
  Valuing the option to invest in the Mark II microcomputer.
  Assumptions
  1. The decision to invest in the Mark II must be made after
     3 years, in 1985.
  2. The Mark II investment is double the scale of the Mark I
    (note the expected rapid growth of the industry). Investment
     required is $900 million (the exercise price), which is taken
     as fixed.
  3. Forecasted cash inflows of the MarkII are also double those
     of the MarkI, which present value of about $800 million in 1985
     and 800/(1.2)3 = $463 million in 1982.
  4. The future value of the Mark II cash flows is highly uncertain.
     This value evolves as a stock price does with a standard deviation
     of 35 percent per year.(Many high-technology stocks have
     standard deviation higher than 35%.)
  5. The annual interest rate is 10 percent.
• Interpretation
  The opportunity to invest in the Mark II is a 3-year
  call option on asset worth $463 million with a $900
  million exercise price.

• Valuation
  PV(EX) =
                900
               (1.1)3 = 676
  Call value = N(d1)P - N(d2) • PV(EX)
  d1 = log[0.685] / 0.606 + 0.606 /2 = -0.3216
  d2 = d1 - 0.606 = -0.9279
  N(d1) = 0.3739     N(d2) = 0.1767
  Call value = 0.3739463 - 0.1767676 = $53.59 mil
21.2 The Option to Abandon

                   Tech A      Tech B
  Good Demand       $18.5        $18
  Bad Demand          8.5          8

  If we bail out Tech B for $10 mil when bad demand
      Exercise option to sell assets
  Value of Tech B
  = DCF + Value of the abandonment Put
            (Value of Flexibility)
Valuing the Abandonment Put
    t=1                 Pr        Payoff          Put
Good Demand            0.5         $ 18
Bad Demand             0.5        $ 8
EX = $10, r = 8.3%, rf = 5%
PV=
E(R) = Pu  (    ) + Pd  (       )=       = rf
Pu =            Pd =
E(P) = 0.46    + 0.54       =
    E(P)
P=        =
    1+rf
Value of project =
21.3 The Timing Option: rf = 5%
      t=0                                t=1
                               Project   Cash   Value of
                               Value     flow   Call
                      Good
If invest $180,       Demand    $250     $25
project worth $200
                      Bad       $160     $16
                      Demand


   If undertake project today,
   capture either $25, or $16 at t=1
   If delay, miss out on this cashflow at t=1, but
   will have more information on how the project
   is lively to work out
Value of
 option
to invest




            Investment can
            be postponed

                             Investment now
                             or never


                      0         Project NPV
RG=

RB=

E(R) = PG (          ) + PB (   )=   = rf
PG =          PB =

t=1, E(C) =
t=0, Value of call =

Q: Do you undertake project now?
   Warrants and Convertibles




                           Chapter 22
22.1 What is warrant?
  Value of
  warrant


                Actual warrant value
                prior to expiration



                                    Theoretical value
                                    (lower limit on
                                    warrant value)
                                                        Stock
             Exercise price = $15                       price
• Two Complications: Dividends and Dilution
• Example: Valuing United Glue‟s Warrants
  Number of shares outstanding (N) …………..    1 million
  Current stock price (P) ……………………..         $12
 Number of warrants issued       …………..
 per share outstanding      (q)               .10

 Total number of warrants issued (Nq) ………. 100,000
 Exercise price of warrants (EX) …………… $10
 Time to expiration of warrants (t) …………… 4 years
 Annual standard deviation of
  stock price changes          () …………… .40
 Rate of interest (r):………………………….. 10%
 United stock pays no dividends.
United Glue‟s market value balance sheet (in $ millions)
                        Before the Issue
 Existing assets         $16      $ 4      Existing loans
                                   12      Common stock
                                            (1 million shares
                                               at $12 a share)
 Total                   $16      $16      Total

                        After the Issue
 Existing assets         $16      $ 4      Existing loans
 New assets financed                1.5    New loan without
 by debt and warrants      2               warrants
                                    5.5    Total debt
                                     .5    Warrants
                                   12      Common stock
 Total                   $18      $18       Total
United Glue has just issued a $ 2million package
of debt and warrant

Suppose
$ 1.5 mil: value of debt without warrants
$ 0.5 mil: value of warrants

Each warrant costs investors =
Value of warrant from Black-Scholes formula
=
• Dilution Effect
 Nq =
 Nq EX =



 V: value of equity
 V = Total asset - debt

 Share price after
 exercise          =
Warrant value
at maturity     = Max (P - EX, 0)
                = Max V + Nq•EX - EX, 0
                          N + Nq
                        V/N + EX
                = Max              ,   0
                          1+q
                   1
                =     Max V - EX ,     0
                  1+q     N
$ 12.5 mil: Current equity value of alternative firm
             (=18 mil - 5.5 mil)
Current share price
of alternative firm  = V = 12.5 = $12.5
                         N       1 mil
Suppose  of alternative firm:  = 0.41
Black-Sholes value of call:
                     1  Value of call on
Value of warrant =
                   1+q      alternative firm

                 =


            deal for United
22.2 What is a Convertible Bond
  • Difference between convertible bond vs.
    bond-warrant package
  • The price of convertible bond depends on its bond
    value and its conversion value

   Bond value:


   Conversion value:
                        • Value at Maturity
                        3                                                                                     3
Bond value, $thousand




                                                                                          Conversion value,
                                                              Bond paid




                                                                                             $thousand
                        2                                       in full                                       2

                            Default
                        1                                                                                     1



                        0       1       2                     3        4          5                           0     1       2       3   4      5
                               Value of firm ($ million)                                                           Value of firm ($ million)
                                                              3
                                      Value of convertible,




                                                                                                              Convert
                                          $ thousand




                                                              2                Bond paid
                                                                                 in full
                                                                  Default
                                                              1



                                                              0            1          2                       3         4       5
                                                                      Value of firm ($ million)
                  • Value before Maturity




                                                                                    Lower limit on Convertible,
                        3                                                                                         3
Bond value, $thousand



                                                                                                                                  Conversion Value




                                                                                            $thousand
                        2                                                                                         2

                                                                                                                      Bond Value
                        1                                                                                         1



                        0    1       2                     3      4         5                                     0       1        2       3   4     5
                            Value of firm ($ million)                                                                    Value of firm ($ million)
                                                           3
                                   Value of convertible,
                                       $ thousand




                                                           2   Value of convertible

                                                                                                                  Lower limit
                                                           1                                                      on value


                                                           0          1         2                                 3           4        5
                                                                          Value of firm ($ million)
Forcing Conversion
Value of Convertible


                            Conversion Value

                                               Call price

                           Bond Value

                       A                B        C
                                                            Stock price



 Value of     Value of
convertible = straight + Conversion - Redemption
   bond         bond       option       option
22.3 Difference between Warrants and Convertibles
  1. Warrants are usually issued privately
  2. Warrants can be deleted
  3. Warrants may be issued on their own
  4. Warrants are exercised for cash
  5. A package of bond & warrants may be
     taxed differently


22.4   Why do companies issue
       Warrants and Convertibles?
   Valuing Debt




                   Chapter 23
• Present Value of Bond
            C        C         C       … + (1000+C)
 PV =            +       2 + (1+r )3 +
          (1+r1)   (1+r2)        3          (1+rn)n
 r1 , r2 , r3 , …. rn : discount rates for cashflows to be received
                        by the bond holders in periods 1, 2, …,n.
Q: What determines the discount rates?
(Ex)
  Same security offers different yields at a different time.
 Bonds maturing at different dates offer different
  rate of interest
 Borrowing rate of government is lower than your
  borrowing rate
23.1 Real and Nominal Rates of Interest
Real Rate: compensation for time value of money
Nominal Rate = Real Rate + Perspective Rate of Inflation


How Real Rate is determined?

 Supply of capital: time preference for today‟s consumption
                    over future consumption
 Demand of capital: Availability for profitable investment
                    opportunities ( Positive NPV Projects)
     S        S

r1
r        r
         r2

     D        D
23.2 Term Structure and Yield to Maturity
PV =        C
           1+r
           C 1      C
PV = 1+r + (1+r )2
              1       2
r1, r2 : Spot rate
The series of spot rates r1, r2 …
                                 Term structure of interest rates
• Yield to Maturity
 Rate of return to bondholders if he/ she keeps the bond
 until maturity
                      C            C        … + C+F n
 Price of Bond =            +          2 +
                    (1+y)       (1+y)                (1+y)
                                     PRESENT VALUE CACULATIONS
                                     5s of „08         10s of „08
  PERIOD   INTEREST RATE          Ct      PV AT rt   Ct       PV AT rt
  t=1           r1 = .05       $ 50       $ 47.62 $ 100     $ 95.24
  t=2           r2 = .06           50       44.50    100         89.00
  t=3           r3 = .07           50       40.81    100         81.63
  t=4           r4 = .08           50       36.75    100         73.50
  t=5           r5 = .09        1,050      682.43  1,100        714.92
                Totals         $1,250     $852.11 $1,500     $1,054.29

                                              YIELD TO MATURITY
                Bond         Price                Percent (IRR)
               5s of „08    85.21%                    8.78%
              10s of „08   105.43                     8.62
23.3 Duration and Volatility
     Duration: Average time to each payment
                1 PV(C1)        2 PV(C2)
     D =                       +             +… …
                    V                V
                                 PROPORTION OF
                                  TOTAL VALUE PROPORTION OF TOTA
YEAR       Ct     PV(Ct) AT 5.5%     [PVt/V]      VALUE TIME

 1      137.5        130.33           .092               .092
 2      137.5        123.54           .087               .175
 3      137.5        117.10           .083               .249
 4      137.5        110.99           .079               .314
 5      137.5        105.21           .075               .373
 6     1137.5        824.97           .584              3.505
                V = 1,412.13         1.000    Duration = 4.708 years
  (A) 13 ¾s of 2004           vs.       (B) 7 ¼s of 2004
      DA = 4.708 years                    DB = 5.115 years

(EX) 1% changes in yield
                      13 ¾s of 2004              7 ¼s of 2004
                NEW PRICE CHANGE             NEW PRICE CHANGE
Yield falls, 0.5%   144.41    +2.26%          111.42     +2.46%
Yield rises, 0.5%   138.11    - 2.20          106.15     - 2.39
Difference            6.30      4.46%           5.27     +4.85%

Volatility (%)        Duration
                       1+yield
VB =

VA =
• Hedging
By equalizing the duration of the asset and that of the liability,
we can immunize against any change in interest rate

(EX) Aztec Learning has just purchased some equipment and
Arranged to rent it out for $ 2mil a year over eight years at 12%

Aztec finances by issuing a packaging of one year and six-year
bond, each with 12% coupon to set up hedged position, find out
proportion of one year and six year bond
Solution
PV of rental =
      income

Duration of Rental income =
Duration of one year bond =
Duration of 6-year bond   =
Let : x is the proportion raised by 6-year bond
     1-x is the proportion raised by 1 year bond

Duration Package = x  duration of + (1-x)  duration of
                       6-year bond           1 year bond
   3.9 years     = x  4.6 years + (1-x)  1 years
23.4 Explaining the Term Structure
Topic
Why do we observe different shape of term- structure?
Ms. Long: invest $1,000 for 2 years
  1,000                   =
  1,000           =

Forward Rate
The extra return that Ms. Long gets by lending for 2 years
rather than 1         Implicit & guaranteed

 (1+r2)2 = (1+ r1 )  (1+f2)

       (1.105)2
 f2 = 1.1      - 1  0.11     11%
   Expected Payoff: L1               Certain Payoff: L2
                                     1,000 (1+r2)2
  1,000 (1+r1) [1+E(1r2)]   vs.             or
                                     1,000 (1+ r1 )(1+f2)

Strategy L1 gives higher-return if

Mr. Short: invest 1 year
 Buy 1 year bond:
 Buy 2 year bond & sell it after 1 year
  PV of 2 year bond at year 1 =
   Certain Payoff: S1            Expected Payoff: S2
                                    1,000 (1+r2)2
                                      1+E(1r2)
      1,000 (1+r1)         vs.          or
                                 1,000 (1+ r1 )(1+f2)
                                       1+E(1r2)


Strategy S2 is better if
• The Expectations Hypothesis
  Ms.Long and Mr. Short try to maximize their expected
  return
                           f2 = E(1r2)
  If f2 > E(1r2)         prefer 2yr. bond
                         price bond of 2yr
                         return of 2yr. Bond and f2
                         Equilibrium: f2 = E(1r2)
  If f2 < E(1r2)         prefer 1 yr. bond

  The only reason for upward sloping term structure is
  investor expect the relationship such that
  f2 > r1   ,   E(1r2) > r1
The Liquidity Preference (Theory)
• Consider “risk”
  Long Case: horizon 2 yr.
  If Ms. Long buys 1 year bond: first year return is certain
                                but, uncertain “reinvestment
                                rate” at the end of year 1
  Ms. Long holds 1 year bond only if E(1r2) f2


  Short Case: horizon: 1 yr.
  If Mr. Short buys 2 year bond: he has to sell it next year at an
                                 “unknown price”.
  Mr. Short holds 2 year bond only if E(1r2) f2

  Other things equal, Ms. Long will prefer to buy year bond
    & Mr. Short will prefer to buy year bond
If more companies want to issue 2 year bond than
there are Ms. Long to hold them,
   They need to offer “Bonus” to attempt some of the
   Mr. Short to buy 2 year bond.

Any bonus shows up as a difference between
f2 & E(1r1)  Liquidity Premium

In reality, there are shortage of long-term lender,
liquidity premium is positive.
      f2 = E(1r2) + Liquidity Premium ( = LP2)
      f2 = E(2r3) + LP3
23.5 Allowing for the risk of Default
  Q: Why do some borrowers have to pay a higher rate
     of interest than others?


                      Default risk premium
     Promised
     yield  y        other risk premium
                                             Expected yield
                      Rf


     Yield= Rf+ Risk Premium
(EX) Rf = 9%       Payoff (t=1)       Probability
                       $ 1,090            0.8
                             0            0.2
Expected payoff ($) at t=1:
If default is totally unrelated to other event of economy,
=            default risk is wholly diversifiable
PV =
Promised yield =
                                (expected yield = 9%)
Since default occurs in recession,  , say risk premium=2%

PV =
Promised yield =
                                (expected yield = 11%)
Bond Ratings
 “relative quality” of bond by Moody‟s
                               Standard & Poor‟s
MOODY‟S         STANDARD AND POOR‟S
  Aaa                   AAA
  Aa                    AA                  Investment
  A                     A
  Baa                   BBB                 grade
  Ba                    BB
  B                     B
  Caa                   CCC                 Junk
  Ca                    CC                  bonds
  C                     C

                      PERCENTAGE DEFAULTING WITHIN
RATING AT         1 YEAR          5 YEAR      10 YEAR
TIME OF ISSUE   AFTER ISSUE     AFTER ISSUE AFTER ISSUE
   AAA               .00             .06        .06
   AA                .00             .67        .74
   A                 .00             .22        .64
   BBB               .03            1.64       2.80
   BB                .37            8.32      16.37
   B                1.47           21.95      33.01
   CCC              2.28           35.42      47.46
   Leasing




              Chapter 25
A rental agreement that extends for a year or more
and involves a series of fixed payments
What to lease?

Lessee
Lessor : Leasing industry
         Equipment manufacturers
         Banks
         Independent leasing company

Operating Lease
Capital Lease(financial/ full payment)
25.2 Why lease ?
   –   Convenient (short-term)
   –   Cancellation option
   –   Maintenance provided
   –   Tax-shield can be used.
   –   Etc.

25.3 Operating lease.
   In real life, idle time is considered.
   In operating lease, the lessor absorbs idle risk, not the lessee.
   The discount rate must include a premium sufficient to
     compensate its shareholder for the risk of idling.
   – For operating lease: Lease vs. Buy
   – For financial lease : Lease vs. Borrow
Table 25-1
Calculating the zero-NPV rental rate (orequivalent annual cost) for Establishment
Industries' pearly white stretch limo (figures in thousands of dollars)

                                                             Year
                                   0         1         2             3       4       5       6
Initial cost                      -75
Maintenance, insurance, selling,-12         -12       -12            -12     -12     -12     -12
and administrative costs
Tax Shield on costs              +4.2      +4.2      +4.2           +4.2    +4.2    +4.2    +4.2
Depreciation tax shield                    +5.25     +8.40          +5.04   +3.02   +3.02   +1.51
Total                           -82.80     -2.55      .60           -2.76   -4.78   -4.78   -6.29
  NPV at 7% = -$98.15

Break-even rent (level)          26.18     26.18     26.18          26.18   26.18   26.18   26.18

Tax                              -9.16     -9.16      -9.16     -9.16     -9.16     -9.16   -9.16
Break-even after tax            17.02#     17.02     17.02      17.02     17.02     17.02   17.02
   NPV at 7% = $98.15
* no inflation; r = 7%; Tc = 35%`                  * Table 6-5: depreciation
* First payment: immediate                         # 17.02 = 65% of 26.18
  7% PVA 7yrs = 5.389         5.389 * 1.07 = 5.766
25. 4 Financial Lease
Table 25-2
Cash-flow consequences of the lease contract offered to Greymare Bus Lines
(figures in thousands of dollars; some columns do not add due to rounding)
NPV of 'Lease' relative to 'Buy'
                                                      Year
                         0        1           2       3         4        5      6      7
Cost of new bus        +100
Lost depreciation tax
  shield                        -7.00      -11.20   -6.72     -4.03    -4.03  -2.02    0
Lease payment          -16.9    -16.9       -16.9   -16.9     -16.9    -16.9  -16.9  -16.9
Tax shield of lease
  payment              +5.92    +5.92      +5.92   +5.92      +5.92   +5.92  +5.92  +5.92
Cash flow of lease +89.02 -17.99           -22.19  -17.71    -15.02   -15.02 -13.00 -10.98
                                                                  D r
* 5 yr: depreciation (Table 6.4), 7yrs/8 times payment, Tc = 35%, = 10%
          D r
* After tax:* (1 - Tc) = 6.5%
       NPVlease =     +89.02 - 17.99 - 22.19 - 17.71 - 15.02 - 15.02 -         13 - 10.98
                                            2         3         4         5         6         7
                             1.065    (1.065)   (1.065)   (1.065)   (1.065)   (1.065)   (1.065)
              =     -0.7               -$700
Creating Equivalent Loan
                                                    Year
                        0       1       2       3          4   5       6       7
Lease cash flows, +89.02 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98
   thousands

Table 25-3: Equivalent loan; exactly same debt service on lease.
                                                       Year
                       0       1       2       3           4   5      6       7
Amount borrowed at
   year-end                 89.72 77.56 60.42 46.64 34.66 21.89 10.31         0
Interest paid at 10%               -8.97 -7.76 -6.04 -4.66 -3.47 -2.19 -1.03
Interest tax shield at 35%         +3.14 +2.71 +2.11 +1.63 +1.21 +.77 +.36
Interest paid after tax            -5.83 -5.04 -3.93 -3.03 -2.25 -1.42 -0.67
Principal repaid                  -12.15 -17.14 -13.78 -11.99 -12.76 -11.58 -10.31
Net cash flow of
  equivalent loan          89.72 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98
                    How much can I borrow when I pay same cash as lease payment?
25.5 When Do Financial Leases Pay?
The value of the lease to the bus manufacturer would be(Tc=35%)
Value of lease to lessor
             17.99   22.19   17.71    15.02    15.02     13      10.98
= -89.02 +         +       +        +        +        +        +
             1.065 (1.065)2 (1.065)3 (1.065)4 (1.065)5 (1.065)6 (1.065)7
= +.70     Zero sum game
Suppose that Greymare paid no tax (Tc = 0).
Then the only cash flows of the bus lease would be:

                                             Year
                  0            1   2        3         4       5      6        7
Cost of new bus +100
Lease payment     -16.9   -16.9 -16.9     -16.9     -16.9   -16.9   -16.9   -16.9
These flows would be discounted at 10 percent,
because rD (1-Tc)= rD when Tc =0
                          10
                           16.9
Value of lease = 100 -  (1.1)t        = +100 - 99.18 = +.82 or $820
                       t=0
The potential gains to lessor and lessee are higher when:


  The lessor‟s tax rate is substantially higher than the lessee‟s

  The depreciation tax shield is received early in the lease
  period

  The lease period is long and the lease payments are
  concentrated toward the end of the period

  The interest rate rD is high - if it were zero, there would be
  no advantage in present value terms to postponing tax
   Mergers




              Chapter 33
 Selling Company      Acquiring Company Payment, billions of dollars

NYNEX                 Bell Atlantic                  21.0
McDonnell Douglas     Boeing                         13.4
Digital Equipment     Compaq Computer                9.1
Schweizerischer       Union Bank of Swiz.            23.0
Energy Group PCC      Texas Utilities                11.0
Amoco Corp.           British Petroleum              48.2
Sun America           American Intl.                 18.0
BankAmerica Corp.     Nationsbank Corp.              61.6
Chrysler              Daimler-Benz                   38.3
Bankers Trust Corp.   Deutsche Bank AG               9.7
Netscape              America Online                 4.2
Citicorp              Travelers Group Inc.           83.0
33.2. Sensible Motives for Mergers
    Economies of Scale
    Vertical Integration
    Complementary Resources
    Unused Tax Shields
    Surplus Fund  Free Cash Flow ?
    Eliminating Inefficiencies
    Diversification
    Increasing Earning Per Share
    Lower Financing Cost
33.3 Estimating Merger Gains and Costs

 A: Buyer        B: Seller
 Synergy Gain = PVA+B - (PVA + PVB)
         Cost = Cash paid - PVB
         NPV = Gain - Cost = PVAB - (Cash-PVB)

 (Ex)
 PVA = 200, PVB = $50, PVA+B = $275
 Gain = PVAB = + $25
 Cash = $65
                    Firm A         Firm B
  Market price        $ 200         $ 100
  per share
  Number
  of share        1,000,000       500,000

  Market value
  of firm             $ 200 mil      $ 50 mil

Cost = Cash - PVB = Cash - MVB + (MVB - PBB)
     = 65 -50 + (50 - 44) = $21 mil
Cash payment depends on the relative bargaining
power of the two participants
• Stock offer
 N : shares received by seller
 PAB: combined firm‟s worth
 Cost= N PAB - PVB
 (Ex) N = 325,000
      A‟s price before merger: $200
      PVB = $50 mil
       Apparent cost =
       If PVAB = $275mil (due to synergy gain)
       New share price =
       Cost = 0.325        -50 =
Takeover Defense
   Preoffer Defenses
    • Shark-repellent Charter Amendments
       – Staggered Board
       – Super Majority
       – Fair price
    • Dual class stock
    • Poison Pill, Poison put
    • ESOP
   Postoffer Defenses
    • Litigation
    • Asset Restructuring
    • Liability Restructuring
Divestitures (sell offs) and Spin offs.
  - Synergy Motivated
  - Focus
  - Complementary Resources
  - More Efficient Contracting
    (Better Organization Structure)
  - Raising Capital

Question:
What is the source of gain and where it is created?
Leveraged Buyouts

• Debt financed (junk-bond)
• Going private
• MBO

				
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posted:11/8/2011
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