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Chapter 15_ Raising Capital

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					                       Chapter 12 & 13, Risk and Return


•   Risk Premium = Average Return - T-Bill Rate.

•   for historic returns, Var® = [(R1-R)2 +…+ (RT-R)2]
                                        T-1

•   for historic returns, SD® = Var®

                                          s
•   For expected returns,   E(R) =        (pi x ri)
                                        i =1

                                     s
•   For expected variance, Var(R) =  [pi x (ri - r )2] where SD® = Var(R)
                                    i =1

•   The CAPM formula:        E(Ri ) = Rf + [E(RM ) - Rf ] x Bi
            Chapter 9, Net Present Value and Other Criteria

•   NPV =     Ct_
              (1+r)t

•   IRR formula:  Ct             =0
                  (1+IRR)t

•   PI =  PV of future cashflows
               Initial Cost

•   Payback period: the length of time it takes the firm to recover the
    project’s initial investment.


                   Average net income
•        AAR =     ------------------------------
                   Average book value
          Chapter 6, Annuities and Perpetuities -- Basic Formulas

• Annuity Present Value

          PV = C x {1 - [1/(1 + r)t]}/r

•   Annuity Future Value

          FVt = C x {[(1 + r)t - 1]/r}

• Annuity Due Value
          Annuity due value = Ordinary Annuity value X (1+r)

• Perpetuity Present Value

          PV = C/r

• The formulas above are the basis of many of the calculations in Corporate
  Finance. It will be worthwhile to keep them in mind!
            Chapter 10, Making Capital Investment Decisions
•   The Tax-Shield Approach

          OCF        =          (S - C - D) + D - (S - C - D) x Tc

                     =          (S - C) x ( 1 - Tc) + (D x Tc)

                   =            (S - C) x (1 - Tc) + depreciation tax shield
•   The Bottom-Up Approach

          OCF        =          (S - C - D) + D - (S - C - D) x Tc
                     =          (S - C - D) x (1 - Tc) + D
                  =             Net income + depreciation
•   The Top-Down Approach
          OCF     =             (S - C - D) + D - (S - C - D) x Tc
                  =             (S - C) - (S - C - D) x Tc
                  =             Sales - costs - taxes



•   The after-tax salvage value is: market value - (market value - book value) x (Tc)

•   Equivalent Annual Cost: EAC = Present Value of Total Cash Flows / PVAF
          PVAF is the Present Value Annuity Factor
               Review of Cash Flow (from Chapter 2)
1.Cash flow from assets or Total Cash Flow

           Cash flow from assets = Operating cash flow
                                 – Net capital spending
                                 – Additions to net working capital (NWC)
           where:
             Operating cash flow = Earnings before interest and taxes (EBIT)
                                            + Depreciation – Taxes


              Net capital spending = Ending net fixed assets – Beginning net fixed assets
                                           + Depreciation


              Change in NWC = Ending NWC – Beginning NWC

   Half-year (50%) rule:
    In the year of acquisition, 1/2 of net acquisitions is added to the UCC balance and used
    to calculate CCA.
    The remaining 1/2 is added the following year.
                   Chapter 11, Project Analysis and Evaluation


•   TC = total variable costs + fixed costs

•   Summary of Break-Even Measures:
                                                where:   FC = total fixed costs
                                                         P = Price per unit
                                                         v = variable cost per unit
     I. The Accounting Break-Even Point
         Q = (FC + D)/(P - v)

     II. The Cash Break-Even Point
          Q = FC/(P - v)

     III. The Financial Break-Even Point
          Q = (FC + OCF*)/(P - v)

•   Degree of Operating Leverage,        DOL = 1 + FC / OCF
                           Chapter 15, Raising Capital


•   The number of new shares to be issued =(Funds to be raised)/Subscription price

•   The new share price = (New firm value)/(Total number of shares outstanding).

•   The value of the right must =          Old share price - new share price.

•   Another formula for the Value of a Right:        R 0= (M0 - S) / (N+1)

				
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