Capital Budgeting NPV and Alternative Investment Rules

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					                 Capital Budgeting
         NPV and Alternative Investment Rules

                               Marcel Rindisbacher

                                     November 27, 2001

Objectives of lecture on captital budgeting rules
In previous lectures we have already argued that the appropriate goal from shareholders
point of view is to maximize NPV. But in practice other method are used as well. ⇒
Comparison of different capital budgeting techniques.

   • Payback period rule

   • Discounted payback period rule

   • Average accounting return (AAR)

   • Internal rate of return (IRR)

   • Profitability index

   Then will discuss in more detail problems using NPV in capital budgeting.

Why should investment rule be based on NPV?
When we discussed the separation theorem, we have shown that management which invests
in projects with positive NPV ⇔ increases shareholder value.
    NPV is appropriate rule since:

   • NPV uses cash flows not earnings: cash flows really what is available to pursue cor-
     porate investment plans.

   • NPV uses all cash flows: Cash flows exhaustively describe an investment opportunity
     from the point of view of valuation. Other methods ignore cash flows after a certain
     point in time.

   • NPV discounts the cash flows properly: Captures the time value of money as revealed
     by the markets.

Why are other methods used in practice?
Answer :

   • Historical reasons and convenience.

   • Alternative methods less complicated.

   • Lack of appropriate estimates for cash flows and risk adjusted discount rates.

Pay Back Period Rule
Idea: Many investment projects start with a cash outflow followed by cash inflows in the
future. ⇒ How many years does it take until initial cash outflow has been paid back ?
Answer: Pay back period .
    Application: Management decides about what it considers as acceptable (upper limit)
time until initial investment is paid back.
    ⇒ Rule: Undertake all investment projects with a pay back period less than say 5 years.
    ⇒ Ranking Criteria: Undertake investment project with shortest pay back period.

Pros of Payback Period

   • Simple.

   • Upper limit on cut off time limits risk exposure of investment projects.

   • Favors liquidity of firm.

   • Respects short term investment horizon.

Cons of Payback Perido
Projects considered as identical with respect to payback period can be extremely different:

   • Different cash flows after cut off period are ignored.

   • Timing of cash flows before cut off period is not taken into account: Two projects
     with same initial cash outflow of $100 followed by cash inflows of $10 over 10 year for
     one project and no cash inflows for 9 year but $ 100 in the 10th year have the same
     pay back period! (Should prefer the first project since intermediate cash inflows can
     be reinvested.) ⇒ Payback period method ignores time value of money.

   • Biased against long-term projects and therefore against shareholder interests.

   • Criteria may not exist and/or acceptance criteria is arbitrary.

Discounted Pay Back Period
Idea: Correct payback period method such that time value of money is taken into account.
    Pros: Same as pay back period. But in addition reflect opportunity costs of money as
valued by the financial markets.
    Cons: As pay back period. But in addition get more complicated since have to discount
as for NPV rule.

Averge Accounting Return (AAR)
Idea: It is often easier to determine projects earning rather than cash flows. Calculate rate
of return of projects earning by dividing its earnings by the project’s book value. Since
both vary offer time take time averages ⇒ Average Accounting Return.

                                         Average net income
                               ARR =
                                         Average investment

Application:Proceed in two steps
  1. Determine average net income:
                    Average Net Income =                   (Revenuen − Expensesn
                                                 −Depreciationn − Taxesn )

  2. Determine average investment:
                     Average Investment =                  (Value of investmentn
                                            − Depreciationn )

Decison Rule for ARR
Decision Rule:
   ⇒ Rule: Management defines hurdle rate. Undertake investment when AAR is higher
than this hurdle rate.
   ⇒ Ranking criteria: Invest in project with highest hurdle rate.

Pros of ARR

   • Accounting information available.

   • Easy to calculate.

   • Does always exist.

Cons of ARR

   • Ignores the time value of money: average net income can be same but income per
     period can be very different.

   • Benchmark (hurdle rate) arbitrary.

   • Based on book values: Do not reflect means available for investment project as cash
     flows to and book values do not reflect valuation by the market.

Internal Rate of Return (IRR)
Idea: Given the cash flow structure of a given investment project at which interest rate is
its NPV equal to zero ?
    Application: Management fixes target rate of return.
    IRR solves the following equation:
                                         Cash flown
                                         (1 + IRR)n

   IRR corresponds to the “yield” of the investment project.

Investing and Financing

  1. Investing: Undertake investment if IRR is higher than a specified hurdle rate which
     may correspond to discount rate from financial markets. (Opportunity cost of capital).

  2. Financing: Accept financing project if IRR is lower than a specified hurdle rate
     which may correspond to the discount rate from financial markets (Opportunity cost
     of capital).

   Ranking criteria: Undertake investment project with highest IRR and accept financing
project with lowest IRR.

Remark: IRR is very close to NPV:

   • Both are based on all cash flows and capture time value of money.

   • Both evaluate investment project by a simple number

   But IRR does not always exist or is not necessarily unique.

Pros of IRR

   • Uses all cash flows.

   • Not based on accounting information.

   • Easy to understand.

   • Easy to communicate.

Cons of IRR

   • Does not capture different scale of project.

   • Does not always exist (“is not always real”) and may not be unique:
        Example: Consider cash flows C0 , C1 , C2 . Then IRR is given by solution

                                            C1       C2
                                  C0 +          +           =0
                                         1 + IRR (1 + IRR)2
        then define X =   1+IRR   and try to find X.

        Technical Illustration

        The equation defining IRR is quadratic and you may remember that the general
        solution for X is then
                                       −C1 + C1 − 4C0 C2
                                X+ =
                                           −C1 −       2
                                                      C1 − 4C0 C2
                                    X− =
        and consequently we will have two solutions for IRR if C1 − 4C0 C2 is not equal to
                              2 − 4C C < 0 we have one IRR which is not a real number !
        zero. Furthermore if C1     0 2

        Remark : As you can see this does not occur if the initial investment is negative and
        all other cash flows are positive (Investment) or vice versa all but the last cash flows
        are positive (Financing).

        Cons IRR continued

   • Does not distinguish between investing and financing. Example: If we multiply all
     cash flows by the same number, the IRR does not change ! Consequently if we compare
     an investment project with a financing project we obtain the same IRR!.

   • Re-investment rate assumption: IRR rule does not discount at opportunity costs
     of capital, it implicitly assumes that the time value of money is the IRR. Implicit
     assumption: ⇒ Re-investment rate assumption.
        Therefore the IRR assumes that investor can reinvest their money at the IRR which
        is different from the market-determined opportunity costs. It is logically not coherent
        that the re-investment rate should be different if they are in the same risk class.
   • Value Additivity Principle: The value of the firm should be equal to the sum of the
     values of the individual projects of the firm.

        Illustration: Violation of Value Additivity Principle
        Therefore if we have choice between two mutually exclusive projects and an indepen-
        dent project, it should not occur that project one is preferred to project two but if
        mixed with the independent project, project two is preferred. But this can happen
        with IRR
          – Project 1: -100,0,550 ⇒ IRR=134.4%
          – Project 2: -100,225,0 ⇒ IRR=125.0%
          – Project 3: -100,450,0 ⇒ IRR=350 %
          – Project 1+3: -200,450,550 ⇒ IRR=212.8%
          – Project 2+3: -200,675,0 ⇒ IRR=237.5%

Profitability Index
Idea: IRR is attractive since it is not dependent on scale of investment. It is a “per dollar”
quantity. The profitability index does the same thing for NPV: Amount of NPV generated
for each investment dollar.

                                     PV of cash inflows
                                 PIInv =
                                     initial cash outflow
                                     PV of cash outflows
                            PIF in =
                                      initial cash inflow
   Application: Management defines benchmark for index
   ⇒ Undertake investment if profitability index is higher than benchmark.
   ⇒ Undertake investment with highest profitability index.

Pros and Cons for Profitability Index
   • respects limited availability of investment funds.
   • easy to understand and communicate
   • same decision as NPV for independent projects
   Cons: As IRR non-additive ⇒ Problems when evaluate mutually exclusive projects.

Conclusion: Valuation principles
Only NPV satisfies all of the following requirements:

   • Considers all cash flows.

   • Cash flows are discounted at the true opportunity cost.

   • Selects from mutually exclusive projects the one that maximizes shareholder value.

   • Respects value-additivity principle.

Conflict among Criteria
Exercise: Consider the following projects:

   • A: -1000,100,900,100,-100,-400

   • B: -1000,0,0,300,700,1300

   • C: -1000,100,200,300,400,1250

   • D: -1000,200,300,500,500,600

Show that payback rule chooses A, ARR rule B, NPV with discount rate 10% C and IRR
rule D.

Difficulties Using NPV Rule
In practice several issues make the use of NPV rule difficult:

   • Measurement of cash flows

   • Incremental cash flows not accounting income

   • Measurement of opportunity costs of capital

   • Investments with unequal lives

 Measurement of cash flows
   • Incremental cash flow: What part of the cash flow is exclusive consequence of invest-
     ment project ? ⇒ Ignore Sunk costs ⇒ Include Opportunity costs ⇒ Correct for Side
     effects (Erosion)

   • Projection of future cash flows.

   • Real versus nominal cash flows.

   • Capital Cost Allowance (CCA). .

If we assume straight-line depreciation then the net cash flow (NCF) can be obtained in
two equivalent ways:

  1. Total project cash flow approach

  2. Tax Shield Approach
     Remark: In practice we have to use Declining Balance CCA

     Total project cash flow approach

                           N CF = (N 0I − CCA) × (1 − tc ) + CCA

        • tc : Corporate tax rate
        • NOI: Net operating income
        • NOI-CCA: Taxable income
        • (N OI − CCA) × (1 − tc ): Net income

     Tax shield approach

                              N CF = N OI × (1 − tc ) + tc × CCA

        • N OI × (1 − tc ): After tax net operating income.
        • tc × CCA: Tax shield (tax savings).

Measurement of opportunity costs of capital
   • Real versus nominal interest rate (The Fisher relation). ⇒ Right discount rate de-
     pends on whether cash flows are real or nominal.

   • Correction of discount factor for risk.

Investments with unequal lives
   • Matching cycles: ⇒ repeat projects until timing matches.
     Example Cost project A −500, 120, 120, 120 project B −600, 100, 100, 100, 100. To
     compare consider smallest common multiple 12 and compare PV of 4 repetitions of
     projection A with 3 repetitions of project B.

• Equivalent annual costs: Consider example as before.
                                        1      1        1
                    EAC A = P V A [        +        +         ]−1
                                      1 + r (1 + r)2 (1 + r)3

                                   1      1          1          1
               EAC B = P V B [        +       2
                                                +        3
                                                           +          ]−1
                                 1 + r (1 + r)    (1 + r)    (1 + r)4