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Capital Budeting with the Net Present Value Rule

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NFV = 121 - 100 1.10 = 11 = C1 - I (1 r) Decision rule: invest if NFV 0 ... Copeland, Koller and Murrin Valuation: Measuring and Managing the Value of ... – PowerPoint PPT presentation

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Title: Capital Budeting with the Net Present Value Rule


1
Capital Budeting with the Net Present Value Rule
  • Professor André Farber
  • Solvay Business School
  • Université Libre de Bruxelles

2
Time value of money introduction
  • Consider simple investment project
  • Interest rate r 10

121
1
0
-100
3
Net future value
  • NFV 121 - 100 ? 1.10 11
  • C1 - I (1r)
  • Decision rule invest if NFVgt0
  • Justification takes into cost of capital
  • cost of financing
  • opportunity cost

121
100
0
1
-100
-110
4
Net Present Value
  • NPV - 100 121/1.10
  • 10
  • - I C1/(1r)
  • - I C1 ? DF1
  • DF1 1-year discount factor
  • a market price
  • C1 ? DF1 PV(C1)
  • Decision rule invest if NPVgt0
  • NPVgt0 ? NFVgt0

121
110
-100
-121
5
Internal Rate of Return
  • Alternative rule compare the internal rate of
    return for the project to the opportunity cost of
    capital
  • Definition of the Internal Rate of Return IRR
    (1-period)
  • IRR (C1 - I)/I
  • In our example IRR (121 - 100)/100
    21
  • The Rate of Return Rule Invest if IRR gt r

6
IRR versus NPV
  • In this simple setting, the NPV rule and the Rate
    of Return Rule lead to the same decision
  • NPV -IC1/(1r) gt0
  • ? C1gtI(1r)
  • ? (C1-I)/Igtr
  • ? IRRgtr

7
IRR a general definition
  • The Internal Rate of Return is the discount rate
    such that the NPV is equal to zero.
  • -I C1/(1IRR) ? 0
  • In our example
  • -100 121/(1IRR)0
  • ? IRR21

8
Extension to several periods
  • Investment project -100 in year 0, 150 in year
    5.
  • Net future value calculation
  • NFV5 150 - 100 ? (1.10)5 150 - 161 -11
    lt0
  • Compound interest
  • Net present value calculation
  • NPV - 100 150/(1.10)5
  • - 100 150 ? 0.621 - 6.86
  • 0.621 is the 5-year discount factor DF5
    1/(1r)5
  • a market price

9
NPV general formula
  • Cash flows C0 C1 C2 Ct CT
  • t-year discount factor DFt 1/(1r)t
  • NPV C0 C1 DF1 Ct DFt CT DFT

10
NPV calculation - example
  • Suppose r 10

11
IRR in multiperiod case
  • Reinvestment assumption the IRR calculation
    assumes that all future cash flows are reinvested
    at the IRR
  • Disadvantages
  • Does not distinguish between investing and
    financing
  • IRR may not exist or there may be multiple IRR
  • Problems with mutually exclusive investments
  • Advantages
  • Easy to understand and communicate

12
Constant perpetuity
Proof PV C d C d² C d3 PV(1r) C C
d C d² PV(1r) PV C PV C/r
  • Ct C for t 1, 2, 3, .....
  • Examples Preferred stock (Stock paying a fixed
    dividend)
  • Suppose r 10 Yearly dividend 50
  • Market value P0?
  • Note expected price next year
  • Expected return

13
Growing perpetuity
  • Ct C1 (1g)t-1 for t1, 2, 3, .....
    rgtg
  • Example Stock valuation based on
  • Next dividend div1, long term growth of dividend
    g
  • If r 10, div1 50, g 5
  • Note expected price next year
  • Expected return

14
Constant annuity
  • A level stream of cash flows for a fixed numbers
    of periods
  • C1 C2 CT C
  • Examples
  • Equal-payment house mortgage
  • Installment credit agreements
  • PV C DF1 C DF2 C DFT
  • C DF1 DF2 DFT
  • C Annuity Factor
  • Annuity Factor present value of 1 paid at the
    end of each T periods.

15
Growing annuity
  • Ct C1 (1g)t-1 for t 1, 2, , T r ? g
  • This is again the difference between two growing
    annuities
  • Starting at t 1, first cash flow C1
  • Starting at t T1 with first cash flow C1
    (1g)T
  • Example What is the NPV of the following project
    if r 10?
  • Initial investment 100, C1 20, g 8, T 10
  • NPV 100 20/(10 - 8)1 (1.08/1.10)10
  • 100 167.64
  • 67.64

16
Review general formula
  • Cash flows C1, C2, C3, ,Ct, CT
  • Discount factors DF1, DF2, ,DFt, , DFT
  • Present value PV C1 DF1 C2 DF2
    CT DFT

If r1 r2 ...r
17
Review Shortcut formulas
  • Constant perpetuity Ct C for all t
  • Growing perpetuity Ct Ct-1(1g)
  • rgtg t 1 to 8
  • Constant annuity CtC t1 to T
  • Growing annuity Ct Ct-1(1g)
  • t 1 to T

18
IRR and NPV - Example
  • Compute the IRR and NPV for the following two
    projects. Assume the required return is 10.
  • Year Project A Project B
  • 0 -200 -150
  • 1 200 50
  • 2 800 100
  • 3 -800 150
  • NPV 42 91
  • IRR 0, 100 36

19
NPV Profiles
20
The Payback Period Rule
  • How long does it take the project to pay back
    its initial investment?
  • Payback Period of years to recover initial
    costs
  • Minimum Acceptance Criteria set by management
  • Ranking Criteria set by management

21
The Payback Period Rule (continued)
  • Disadvantages
  • Ignores the time value of money
  • Ignores CF after payback period
  • Biased against long-term projects
  • Payback period may not exist or multiple payback
    periods
  • Requires an arbitrary acceptance criteria
  • A project accepted based on the payback criteria
    may not have a positive NPV
  • Advantages
  • Easy to understand
  • Biased toward liquidity

22
The Profitability Index (PI) Rule
  • PI Total Present Value of future CFs / Initial
    Investment
  • Minimum Acceptance Criteria Accept if PI gt 1
  • Ranking Criteria Select alternative with highest
    PI
  • Disadvantages
  • Problems with mutually exclusive investments
  • Advantages
  • May be useful when available investment funds are
    limited
  • Easy to understand and communicate
  • Correct decision when evaluating independent
    projects

23
Incremental Cash Flows
  • Cash, Cash, Cash, CASH
  • Incremental
  • Sunk Costs
  • Opportunity Costs
  • Side Effects
  • Tax and Inflation
  • Estimating Cash Flows
  • Cash flows from operation
  • Net capital spending
  • Changes in net working capital
  • Interest Expense

24
Summarized balance sheet
  • Assets
  • Fixed assets (FA)
  • Working capital requirement (WCR)
  • Cash (Cash)
  • Liabilities
  • Stockholders' equity (SE)
  • Interest-bearing debt (D)
  • FA WCR Cash SE D

25
Working capital requirement definition
  • Accounts receivable
  • Inventories
  • Prepaid expenses
  • - Account payable
  • - Accrued payroll and other expenses
  • (WCR sometimes named "operating working capital")
  • Copeland, Koller and Murrin Valuation Measuring
    and Managing the Value of Companies, 2d ed. John
    Wiley 1994

26
Interest-bearing debt definition
  • Long-term debt
  • Current maturities of long term debt
  • Notes payable to banks

27
The Cash Flow Statement
  • Let us start from the balance sheet identity
  • FA WCR CASH SE D
  • Over a period
  • ?FA ?WCR ?CASH ?SE ?D
  • But
  • DSE STOCK ISSUE RETAINED EARNINGS
  • SI NET INCOME - DIVIDENDS
  • DFA INVESTMENT - DEPRECIATION
  • (INV - DEP) ?WCR ?CASH (SI NI - DIV) ?D

28
  • (NI DEP - ?WCR) - (INV) (SI ?D - DIV)
    ?CASH
  • ???????
  • Net cash flows from
  • operating activities (CFop)
  • ??
  • Cash flow from
  • investing
    activities (CFinv)

  • ???????

  • Cash flow from

  • financing activities (CFfin)

29
Free cash flow
  • FCF (NI DEP - ?WCR) - (INV)
  • CFop CFinv
  • From the statement of cash flows
  • FCF - (SI ?D - DIV) ?CASH

30
Understanding FCF
  • CF from operation CF from investment CF from
    financing ?CASH

Cash flow from operation
Cash flow from financing
Cash flow from investment
Cash
31
NPV calculation example
  • Length of investment 2 years
  • Investment 60 (t 0)
  • Resale value 20 (t 3, constant
    price)
  • Depreciation linear over 2 years
  • Revenue 100/year (constant
    price)
  • Cost of sales 50/year
    (constant price)
  • ?WCR/?Sales 25
  • Real discount rate 10
  • Corporate tax rate 40

32
Scenario 1 no inflation
33
Inflation
  • Use nominal cash flow
  • Use nominal discount rate
  • Nominal versus Real Rate (The Fisher Relation)
  • (1 Nominal Rate) (1 Real Rate) x (1
    Inflation Rate)
  • Example
  • Real cash flow year 1 110
  • Real discount rate 10
  • Inflation 20
  • Nominal cash flow 110 x 1.20
  • Nominal discount rate 1.10 x 1.20 - 1
  • NPV (110 x 1.20)/(1.10 x 1.20) 110/1.10 100

34
Scenario 2 Inflation 100
Nominal discount rate (110) x (1100)
2.20 Nominal rate 120
NPV now negative. Why?
35
Decomposition of NPV
  • EBITDA after taxes 52.07
    52.07
  • Depreciation tax shield 20.83
    7.93
  • ?WCR -3.94
    -23.67
  • Investment -60
    -60
  • Resale value after taxes 9.02
    9.02
  • NPV 17.96
    14.65
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