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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
• 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
• Does not distinguish between investing and
financing
• IRR may not exist or there may be multiple IRR
• Problems with mutually exclusive investments
• 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)
• 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
• 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
• Problems with mutually exclusive investments
• 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