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Vietnam 2004 1 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

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Page 1: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 1

Capital Budeting with the Net Present Value Rule

Professor André Farber

Solvay Business School

Université Libre de Bruxelles

Page 2: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |2

Time value of money: introduction

• Consider simple investment project:

• Interest rate r = 10%

121

-100

0 1

Page 3: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |3

Net future value

• NFV = +121 - 100 1.10 = 11

• = + C1 - I (1+r)

• Decision rule: invest if NFV>0

• Justification: takes into cost of capital

– cost of financing

– opportunity cost

-100

+100+121

-110

0 1

Page 4: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |4

Net Present Value

• NPV = - 100 + 121/1.10

• = + 10

• = - I + C1/(1+r)

• = - I + C1 DF1

• DF1 = 1-year discount factor

• a market price

• C1 DF1 =PV(C1)

• Decision rule: invest if NPV>0

• NPV>0 NFV>0

-100

+121

-121

+110

Page 5: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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 > r

Page 6: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |6

IRR versus NPV

• In this simple setting, the NPV rule and the Rate of Return Rule lead to the same decision:

• NPV = -I+C1/(1+r) >0

C1>I(1+r)

• (C1-I)/I>r

IRR>r

Page 7: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |7

IRR: a general definition

• The Internal Rate of Return is the discount rate such that the NPV is equal to zero.

• -I + C1/(1+IRR) 0

• In our example:

• -100 + 121/(1+IRR)=0

• IRR=21% -25.0-20.0

-15.0-10.0

-5.00.05.0

10.015.0

20.025.0

0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Discount rateNe

t Pre

sent

Val

ue

IRR

Page 8: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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 <0

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/(1+r)5

a market price

Page 9: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |9

NPV: general formula

• Cash flows: C0 C1 C2 … Ct … CT

• t-year discount factor: DFt = 1/(1+r)t

• NPV = C0 + C1 DF1 + … + Ct DFt + … + CT DFT

Page 10: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |10

NPV calculation - example

• Suppose r = 10%

t 0 1 2 3Cash flow -100 30 60 40Discount Factor 1 0.9091 0.8264 0.7513PresentValue -100.0 27.3 49.6 30.1NPV 6.9

Page 11: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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

Page 12: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |12

Constant perpetuity

• 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 =

50010.

501 P

r

CPV

Proof:PV = C d + C d² + C d3 + …PV(1+r) = C + C d + C d² + …PV(1+r)– PV = CPV = C/r

50010.

500 P

%10500

)500500(50)(

0

011

P

PPdiv

Page 13: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |13

Growing perpetuity

• Ct =C1 (1+g)t-1 for t=1, 2, 3, ..... r>g

• 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 =

gr

CPV

1

000,105.10.

500

P

050,105.10.

5.521

P

%10000,1

)000,1050,1(50)(

0

011

P

PPdiv

Page 14: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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.

Page 15: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |15

Growing annuity

• Ct = C1 (1+g)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 = T+1 with first cash flow = C1 (1+g)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

T

r

g

gr

CPV

1

111

Page 16: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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

TT

Tt

t

t

r

C

r

C

r

C

r

CPV

)1(...

)1(...

)1()1( 22

2

1

1

TT

tt

r

C

r

C

r

C

r

CPV

)1(...

)1(...

)1()1( 221

If r1 = r2 = ...=r

Page 17: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |17

Review: Shortcut formulas

• Constant perpetuity: Ct = C for all t

• Growing perpetuity: Ct = Ct-1(1+g)

r>g t = 1 to ∞

• Constant annuity: Ct=C t=1 to T

• Growing annuity: Ct = Ct-1(1+g)

t = 1 to T

r

CPV

gr

CPV

1

))1(

11(

Trr

CPV

))1(

)1(1(1

T

T

r

g

gr

CPV

Page 18: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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%

Page 19: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |19

NPV Profiles

-150.0

-100.0-50.0

0.0

50.0

100.0150.0

200.0

Project A Project B

Page 20: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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

Page 21: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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

Page 22: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |22

The Profitability Index (PI) Rule

• PI = Total Present Value of future CF’s / Initial Investment

• Minimum Acceptance Criteria: Accept if PI > 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

Page 23: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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

Page 24: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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

Page 25: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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

Page 26: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |26

Interest-bearing debt: definition

• + Long-term debt

• + Current maturities of long term debt

• + Notes payable to banks

Page 27: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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:

SE = STOCK ISSUE + RETAINED EARNINGS

= SI + NET INCOME - DIVIDENDS

FA = INVESTMENT - DEPRECIATION

• (INV - DEP) + WCR + CASH = (SI + NI - DIV) + D

Page 28: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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)

Page 29: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |29

Free cash flow

• FCF = (NI +DEP - WCR) - (INV)

• = CFop + CFinv

• From the statement of cash flows

• FCF = - (SI + D - DIV) + CASH

Page 30: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |30

Understanding FCF

CF from operation + CF from investment + CF from financing = CASHCF from operation + CF from investment + CF from financing = CASH

Cash flow from operation

Cash flow from investment

Cash flow from financing

Cash

Page 31: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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%

Page 32: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |32

Scenario 1: no inflation

Year 0 1 2 3Sales 100 100Cost of sales 50 50EBITD 50 50Depreciation 30 30EBIT 20 20Taxes 8 8 8Net Income 12 12 -8

Net Income 12 12 -8+ Depreciation 30 30-DWCR 25 0 -25Investment -60 20Free cash flow -60 17 42 37

NPV 17.96 IRR 24%

Page 33: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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

Page 34: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |34

Scenario 2 : Inflation = 100%

Year 0 1 2 3Sales 200 400Cost of sales 100 200EBITD 100 200Depreciation 30 30EBIT 70 170Taxes 28 68 64Net Income 42 102 -64

Net Income 42 102 -8+ Depreciation 30 30-DWCR 50 50 -100Investment -60 160Free cash flow -60 22 82 196

NPV -14.65 IRR 94%

Nominal discount rate:

(1+10%) x (1+100%) = 2.20

Nominal rate = 120%

NPV now negative. Why?

Page 35: Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

Vietnam 2004 |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