Capital Budgeting and Project Valuation

Chapter 2

2

Overview

�Different Investment criteria• Payback period

• NPV

• IRR

�Project Valuation. Determining relevant Cash Flow

�Additional factors (options)

3

Capital budgeting methods used by companies

�Graham-Harvey, page 197;• IRR: 75.7% (Hurdle rate 56.94%)

• NPV: 74.9%

• Payback: 56.74%

• Sensitivity analysis: 51.54%

• Real options: 26.59%

4

The difference between independent and mutually exclusive projects

�Projects are:

� Independent, if the cash flows of one are unaffected by the acceptance of the other.

� Mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.

5

Normal and Abnormal Cash Flows

�Normal cash flow project:

� One change of signs• For example, cost (negative CF) followed by

a series of positive cash inflows

�Abnormal Cash Flow project:

� Two or more changes of signs• Most common: Cost (negative CF), then

string of positive CFs, then cost to close project

• Nuclear power plant, strip mine.

6

Inflow (+) or Outflow (-) in Year n

- + + + + + N- + + + + - NN- - - + + + N+ + + - - - N- + + - + - NN

0 1 2 3 4 5 N NN

7

What is the payback period?

�The number of years required to recover a project’s cost,

or

�How long does it take to get our money back?

8

Cumulative -100 -90 -30 50

=PaybackL 2 + 30/80 = 2.375 years

0

2.375

CFt 10 60

0 1 2 3

-100 80

Payback for Project L(Long: large CFs in later years)

9

5070 20

0 1 2 3

-100CFt

Cumulative -100 -30 20 40

1 + 30/50 = 1.6 yearsPaybackL =

Project S (Short: CFs come quickly)

0

1.6

10

The payback rule�Accept the projects with the payback period

shorter than a predetermined time

�Strengths:

� Provides an indication of a project’s risk and liquidity

� Easy to calculate and understand

�Weaknesses:

� Ignores the TVM

� Ignores CFs occurring after the paybackperiod

11

Discounted Payback: Uses discountedrather than raw CFs

Cumulative -100 -90.91 -41.32 18.79

2 + 41.32/60.11 = 2.7 years

10 8060

0 1 2 3

CFt -100

10%

PVCFt -100 9.09 49.59 60.11

Discountedpayback =

Recover invest. + cap. costs in 2.7 years.

2.7

0

12

(((( )))) .k1

CFNPV tt

n

0t ++++==== ����

====

NPV Method

�Definition: NPV is the sum of the PVs of all project cash flows

�The logic of NPV: NPV = PV inflows – Cost = Net gain in wealth

�Accept project if NPV > 0

�Choose between mutually exclusiveprojects on basis of higher NPV, because this project adds most value

13

10 8060

0 1 2 310%

Project L:

-100.00

60.1118.79 = NPVL

49.59

NPVS = $19.98.

9.09

What’s Project L’s NPV?

14

Using NPV method, which project(s) should be accepted?

� If S and L are independent, accept both; NPV > 0

� If Projects S and L are mutually exclusive, accept S because NPVS > NPVL

15

Steps for NPV valuation

�Estimate CFs (inflows & outflows)

�Assess riskiness of CFs

�Determine k = WACC (adj.)

� WACC: Weighted Average Cost of Capital

�Find NPV and/or IRR

16

0 1 2 3

CF0 CF1 CF2 CF3Cost Inflows

IRR is the discount rate that forcesPV inflows = cost. This is the sameas forcing NPV = 0

Internal Rate of Return: IRR

17

Rationale for the IRR Method

� If IRR > WACC = k, then the project’s rate of return is greater than its cost - some return is left over to boost stockholders’ returns

� IRR Acceptance Criteria

� If IRR > k, accept project

� If IRR < k, reject project

� Example: WACC = 10%, IRR = 15% Profitable

18

10 8060

0 1 2 3IRR = ?

-100.00

PV3

PV2

PV1

0 = NPV

IRRL = 18.13%. IRRS = 23.56%.

What is Project L’s IRR?

( ) ( ) 01

801

601

10100 32 =

++

++

++−

IRRIRRIRR

19

Decisions on Projects S and L using IRR

� If S and L are independent, accept both IRRS > k = 10%, IRRL > k = 10%

� If S and L are mutually exclusive, accept S because IRRS > IRRL

20

(((( )))) .NPVk1

CFt

tn

0t

====++++����

====

(((( )))) .0IRR1

CFt

tn

0t

====++++����

====

NPV: Enter k, solve for NPV

IRR: Enter NPV = 0, solve for IRR

Comparing NPV and IRR rules

21

NPV and IRR always lead to the same accept/reject decision for independent projects with normal cash flows:

k > IRRand NPV < 0.

Reject.

NPV ($)

k (%)IRR

IRR > kand NPV > 0

Accept.

Comparing NPV and IRR rules

22

Potential problems with IRR

�Hard to evaluate projects with alternating cash flows. Which IRR to choose?

�Ranking problems: Project with highest IRR is not always the best

�Ergo, IRR might lead to a wrong choice from mutually exclusive projects

23

Why the project with highest IRR is not always the best:

� Abnormal cash flows� Different risks for different projects

Impossible to compare a risky project (IRR =15%; k=12%) with a safe project (IRR = 12%; k = 10%)

� Size (scale) differencesSmaller project frees up funds at t = 0 for

investment. The higher k, the more valuable these funds, so high k favors small projects

� Timing differences• Project with faster payback provides more CF for

early reinvestment. Implicit reinvestment rate assumption

24

Crossover Point = 8.7%

k05

101520

NPVL

5033197

(4)

NPVS

402920125

IRRL = 18.1%

L

205 10 15 23.6

Discount Rate (%)

-10

0

10

20

30

40

50

60NPV ($)

.

.

IRRS = 23.6%S

.

..

. .

25

k < 8.7: NPVL> NPVS , IRRS > IRRLCONFLICT

k > 8.7: NPVS> NPVL , IRRS > IRRLNO CONFLICT

Mutually Exclusive Projects

k 8.7 k

NPV

%

IRRS

IRRL

L

S

26

Reinvestment Rate Assumptions

�NPV assumes reinvest at k (opportunity cost of capital)

� IRR assumes reinvest at IRR

�Reinvest at opportunity cost, k, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects

27

Modified IRR (MIRR)

� Managers like IRR (easier to compare rates than NPVs). Can we give them a better IRR rule?

� Modified IRR (MIRR) rule works correctly with projects that have alternating CFs or different time horizon

� MIRR is the discount rate that causes the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC to the final date of the longest project

� Thus, MIRR assumes cash inflows are reinvested at WACC

28

How to use MIRR

� Identify the longest project. Its horizon, T, will be used to calculate the terminal value (TV) for all projects in question

� Calculate each project’s TV as a sum of FVs of all CFs (except the original investment, I) compounded at WACC to the final date of the longest project

� Find each project’s MIRR as

1

1

−��

���

�=T

ITV

MIRR

29

MIRR = 16.5%

10.0 80.060.0

0 1 2 310%

66.012.1

158.1

MIRR for Project L (k = 10%)

-100.010%

10%

TV inflows-100.0

PV outflowsMIRRL = 16.5%

$100 = $158.1

(1 + MIRRL)3

30

Why use MIRR versus IRR?

�MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs

�Managers like rate of return comparisons, and MIRR is better for this than IRR

31

Why is NPV better than MIRR?

�Allows to compare the projects of different risk (different WACC)

�Allows to compare the projects of different scale

� In MIRR we implicitly use NPV concept!

�Problem with NPV?

� Sensitive to WACC

32

Steps for NPV valuation1 Draw the time line define the forecast

horizon

2 Identify all relevant free cash flows over the forecast horizon (next slide)(FCF here = operating CF + investment CF)

3 For each cash flow item write the relevant time period and discount factor

4 Calculate PV of this cash item; repeat 3 and 4

5 Calculate NPV by adding all PV’s together

33

Identify all relevant FCFs over the forecast horizon

�Recover FCF from accounting data• Estimate cash flow on an incremental basis

• Disregard sunk costs

• Treat depreciation properly

�Adjust for changes in working capital requirements

34

Fundamental Principles of Project Evaluation

• Relevant cash flows - the incremental cash flows associated with the decision to invest in a project

• The incremental cash flows for project evaluation consist of any and all changes in the firm’s future cash flows that are a direct consequence of taking the project

• Stand-alone principle - evaluation of a project based on the project’s incremental cash flows

35

Incremental Cash Flows

When is a cash flow incremental?� Sunk costs?

� Opportunity costs?

� Side effects?

� Net working capital?

� Financing costs?

� Other issues?

36

Special issues:

� Treat inflation consistently

� Ignore financing costs (interest) in calculating cash flows

� Don’t forget about depreciation tax shield

� Use Equivalent Annual Cost (EAC) method to compare projects with different lengths

37

Free Cash Flow

FCF = NOPAT(All equity) + Depreciation -∆NWC - CapEx

Alternatively

FCF = EBITDA x (1-tax rate) + Depreciation x tax rate - ∆NWC - CapEx

38

1999 2000 2001 2002 2003Sales 1500 1575 1654 1736 1823Cost of goods sold 450 473 496 521 547Labour costs 350 364 379 394 409Other operating expenses 20 20 20 20 20Gross operating surplus 680 719 759 802 847Depreciation 200 150 100 50 50Operating income 480 569 659 752 797

1998 1999 2000 2001 2002 2003Net working capital 600 630 662 695 729 766

Investments 200 150 100 50 50 50

Example - Thorelle exercise

� You estimate that at the end of 2003 the lab will be sold at 4,000

� WACC = 10%; Tax rate = 40%� Which cash flows should you take into account in

order to value your investment?

� At what price would you buy this laboratory?

� At this price, what is the IRR?

39

Example - Thorelle exercise

Thorelle Exercise1998 1999 2000 2001 2002 2003

Gross operating margin 680 719 759 802 847- Taxes -272 -287.6 -303.6 -320.8 -338.8- Investment -200 -150 -100 -50 -50 -50- Change in NWC* -600 -30 -32 -33 -34 729Depreciation tax shield 80 60 40 20 20Sale of asset 4000Cash Flow -800 308 359.4 412.4 417.2 5207.2PV (10 %) -800 280 297.024793 309.842224 284.953214 3233.26151NPV 3605.08174

-4405.08174 308 359.4 412.4 417.2 5207.2IRR= 10%

Assume that all NWC is recovered at the end of 2003

40

Equivalent Annual Cost Method (EAC)

� Helpful to compare repeated projects with different lengths

� Principle: PV(full cost)=PV(equivalent annual cost or rent)

� Example: Choose between machines A and B with the same production capacity

� A has economic life of 3 years, costs 4,500 and requires 2,200 annually for maintenance;

� B has economic life of 5 years, costs 10,000 and requires 1,200 annually for maintenance

� assume r=10%

41

Equivalent Annual Cost Method (EAC)

�We can solve it by calculating EAC or rent cost (R) for each machine

1. We calculate the PV of each machine

2. We find annual rents such that

PV(R)=PV( machine)

3. We compare R(A) and R(B)

42

Machine A

4,500 2,200 2,200 2,200PV(A)=4,500+2,200×A(3years; 10%)=9,971.4

PV(A)=A(3years; 10%) ×R(A);

R(A)=9,971.4/2.487=4,009.41Machine B

10,000 1,200 1,200 1,200

PV(B)=10,000+1,200×A(5 years; 10%)=14,549.2

PV(B)=A(5 years; 10%) ×R(A); R(B)= 14,549.2 /3.791=3,837.83

R(A)>R(B) !

1,200 1,200

43

The basic problem: How reliable is our NPV estimate?

�Projected vs. Actual cash flows

�Estimated cash flows are average of possible outcomes each period

�The possibility of a bad decision due to errors in cash flow projections

� “What If” analysis

� Scenario analysis

� Sensitivity analysis

44

“What-If” Analyses:

� “Base case” estimation

�Scenario analysis• Posit best- and worst-case scenarios and

calculate NPVs

�Sensitivity analysis• How does the estimated NPV change when

one of the input variables changes?

�Simulation analysis• Vary several input variables simultaneously,

then construct a distribution of possible NPV estimates

45

MeasureX Balance Sheet

Thousands of dollars 1996 % Sales 1997 %Sales

1998 % Sales

AssetsCash 2,790 3,030 3,470Others 80 130 240 0.2%

Accounts Receivable 6,930 19% 9,600 17% 18,550 17.4%

Inventories 2,590 7% 5,220 9% 6,170 5.8%

Net Fixed Assets 4,400 6,780 10,820Total Assets 16,790 24,760 39,250

Liabilities & EquityAccounts Payable 1,590 4% 3,000 5% 2,850 2.7%

Accrued Taxes 90 560 3,830 3.6%

Short-term liabilities 980 1,480 2,000 1.9%

Long-term Bank debt 5,910 10,720 17,246Equity (a) 8,040 8,170 8,240Reserves 180 830 5,084Total Equity 8,220 9,000 13,324Total Liabilities 16,790 24,760 39,250

Number of shares in 000 5,760 5,825 5,950

46

MeasureX Income Statement

Thousands of dollars 1996 % 1997 % 1998 %

Sales 36,160 55,440 106,370Cost of Goods Sold 22,970 36,260 61,695Gross Margin 13,190 36.5% 19,180 34.6% 44,675 42.0%R & D 4,220 11.7% 5,290 9.5% 10.770 10.1%Other 7.820 21.6% 11.190 20.2% 24.250 22.8%EBITDA 1.150 3.2% 2.700 4.9% 9.655 9.1%Depreciation 620 1.050 1.570EBIT (Operating Income) 530 1.5% 1.650 3.0% 8.085 7.6%Financial Expenses 300 0.8% 530 1.0% 1.280 1.2%Exceptional items -150 -120 - 360Earnings Before Taxes 80 1.000 6.445Taxes * 30 38% 350 35% 2.191 34%Net Income 50 0.1% 650 1.2% 4.254 4.0%

47

MeasureX Project 1

�What is Project 1 relevant Cash Flow?

� Investment?

� EBITDA?

� Depreciation?

� Changes in the NWC?

�What is the relevant range for the cost of capital?

48

MeasureX Project 1Pro ject 1: New pro duct

1998 1999 2000 2001 2002 2003 2004Inves tment 10,000Deprecia tion 2,000 2,000 2,000 2,000 2,000

1998 1999 2000 2001 2002 2003 2004S a le s 20,000 25,000 25,000 16,000 8,000 0Gross margin 42% 8,400 10,500 10,500 6,720 3,360 0S ta rt-up expenses 500Resea rch & Admin 15% 3,000 3,750 3,750 2,400 1,200 0EBITDA 4,900 6,750 6,750 4,320 2,160 0∆ NWC 22% 4,400 1,100 0 -1,980 -1,760 -1,760Opera ting CF 500 5,650 6,750 6,300 3,920 1,760Inves tment 10,000Flow bef. Taxes -10,000 500 5,650 6,750 6,300 3,920 1,760Tax on EBIT 34% 986 1,615 1,615 789 54 0P roject flows -10,000 -486 4,035 5,135 5,511 3,866 1,760IRR 20.571%

WACC NP V10% 3,908.8315% 1,838.6120% 169.44

20.57% 0.1725% - 1 192

49

MeasureX Project2

�Finished goods - one third of the inventory

� Increase in NWC is 22% of incremental sales

�What are the gains from going from the current level to A?

�What are the additional costs from going from the current level to A?

50

MeasureX Project 2

Proje ct 2: Inve ntoryInventory Mis s ed ∆ S ales Inventory LevelLevel S ales as a % of S ales

Curre nt 3,110 7,500 340 2.9%A 5,000 5,200 420 2,300 4.7%B 7,000 3,200 500 2,000 6.6%C 9,000 1,500 600 1,700 8.5%D 11,000 560 700 940 10.3%E 13,000 170 740 390 12.2%

- ∆ Inventory ∆ NWC Total ∆ Gros s margin margin -(inves t) 15% Inves tt 42% cos ts -Taxes IRR NPV 5yrs NPV 10yrs P erpetuity

= NOPAT 21% 21% 21%A -1,890 339 -2,229 966 80 585 26.2% 373 519 614B -2,000 295 -2,295 840 80 502 21.9% 87 122 144C -2,000 251 -2,251 714 100 405 18.0% -170 -237 -281D -2,000 139 -2,139 395 100 195 9.1% -725 -1009 -1193E -2,000 57 -2,057 164 40 82 4.0% -1009 -1405 -1660

1+WACC 121%

Inventory holding cos ts

∆ Inventory holding cos ts

O ther thaninventory

51

Managerial Options and Capital BudgetingGenerally, the exclusion of managerial options from the analysis causes us to underestimate the “true” NPV of a project. Why?

Options and capital budgeting• Contingency planning 1.The option to expand2.The option to abandon3.The option to wait

• Strategic options“Toehold” investmentsResearch and development

52

Option to expand

Telecom 3 G license � Market : 50% small (0-10 min, average 5 mln),

50% big (10-50 mln, average 30 mln) in 4 years

� Investment: 1.5 bln Euro (capacity 10 mln)

5 bln Euro (capacity 50 mln)

scalable: 2 bln (10 mln) + 4 bln in year 4 (50 mln)

� Variable cost margin 100 euro per customer

� No taxes. 25 % cost of capital. A4 years; 25%=2.362

� License fee to pay?

53

Option to expand

� Small investment (can’t serve more than 100 mln customers)Naive approach:

Perpetuity of 500 M Euro with investment of 1.5

5.05.125.

5.0 =−

91.05.125.75.0

25.11

5.04

%25;4 =−��

���

���

���

�+A

� Taking into account big market:

Average 500 M Euro for years 1-4

In years 5 - ∝∝∝∝ + 500 M Euro with probability 1/2

+ 1 bln Euro with probability 1/2

54

Option to expand

� Big investment

- Investment of 5 bln Euro in year 0

Average + 500 M for years 1-4

In years 5 - ∝∝∝∝ + 500 M Euro with probability 1/2

+ 3 bln Euro with probability 1/2

95.095.2225.125.75.1

5 %25;4 −=−=−+− A

=��

���

�++−25.075.1

25.11

5.054

%25;4A

55

Option to expand

� Scaleable investment

Naïve approach

- Investment of 2 bln Euro in year 0

- Investment of 4 bln Euro in year 4

Average + 500 M for years 1-4

In years 5 - ∝∝∝∝ + 500 M Euro with probability 1/2

+ 3 bln Euro with probability 1/2

( )41.005.464.12

25.075.1

25.11

5.025.14

24

%25;44

=+−−=

��

���

�++−− A

56

Option to expand

� Scaleable investmentMore complicated approach

- Investment of 2 bln Euro in year 0

- Investment of 4 bln Euro in year 4 ONLY IF THE MARKET IS BIG

Average + 500 M for years 1-4

In years 5 - ∝∝∝∝ + 500 M Euro with probability 1/2

+ 3 bln Euro with probability 1/2

( ) ( )( ) 23.182205.018.12

425.03

25.05.0

25.11

21

36.25.02 4

=+++−=

��

���

���

���

� −+++−

57

Option to wait

�Oil drilling projectOil price per barrel:10 or 30 euros

Cost 12 euros per barrel

Production 1000 barrels

How much to pay for 25 year lease?

r=15% (A25;0.2=6.464)

NPV1=(20-12)x1000xA25;0.15=51,712

NPV2=0.5(30-12)x1000xA25;0.15=58,176