Lecture 7 - Capital Budgeting: Decision

Criteria

2

What is Capital Budgeting?

Analysis of potential projects.

Long-term decisions; involve large expenditures.

Very important to a firm’s future.

The Ideal Evaluation Method should:

a) include all cash flows that occur during the life of the project,

b) consider the time value of money,

c) incorporate the required rate of return on the project. Determine r = WACC for project.

3

What is 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.

10 8060

0 1 2 3

-100

=

CFt

Cumulative -100 -90 -30 50

PaybackL 2 + 30/80 = 2.375 years

0100

2.4

Payback Period - The number of years required to recover a project’s cost

Payback for Franchise Long(Long: Most CFs in out years)

4

Franchise Short (Short: CFs come quickly)

70 2050

0 1 2 3

-100CFt

Cumulative -100 -30 20 40

PaybackS 1 + 30/50 = 1.6 years

100

0

1.6

=

5

Another Example

Ms. Hoa is is evaluating a new project for her firm, Basket Wonders (BW). She has determined that the after-tax cash flows for the project will be

$10,000; $12,000; $15,000; $10,000; and $7,000,

respectively, for each of the Years 1 through 5.

The initial cash outlay will be $40,000.

6

7

PBPPBP is the period of time required for the cumulative expected cash flows from an investment project to equal the initial cash outflow.

Note : K = 1000s

PBPPBP is the period of time required for the cumulative expected cash flows from an investment project to equal the initial cash outflow.

Note : K = 1000s

0 1 2 3 4 5

-40 K 10 K 12 K 15 K 10 K 7 K

Payback period

8

(c)10 K 22 K 37 K 47 K 54 K

PBPPBP = a + ( b - c ) / d= 3 + (40 - 37) /

10 = 3 + (3) / 10 = 3.3 3.3 YearsYears

PBPPBP = a + ( b - c ) / d= 3 + (40 - 37) /

10 = 3 + (3) / 10 = 3.3 3.3 YearsYears

0 1 2 3 4 5

-40 K 10 K 12 K 15 K 10 K 7 K

CumulativeInflows

(a)

(-b) (d)

A Payback solution

Strengths of Payback:

1. Provides an indication of a project’s risk and liquidity.

2. Easy to calculate and understand.

Weaknesses of Payback:

1. Ignores the Time Value of Money.

2. Ignores CFs occurring after the payback period.

9

10 8060

0 1 2 3

CFt

Cumulative -100 -90.91 -41.32 18.79

Discountedpayback 2 + 41.32/60.11 = 2.7 yrs

Discounted Payback: Uses discountedrather than raw CFs.

PVCFt -100

-100

10%

9.09 49.59 60.11

=

Recover invest. + cap. costs in 2.7 yrs.

10

11

.

10t

tn

t r

CFNPV

NPV: Sum of the PVs of inflows and outflows.

Cost often is CF0 and is negative.

.

10

1

CFr

CFNPV t

tn

t

Notice difference in t

Net Present Value (NPV) Method

What is Franchise Long’s NPV?

10 8060

0 1 2 310%

Project L:

-100.00

9.09

49.59

60.1118.79 = NPVL NPVS = $19.98.

12

Basket Wonders has determined that the appropriate discount rate (r) for this project is 13%.

$10,000 $7,000

$10,000 $12,000 $15,000

(1.13)1 (1.13)2 (1.13)3 + +

+ - $40,000$40,000(1.13)4 (1.13)5

NPVNPV =

+

Basket Wonders Example

NPVNPV = $8,850 + $9,396 + $10,395 + $6,130 + $3,801 - $40,000$40,000

= - $1,428$1,428

13

Rationale for the NPV Method

NPV = PV inflows – Cost = Net gain in wealth.

Accept project if NPV > 0.

Choose between mutually exclusive projects on basis of higher NPV. Adds most value.

14

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

If Franchise S and L are mutually exclusive, accept S because NPVs > NPVL .

If S & L are independent, accept both; NPV > 0.

Internal Rate of Return: IRR

0 1 2 3

CF0 CF1 CF2 CF3

Cost Inflows

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

15

.

10

NPVr

CFt

tn

t

0

0.1

nt

tt

CF

IRR

NPV: Enter r, solve for NPV.

IRR: Enter NPV = 0, solve for IRR.

16

What’s Franchise Long’s IRR?

10 (70s) 80 (20s)60 (50s)

0 1 2 3IRR = ?

-100.00

PV3

PV2

PV1

0 = NPV

IRRL = 18.13%. IRRS = 23.56%.17

Rationale for the IRR Method

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

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

18

19

Decisions on Projects S and L per IRR

If S and L are independent, accept both. IRRs > r = 10%.

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

We can construct NPV profiles

We find NPVL and NPVS at different discount rates:

r

0

5

10

15

20

NPVL

50

33

19

7

NPVS

40

29

20

12

5 (4)

20

-10

0

10

20

30

40

50

60

0 5 10 15 20 23.6

NPV ($)

Discount Rate (%)

IRRL = 18.1%

IRRS = 23.6%

Crossover Point = 8.7%

r

0

5

10

15

20

NPVL

50

33

19

7

(4)

NPVS

40

29

20

12

5

S

L

21

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

r > IRRand NPV < 0.

Reject.

NPV ($)

r (%)IRR

IRR > rand NPV > 0

Accept.

22

Mutually Exclusive Projects

r 8.7 r

NPV

%

IRRS

IRRL

L

S

r < 8.7: NPVL> NPVS , IRRS > IRRL

CONFLICT r > 8.7: NPVS> NPVL , IRRS > IRRL

NO CONFLICT

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Two Reasons NPV Profiles Cross

1. Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high r favors small projects.

2. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If r is high, early CF especially good, NPVS > NPVL.

Reinvestment Rate Assumptions

NPV assumes reinvest at r (opportunity cost of capital).

IRR assumes reinvest at IRR.

Reinvest at opportunity cost, r, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects. 24

Managers like rates--prefer IRR to NPV comparisons. Can we give them a

better IRR?

Yes, MIRR is the discount rate whichcauses the PV of a project’s terminalvalue (TV) to equal the PV of costs.TV is found by compounding inflowsat WACC.

Thus, MIRR assumes cash inflows are reinvested at WACC.

25

MIRR = 16.5%

10.0 80.060.0

0 1 2 310%

66.0 12.1

158.1

MIRR for Franchise L (r = 10%)

-100.010%

10%

TV inflows-100.0

PV outflowsMIRRL = 16.5%

$100 = $158.1

(1+MIRRL)3

26

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.

27

Normal Cash Flow Project:

Cost (negative CF) followed by a series of positive cash inflows. One change of signs.

Nonnormal 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.

28

Inflow (+) or Outflow (-) in Year

0 1 2 3 4 5 N NN

- + + + + + N

- + + + + - NN

- - - + + + N

+ + + - - - N

- + + - + - NN

29

Pavilion Project: NPV and IRR?

5,000 -5,000

0 1 2r = 10%

-800

NPV = -386.78

IRR = ERROR. Why?

30

We got IRR = ERROR because there are 2 IRRs. Nonnormal CFs--two signchanges. Here’s a picture:

NPV Profile

450

-800

0400100

IRR2 = 400%

IRR1 = 25%

r

NPV

31

Logic of Multiple IRRs

1. At very low discount rates, the PV of CF2 is large & negative, so NPV < 0.

2. At very high discount rates, the PV of both CF1 and CF2 are low, so CF0 dominates and again NPV < 0.

3. In between, the discount rate hits CF2 harder than CF1, so NPV > 0.

4. Result: 2 IRRs.

32

When there are nonnormal CFs and more than one IRR, use MIRR:

0 1 2

-800,000 5,000,000 -5,000,000

PV outflows @ 10% = -4,932,231.40.

TV inflows @ 10% = 5,500,000.00.

MIRR = 5.6%Should We Accept Project P?

33

34

Accept Project P?

NO. Reject because MIRR = 5.6% < r = 10%.

Also, if MIRR < r, NPV will be negative: NPV = -$386,777.

PI is the ratio of the present value of a project’s future net cash flows to the project’s initial cash outflow.

CF1 CF2 CFt (1+r)1 (1+r)2 (1+r)t

+ . . . ++ ICOICOPI =

Profitability Index (PI)

35

It measures the “bang for the buck.”

Profitability Index Acceptance Criterion

Reject if PIReject if PI < 1.001.00 ]

0 1 2 3 4

Project S:(100)

Project L:(100)

60

33.5

60

33.5 33.5 33.5

S and L are mutually exclusive and will be repeated. r = 10%.

36

NPVL > NPVS. But is L better?

S L

CF0 -100,000 -100,000

CF1 60,000 33,500

NJ 2 4

I 10 10

NPV 4,132 6,190

37

Note that Project S could be repeated after 2 years to generate additional profits.

Replacement Chain Approach Franchise S with Replication:

NPV = $7,547.

0 1 2 3 4

Franchise S:(100) (100)

60 60

60(100) (40)

6060

6060

All values in thousands

38

Compare to Franchise L, where NPV = $6,190.Compare to Franchise L, where NPV = $6,190.

0 1 2 3 4

4,1323,4157,547

4,13210%

Or, use NPVs:

39

NPVS = $3,415 < NPVL = $6,190.Now choose L.NPVS = $3,415 < NPVL = $6,190.Now choose L.

0 1 2 3 4

Franchise S:(100)

60 60(105) (45)

60 60

Suppose cost to repeat S in two years rises to $105,000.

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41

Economic Life versus Physical Life

Consider another project with a 3-year life.

If terminated prior to Year 3, the machinery will have positive salvage value.

Should you always operate for the full physical life?

See next slide for cash flows.

Economic Life versus Physical Life (Continued)

Year CF Salvage Value

0 ($5000) $5000

1 2,100 3,100

2 2,000 2,000

3 1,750 0

42

CFs Under Each Alternative (000s)

0 1 2 3

1. No termination (5) 2.1

2 1.75

2. Terminate 2 years (5) 2.1

4

3. Terminate 1 year (5) 5.2

43

NPVs under Alternative Lives (Cost of capital = 10%)

NPV(3) = -$123.

NPV(2) = $215.

NPV(1) = -$273.

The project is acceptable only if operated for 2 years.

A project’s engineering life does not always equal its economic life.

44

Choosing the Optimal Capital Budget

Finance theory says to accept all positive NPV projects.

Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects:

An increasing marginal cost of capital.

Capital rationing

45

Increasing Marginal Cost of Capital

Externally raised capital can have large flotation costs, which increase the cost of capital.

Investors often perceive large capital budgets as being risky, which drives up the cost of capital.

If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.

46

Capital Rationing

Capital rationing occurs when a company chooses not to fund all positive NPV projects.

The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year.

Reason: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital.

Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital.

Reason: Companies don’t have enough managerial, marketing, or engineering staff to implement all positive NPV projects.

Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing.

Reason: Companies believe that the project’s managers forecast unreasonably high cash flow estimates, so companies “filter” out the worst projects by limiting the total amount of projects that can be accepted.

Solution: Implement a post-audit process and tie the managers’ compensation to the subsequent performance of the project.

47

Increasing Marginal Cost of Capital

Externally raised capital can have large flotation costs, which increase the cost of capital.

Investors often perceive large capital budgets as being risky, which drives up the cost of capital.

If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.

48

Find the PV of the foreign CF’s denominated in the foreign currency and discounted by the foreign country’s cost of capital

Convert the PV of the CF’s to the home country’s currency multiplying by the spot exchange rate

Subtract the parent company’s initial cost from the Present values of net cash flows to get the NPV

International Capital Budgeting

Amount and Timing of Foreign CF’s will depend on Differential tax rates

Legal and political constraints on CF

Government subsidized loans