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CHAPTER 13 The Basics of Capital Budgeting: Evaluating Cash Flows. Should we build this plant?. What is capital budgeting?. Analysis of potential additions to fixed assets. Long-term decisions; involve large expenditures. Very important to firm’s future. Steps.

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what is capital budgeting
What is capital budgeting?
  • Analysis of potential additions to fixed assets.
  • Long-term decisions; involve large expenditures.
  • Very important to firm’s future.
steps
Steps

1. Estimate CFs (inflows & outflows).

2. Assess riskiness of CFs.

3. Determine k = WACC for project.

4. Find NPV and/or IRR.

5. Accept if NPV > 0 and/or IRR > WACC.

what is the difference between independent and mutually exclusive projects
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.

an example of mutually exclusive projects
An Example of Mutually Exclusive Projects

BRIDGE vs. BOAT to get

products across a river.

normal cash flow project
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.

slide7

Inflow (+) or Outflow (-) in Year

0

1

2

3

4

5

N

NN

-

+

+

+

+

+

N

-

+

+

+

+

-

NN

-

-

-

+

+

+

N

+

+

+

-

-

-

N

-

+

+

-

+

-

NN

what is the payback period
What is the payback period?

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

or how long does it take to get the business’s money back?

payback for project l long most cfs in out years
Payback for Project L(Long: Most CFs in out years)

2.4

0

1

2

3

CFt

-100

10

60

100

80

Cumulative

-100

-90

-30

0

50

PaybackL

=

2 + 30/80 = 2.375 years

project s short cfs come quickly
Project S (Short: CFs come quickly)

1.6

0

1

2

3

CFt

-100

70

100

50

20

Cumulative

-100

-30

0

20

40

PaybackS

=

1 + 30/50 = 1.6 years

slide11

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 TVM.

2. Ignores CFs occurring after the payback period.

slide12

Discounted Payback: Uses discounted

rather than raw CFs.

0

1

2

3

10%

CFt

-100

10

60

80

PVCFt

-100

9.09

49.59

60.11

Cumulative

-100

-90.91

-41.32

18.79

Discounted

payback

2 + 41.32/60.11 = 2.7 yrs

=

Recover invest. + cap. costs in 2.7 yrs.

slide13

NPV: Sum of the PVs of inflows and outflows.

Cost often is CF0 and is negative.

what s project l s npv
What’s Project L’s NPV?

Project L:

0

1

2

3

10%

-100.00

10

60

80

9.09

49.59

60.11

18.79 = NPVL

NPVS = $19.98.

calculator solution
Calculator Solution

Enter in CFLO for L:

-100

10

60

80

10

CF0

CF1

CF2

CF3

I

NPV

= 18.78 = NPVL

rationale for the npv method
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.

using npv method which project s should be accepted
Using NPV method, which project(s) should be accepted?
  • If Projects 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
Internal Rate of Return: IRR

0

1

2

3

CF0

CF1

CF2

CF3

Cost

Inflows

IRR is the discount rate that forces

PV inflows = cost. This is the same

as forcing NPV = 0.

slide19

NPV: Enter k, solve for NPV.

IRR: Enter NPV = 0, solve for IRR.

what s project l s irr
What’s Project L’s IRR?

0

1

2

3

IRR = ?

-100.00

10

60

80

PV1

PV2

PV3

0 = NPV

Enter CFs in CFLO, then press IRR:

IRRL = 18.13%.

IRRS = 23.56%.

slide21

N

I/YR

PV

PMT

FV

Find IRR if CFs are constant:

0

1

2

3

IRR = ?

-100

40

40

40

INPUTS

3 -100 40 0

9.70%

OUTPUT

Or, with CFLO, enter CFs and press

IRR = 9.70%.

slide22

Q. How is a project’s IRR

related to a bond’s YTM?

A. They are the same thing.

A bond’s YTM is the IRR

if you invest in the bond.

0

1

2

10

IRR = ?

...

-1,134.2

90

90

1,090

IRR = 7.08% (use TVM or CFLO).

rationale for the irr method
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.

irr acceptance criteria
IRR Acceptance Criteria
  • If IRR > k, accept project.
  • If IRR < k, reject project.
decisions on projects s and l per irr
Decisions on Projects S and L per IRR
  • If S and L are independent, accept both. IRRs > k = 10%.
  • If S and L are mutually exclusive, accept S because IRRS > IRRL .
construct npv profiles
Construct NPV Profiles

Enter CFs in CFLO and find NPVL and

NPVS at different discount rates:

NPVL

50

33

19

7

NPVS

40

29

20

12

5

k

0

5

10

15

20

(4)

slide27

NPV ($)

k

0

5

10

15

20

NPVL

50

33

19

7

(4)

NPVS

40

29

20

12

5

Crossover

Point = 8.7%

S

IRRS = 23.6%

L

Discount Rate (%)

IRRL = 18.1%

slide28

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

NPV ($)

IRR > k

and NPV > 0

Accept.

k > IRR

and NPV < 0.

Reject.

k (%)

IRR

slide29

Mutually Exclusive Projects

k < 8.7: NPVL> NPVS , IRRS > IRRL

CONFLICT

NPV

L

k > 8.7: NPVS> NPVL , IRRS > IRRL

NO CONFLICT

IRRS

S

%

k 8.7 k

IRRL

to find the crossover rate
To Find the Crossover Rate

1. Find cash flow differences between the projects. See data at beginning of the case.

2. Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68%, rounded to 8.7%.

3. Can subtract S from L or vice versa, but better to have first CF negative.

4. If profiles don’t cross, one project dominates the other.

two reasons npv profiles cross
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 k favors small projects.

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

reinvestment rate assumptions
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.
managers like rates prefer irr to npv comparisons can we give them a better irr
Managers like rates--prefer IRR to NPV comparisons. Can we give them a better IRR?

Yes, MIRR is the discount rate which

causes the PV of a project’s terminal

value (TV) to equal the PV of costs.

TV is found by compounding inflows

at WACC.

Thus, MIRR assumes cash inflows are reinvested at WACC.

slide34

$158.1

(1+MIRRL)3

$100 =

MIRR for Project L (k = 10%)

0

1

2

3

10%

-100.0

10.0

60.0

80.0

10%

66.0

12.1

10%

MIRR = 16.5%

158.1

-100.0

TV inflows

PV outflows

MIRRL = 16.5%

slide35

To find TV with 10B, enter in CFLO:

CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80

I = 10

NPV = 118.78 = PV of inflows.

Enter PV = -118.78, N = 3, I = 10, PMT = 0.

Press FV = 158.10 = FV of inflows.

Enter FV = 158.10, PV = -100, PMT = 0, N = 3.

Press I = 16.50% = MIRR.

why use mirr versus irr
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.

pavilion project npv and irr
Pavilion Project: NPV and IRR?

0

1

2

k = 10%

-800

5,000

-5,000

Enter CFs in CFLO, enter I = 10.

NPV = -386.78

IRR = ERROR. Why?

slide38

We got IRR = ERROR because there

are 2 IRRs. Nonnormal CFs--two sign

changes. Here’s a picture:

NPV Profile

NPV

IRR2 = 400%

450

0

k

100

400

IRR1 = 25%

-800

logic of multiple irrs
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.

slide40

Could find IRR with calculator:

1. Enter CFs as before.

2. Enter a “guess” as to IRR by storing the guess. Try 10%:

10 STO

IRR = 25% = lower IRR

Now guess large IRR, say, 200:

200 STO

IRR = 400% = upper IRR

slide41

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%

accept project p
Accept Project P?

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

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

slide43

S and L are mutually exclusive and will be repeated. k = 10%. Which is better? (000s)

0

1

2

3

4

Project S:

(100)

Project L:

(100)

60

33.5

60

33.5

33.5

33.5

slide44

S L

CF0 -100,000 -100,000

CF1 60,000 33,500

Nj 2 4

I 10 10

NPV 4,132 6,190

NPVL > NPVS. But is L better?

Can’t say yet. Need to perform common life analysis.

slide45
Note that Project S could be repeated after 2 years to generate additional profits.
  • Can use either replacement chain or equivalent annual annuity analysis to make decision.
project s with replication
Project S with Replication:

Replacement Chain Approach (000s)

0

1

2

3

4

Project S:

(100)

(100)

60

60

60

(100)

(40)

60

60

60

60

NPV = $7,547.

slide47

Or, use NPVs:

0

1

2

3

4

4,132

3,415

7,547

4,132

10%

Compare to Project L NPV = $6,190.

slide48

If the cost to repeat S in two years rises to $105,000, which is best? (000s)

0

1

2

3

4

Project S:

(100)

60

60

(105)

(45)

60

60

NPVS = $3,415 < NPVL = $6,190.

Now choose L.

slide49

Consider another project with a 3-year life. If terminated prior to Year 3, the machinery will have positive salvage value.

Year

0

1

2

3

CF

($5,000)

2,100

2,000

1,750

Salvage Value

$5,000

3,100

2,000

0

slide50

CFs Under Each Alternative (000s)

0

1

2

3

1. No termination

2. Terminate 2 years

3. Terminate 1 year

(5)

(5)

(5)

2.1

2.1

5.2

2

4

1.75

slide51

Assuming a 10% cost of capital, what is the project’s optimal, or economic life?

NPV(no) = -$123.

NPV(2) = $215.

NPV(1) = -$273.

slide52

Conclusions

  • The project is acceptable only if operated for 2 years.
  • A project’s engineering life does not always equal its economic life.
choosing the optimal capital budget
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
increasing marginal cost of capital
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.

(More...)

slide55
If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.
capital rationing
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.

(More...)

slide57
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.

(More...)

slide58
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.

(More...)

slide59
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.

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