Should we build thisplant?

The Basics of Capital Budgeting

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.

StepsSteps

1. Estimate CFs (inflows & outflows).2. Assess riskiness of CFs.3. Determine k = WACC (adjusted).4. Find NPV, IRR, MIRR, etc.5. Accept if NPV > 0, IRR > WACC,

etc.

What is the difference between What is the difference between independent and mutually exclusive independent and mutually exclusive projects?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 An Example of Mutually Exclusive ProjectsExclusive 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.

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 our money back?

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

10 60

0 1 2 3

-100

=

CFt

Cumulative -100 -90 -30 50

PaybackL 2 + 30/80 = 2.375 years

80

Project S (Short: CFs come quickly)Project S (Short: CFs come quickly)

70 2050

0 1 2 3

-100CFt

Cumulative -100 -30 20 40

PaybackL 1 + 30/50 = 1.6 years=

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.

3. Subjective

Discounted Payback: Uses discountedrather than raw CFs.

10 8060

0 1 2 3

CFt

Cumulative -100 -90.91 -41.32 18.79

Discountedpayback 2 + 41.32/60.11 = 2.7 years

PVCFt -100

-100

10%

9.09 49.59 60.11

=

Recover invest. + cap. costs in 2.7 years.

.

k1CF

NPV tt

n

0t

NPV: Sum of the PVs of inflows and outflows.

What’s Project L’s NPV?What’s Project L’s NPV?

10 8060

0 1 2 310%

Project L:

-100.00

9.09

49.59

60.11

18.79 = NPVLNPVS = $19.98.

Calculator SolutionCalculator Solution

Enter in CFLO for L:

-100

10

60

80

10

CF0

CF1

NPV

CF2

CF3

I = 18.78 = NPVL

Rationale for the NPV Rationale for the NPV MethodMethod

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

Accept project if NPV > 0.

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

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

.NPV

k1CF

tt

n

0t

.0

IRR1CF

tt

n

0t

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?

10 8060

0 1 2 3IRR = ?

-100.00

PV3

PV2

PV1

0 = NPV

Enter CFs in CFLO, then press IRR:IRRL = 18.13%. IRRS = 23.56%.

40 40 40

0 1 2 3IRR = ?

Find IRR if CFs are constant:

-100

Or, with CF keys, enter CFs and press IRR = 9.70%.

3 -100 40 0

9.70%

INPUTS

OUTPUTN I/YR PV PMT FV

90 109090

0 1 2 10IRR = ?

Q. How is a project’s IRRrelated to a bond’s YTM?

A. They are the same thing.A bond’s YTM is the IRRif you invest in the bond.

-1134.2

IRR = 7.08% (use TVM or CF keys).

...

Rationale for the IRR Rationale for the IRR MethodMethod

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 CriteriaIRR Acceptance Criteria

If IRR > k, accept project.

If IRR < k, reject project.

Decisions on Projects S and L per Decisions on Projects S and L per IRRIRR

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

If S and L are mutually exclusive?

Construct NPV ProfilesConstruct NPV Profiles

Enter CFs in CFLO and find NPVL andNPVS at different discount rates:

k

0

5

10

15

20

NPVL

50

33

19

7

(4

NPVS

40

29

20

12

5 (4)

-10

0

10

20

30

40

50

60

5 10 15 20 23.6

NPV ($)

Discount Rate (%)

IRRL = 18.1%

IRRS = 23.6%

Crossover Point = 8.7%

k

0

5

10

15

20

NPVL

50

33

19

7

(4)

NPVS

40

29

20

12

5

S

L

.

.

...

.

..

.

..

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

k > IRRand NPV < 0.

Reject.

NPV ($)

k (%)IRR

IRR > kand NPV > 0

Accept.

Mutually Exclusive Projects

k 8.7 k

NPV

%

IRRS

IRRL

L

S

k < 8.7: NPVL> NPVS , IRRS > IRRL

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

NO CONFLICT

To Find the Crossover RateTo 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 Two Reasons NPV Profiles CrossCross

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 Reinvestment Rate AssumptionsAssumptions

NPV assumes reinvestment 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 Managers like rates--prefer IRR to NPV comparisons. Can we give NPV comparisons. Can we give them a better IRR?them a better IRR?

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

MIRR = 16.5%

10.0 80.060.0

0 1 2 310%

66.0 12.1

158.1

MIRR for Project L (k = 10%)

-100.010%

10%

TV inflows

-100.0

PV outflows

MIRRL = 16.5%

To find TV with HP 10B, enter in CF’s:

I = 10

NPV = 118.78 = PV of inflows.

Enter PV = -118.78, N = 3, I = 10, Press FV = 158.10 = FV of inflows.

Enter FV = 158.10, PV = -100, N = 3.Press I = 16.50% = MIRR.

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

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.

Project P: NPV and IRR?Project P: NPV and IRR?

5,000 -5,000

0 1 2k = 10%

-800

Enter CFs in CFLO, enter I = 10.

NPV = -386.78

IRR = ERROR. Why?

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%

k

NPV

Logic of Multiple IRRsLogic 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.

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

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.

The EndThe End