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Should we build thisplant?

Lecture TwelveCapital Budgeting

The Basics

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What is capital budgeting?

A process for planning and evaluating opportunities (projects/assets) that have an unexpected cash flow or will yield returns (have repercussions) for periods longer than one year

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Steps

1.A: Identify Projects

a. Types b. Categories

i. Environmental i. Independent

ii. New machine ii. Mutually exclusive

iii. Replacement iii. Compliments

1.B: Estimates CFs (inflows & outflows)

a. Normal b. Non-normal

2. Assess riskiness of CFs

a. High b. Average c. Low

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Steps (cont.)

3. Determine k = WACC (adj.).

4. Evaluate Cash Flows or Project

a. Payback d. IRR

b. Discounted Payback e. MIRR

c. NPV

5. Criteria for Accepting/Rejecting Projects

a. Example: accept if NPV > 0 and/or IRR > WACC.

6. Review Process after 1 or More years of Operation

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An Example of Mutually Exclusive Projects

BRIDGE vs. BOAT to get products across a river.

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Normal Cash Flow Project:

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

Nonnormal Cash Flow Project:

Two or more changes of signs.Most common: Cost (negativeCF), then string of positive CFs,then cost to close project.Nuclear power plant, strip mine.

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Inflow (+) or Outflow (-) in Year

0 1 2 3 4 5 N NN

- + + + + + N

- + + + + - NN

- - - + + + N

+ + + - - - N

- + + - + - NN

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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?

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Payback for Project L(Long: Most CFs in out years)

10 8060

0 1 2 3

-100

=

CFt

Cumulative -100 -90 -30 50

PaybackL 2 + 30/80 = 2.375 years

0100

2.4

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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

100

0

1.6

=

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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.

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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.

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NPV

CF

kt

nt

t 0 1

.

NPV: Sum of the PVs of inflows and outflows.

Cost often is CF0 and is negative.

NPVCF

kCF

t

nt

t

001.

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What’s Project L’s NPV?

10 8060

0 1 2 310%

Project L:

-100.00

9.09

49.59

60.1118.79 = NPVL NPVS = $19.98.

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Calculator Solution

Enter in CFLO for L:

-100

10

60

80

10

CF0

CF1

NPV

CF2

CF3

I = 18.78 = NPVL

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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 ofhigher NPV. Adds most value.

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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.

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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.

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t

nt

t

CF

kNPV

0 1.

t

nt

t

CF

IRR

0 10.

NPV: Enter k, solve for NPV.

IRR: Enter NPV = 0, solve for IRR.

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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%.

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40 40 40

0 1 2 3IRR = ?

Find IRR if CFs are constant:

-100

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

3 -100 40 0

9.70%N I/YR PV PMT FV

INPUTS

OUTPUT

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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 CFLO).

...

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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.

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IRR Acceptance Criteria

If IRR > k, accept project.

If IRR < k, reject project.

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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 .

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Construct 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

NPVS

40

29

20

12

5 (4)

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-10

0

10

20

30

40

50

0 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

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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.

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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

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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.

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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 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.

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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.

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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.

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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 outflowsMIRRL = 16.5%

$100 = $158.1

(1+MIRRL)3

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To find TV with 10B, enter in CFLO:

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.

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

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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.

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Pavilion Project: 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?

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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

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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.

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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

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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%

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Accept Project P?

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

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