CapitalBudgeting Payback Net present value (NPV) Internal rate of return (IRR) Profitability index (PI) Modified internal rate of return (MIRR)

CapitalBudgeting

PaybackNet present value (NPV)Internal rate of return (IRR)Profitability index (PI)Modified internal rate of return (

MIRR)

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. Generate ideas.

2. Estimate CFs (inflows & outflows).

3. Assess riskiness of CFs.

4. Determine k = WACC (adj.).

5. Find NPV and/or IRR.

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

An Example of Mutually Exclusive Projects

BRIDGE VS. BOAT TO GET PRODUCTS ACROSS A RIVER.

Normal Project

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

Nonnormal Project

One or more outflows occur after inflows have begun. 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

+ + + - - - NN

- + + - + - NN

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 L(Long: Most CFs in out years)

10 8060

0 1 2 3

-100CFt

Cumul -100 -90 -30 50

PaybackL = 2 + 30/80 = 2.375 years.

0

2.4

CFt

Cumul -100 -30 20 40

PaybackS = 1 + 30/50 = 1.6 years.

70 2050

0 1 2 3

Project S (Short: CFs come quickly)

-100

0

1.6

Payback is a type of breakeven analysis.

Ignores the TVM. Ignores CFs occurring

after the payback period.

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

Easy to calculate and understand.

Weaknesses of Payback

Strengths of Payback

= 2 + 41.32/60.11 = 2.7 years.

-41.32

60.11

10 8060

0 1 2 3

CFt

Cumul -100 -90.91 18.79

Disc.payback

Discounted Payback: Uses discountedrather than raw CFs. Apply to Project L.

PVCFt -100

-100

10%

9.09 49.59

Recover invest. + cap. costs in 2.7 years.

2.7

Sum of the PVs of inflows and outflows.

Net Present Value (NPV)

If one expenditure at t = 0, then

NPV =

n

t=0

CFt

(1 + k)t

NPV = - CF0.n

t=1

CFt

(1 + k)t

What is Project L’s NPV?

10 8060

0 1 2 310%

Project L:

-100.00

9.09

49.58

60.11

18.78 = NPVL

NPVS = $19.98.

= 18.78 = NPVL.

Calculator Solution

Enter in CFLO for L:

-100

10

60

80

10

CF0

CF1

NPV

CF2

CF3

I

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.

Rationale for the NPV MethodRationale for the NPV Method

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

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

L .If S & L are independent, accept bot

h; NPV > 0.

Note that NPVs change as cost of capital changes.

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 forcesPV inflows = cost. This is the sameas forcing NPV = 0.

t

nt

t

CF

IRR

0 10.

NPV: Enter k, solve for NPV.

IRR: Enter NPV = 0, solve for IRR.

t

nt

tCF

kNPV

ๅ

0 1.

What is Project L’s IRR?What is 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%.

Rationale for the IRR MethodRationale 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.

If IRR > k, accept project.

If IRR < k, reject project.

IRR Acceptance CriteriaIRR Acceptance Criteria

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

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

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

Note that IRR is independent of the cost of capital, but project acceptability depends on k.

PI = . PV of inflows PV of outflows

Define Profitability Index (PI)Define Profitability Index (PI)

Calculate each project’s PI.Calculate each project’s PI.

Project L:

$9.09 + $49.59 + $60.11$100

Project S:

$63.64 + $41.32 + $15.03$100

PIL = = 1.19.

PIS = = 1.20.

If PI > 1, accept.If PI < 1, reject.

The higher the PI, the better the project.

For mutually exclusive projects, take the one with the highest PI. Therefore, accept L and S if independent; only accept S if mutually exclusive.

PI Acceptance CriteriaPI Acceptance Criteria

Yes, modified IRR (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 forces cash inflows to be reinvested at WACC.

Managers prefer IRR to NPV. Can we givManagers prefer IRR to NPV. Can we give them a better IRR?e them a better IRR?

$158.1(1+MIRRL)3

10.0 80.060.0

0 1 2 310%

66.0

12.1

158.1

MIRR for Project L (k = 10%):

-100.0

10%

10%

TV inflows-100.0

PV outflows

MIRR = 16.5%

MIRRL = 16.5%

$100 =

MIRR correctly assumes reinvestment at opportunity cost = k.

MIRR also avoids problems with nonnormal projects.

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

Why use MIRR rather than IRR?Why use MIRR rather than IRR?

When there are nonnormal CFs, 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.