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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.