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8/10/2019 Capital Budgeting Session
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TopicsOverview and vocabulary Methods
NPVIRR, MIRRProfitability Index
Payback, discounted paybackUnequal livesEconomic life
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What is capital budgeting? Analysis of potential projects.Long-term decisions; involve largeexpenditures.
Very important to firms future.
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Steps in Capital BudgetingEstimate cash flows (inflows &outflows).
Assess risk of cash flows.Determine r = cost of capital forproject.Evaluate cash flows.
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Independent versus Mutually
Exclusive ProjectsProjects are:
independent, if the cash flows of one areunaffected by the acceptance of the other.mutually exclusive, if the cash flows of onecan be adversely impacted by the acceptance
of the other.
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Cash Flows for Franchise L
and Franchise S
10 8060
0 1 2 310%Ls CFs:
-100.00
70 2050
0 1 2 3
10%Ss CFs:
-100.00
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NPV: Sum of the PVs of all
cash flows.
Cost often is CF 0 and is negative.
NPV = n
t = 0
CF t
(1 + r)t
.
NPV = n
t = 1
CF t(1 + r) t
. - CF 0 .
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Whats Franchise Ls NPV?
10 8060
0 1 2 310%Ls CFs:
-100.00
9.09
49.5960.1118.79 = NPV L NPV S = Rs.19.98.
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Rationale for the NPV MethodNPV = PV inflows Cost
This is net gain in wealth, so acceptproject if NPV > 0.
Choose between mutually exclusiveprojects on basis of higher NPV. Addsmost value.
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Using NPV method, which
franchise(s) should be accepted?If Franchise S and L are mutuallyexclusive, accept S because NPV s >NPVL .If S & L are independent, accept both;NPV > 0.
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Internal Rate of Return: IRR0 1 2 3
CF 0 CF 1 CF 2 CF 3Cost Inflows
IRR is the discount rate that forcesPV inflows = cost. This is the sameas forcing NPV = 0.
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NPV: Enter r, solve for NPV.
IRR: Enter NPV = 0, solve for IRR.
= NPV n
t = 0
CF t
(1 + r)t
.
= 0 n
t = 0
CF t(1 + IRR) t
.
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Rationale for the IRR MethodIf IRR > cost of capital, then the projectsrate of return is greater than its cost--
some return is left over to booststockholders returns.
Example:cost of capital = 10%, IRR = 15%.So this project adds extra return toshareholders.
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Decisions on Projects S and L
per IRRIf S and L are independent, acceptboth: IRR S > r and IRR L > r.
If S and L are mutually exclusive,accept S because IRR S > IRR L .
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NPV Profile
-10
0
10
20
30
40
50
0 5 10 15 20 23.6
Discount rate r (%)
N P V
( $ )
IRR L = 18.1%
IRR S = 23.6%
Crossover
Point = 8.7%
S
L
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r > IRRand NPV < 0.
Reject.
NPV (Rs.)
r (%)IRR
IRR > rand NPV > 0
Accept.
NPV and IRR: No conflict forindependent projects.
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To Find the Crossover Rate
What is crossover rate?
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Mutually Exclusive Projects
8.7
NPV
%
IRR S
IRR L
L
S
r < 8.7: NPV L> NPV S , IRR S > IRR L CONFLICT
r > 8.7: NPV S > NPV L , IRR S > IRR L NO CONFLICT
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Two Reasons NPV ProfilesCross
Size (scale) differences. Smaller project frees upfunds at t = 0 for investment. The higher the
opportunity cost, the more valuable these funds,so high r favors small projects.Timing differences. Project with faster paybackprovides more CF in early years for reinvestment.If r is high, early CF especially good, NPV S >NPVL.
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Reinvestment Rate Assumptions
NPV assumes reinvest at r (opportunitycost of capital).IRR assumes reinvest at IRR.Reinvest at opportunity cost, r, is morerealistic, so NPV method is best. NPVshould be used to choose betweenmutually exclusive projects.
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Modified Internal Rate ofReturn (MIRR)
MIRR is the discount rate which causesthe PV of a projects terminal value (TV)to equal the PV of costs.TV is found by compounding inflows atcost of capital.Thus, MIRR assumes cash inflows arereinvested at cost of capital.
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10.0 80.060.0
0 1 2 3
10%
66.0
12.1158.1
-100.010%
10%
TV inflows-100.0
PV outflows
MIRR for Franchise L: First,find PV and TV (r = 10%)
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Second, find discount rate thatequates PV and TV
MIRR = 16.5% 158.1
0 1 2 3
-100.0
TV inflowsPV outflows
MIRR L = 16.5%
Rs.100 =
Rs.158.1(1+MIRR L)3
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To find TV with 10B: Step 1,find PV of Inflows
First, enter cash inflows in CFLO register:CF0 = 0, CF 1 = 10, CF 2 = 60, CF 3 = 80
Second, enter I = 10.
Third, find PV of inflows:Press NPV = 118.78
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Step 2, find TV of inflows.
PV = -118.78, N = 3, I = 10, PMT = 0.
FV = 158.10 = FV of inflows.
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Step 3, find PV of outflows.
For this problem, there is only oneoutflow, CF 0 = -100, so the PV of outflows
is -100.For other problems there may be negativecash flows for several years, and you must
find the present value for all negative cashflows.
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Why use MIRR versus IRR?
MIRR correctly assumes reinvestment atopportunity cost = cost of capital. 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 2r = 10%
-800
Enter CFs in CFLO, enter I = 10.NPV = -386.78IRR = ?
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NPV Profile
450
-800
0 400100
IRR 2 = 400%
IRR 1 = 25%
r
NPV
Nonnormal CFs--two signchanges, two IRRs.
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Logic of Multiple IRRs
At very low discount rates, the PV of CF 2 islarge & negative, so NPV < 0.
At very high discount rates, the PV of bothCF1 and CF 2 are low, so CF 0 dominatesand again NPV < 0.
In between, the discount rate hits CF 2 harder than CF 1, so NPV > 0.Result: 2 IRRs.
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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%
When there are nonnormal CFs andmore than one IRR, use MIRR:
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Accept Project P?
NO. Reject because MIRR = 5.6% < r= 10%.
Also, if MIRR < r, NPV will be negative:NPV = -Rs.386,777.
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Profitability Index
The profitability index (PI) is thepresent value of future cash flows
divided by the initial cost.
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Franchise Ls PV of FutureCash Flows
10 8060
0 1 2 310%
Project L:
9.0949.5960.11
118.79
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Franchise Ls ProfitabilityIndex
PI L =PV future CF
Initial Cost
Rs.118.79=
PI L = 1.1879
Rs.100
PI S = 1.1998
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What is the payback period?
The number of years required to recover aprojects cost,
or how long does it take to get thebusinesss money back?
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Payback for Franchise L
10 8060
0 1 2 3
-100
=
CF tCumulative -100 -90 -30 50
Payback L 2 + 30/80 = 2.375 years
0
2.4
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Payback for Franchise S
70 2050
0 1 2 3
-100CF t
Cumulative -100 -30 20 40
Payback S 1 + 30/50 = 1.6 years
0
1.6
=
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10 8060
0 1 2 3
CF t
Cumulative -100 -90.91 -41.32 18.79Discountedpayback 2 + 41.32/60.11 = 2.7 yrs
PVCF t -100
-100
10%
9.09 49.59 60.11
=
Recover invest. + cap. costs in 2.7 yrs.
Discounted Payback: Usesdiscounted rather than raw CFs.
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S and L are mutually exclusiveand will be repeated. r = 10%.
0 1 2 3 4
Project S:(100)
Project L:(100)
60
33.5
60
33.5 33.5 33.5Note: CFs shown in Rs. Thousands
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Equivalent Annual Annuity Approach (EAA)
Convert the PV into a stream of annuitypayments with the same PV.
S: N=2, I/YR=10, PV=-4.132, FV = 0.Solve for PMT = EAA S = Rs.2.38.L: N=4, I/YR=10, PV=-6.190, FV = 0.Solve for PMT = EAA
L = Rs.1.95.
S has higher EAA, so it is a better project.
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Economic Life versus PhysicalLife
Consider another project with a 3-year life.If terminated prior to Year 3, the
machinery will have positive salvage value.Should you always operate for the fullphysical life?
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Economic Life versus PhysicalLife (Continued)
Year CF Salvage Value
0 (Rs.5000) Rs.50001 2,100 3,100
2 2,000 2,0003 1,750 0
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CFs Under Each Alternative(000s)
0 1 2 3
1. No termination (5) 2.1 2 1.75
2. Terminate 2 years (5) 2.1 4
3. Terminate 1 year (5) 5.2
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NPVs under Alternative Lives (Cost ofcapital = 10%)
NPV(3) = -Rs.123.NPV(2) = Rs.215.NPV(1) = -Rs.273.
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Choosing the Optimal CapitalBudget
Finance theory says to accept all positiveNPV projects.Two problems can occur when there is notenough internally generated cash to fundall positive NPV projects:
An increasing marginal cost of capital.Capital rationing
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Increasing Marginal Cost ofCapital
Externally raised capital can have largeflotation costs, which increase the cost ofcapital.Investors often perceive large capitalbudgets as being risky, which drives upthe cost of capital.
(More...)
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If external funds will be raised, then theNPV of all projects should be estimated
using this higher marginal cost ofcapital.
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Capital RationingCapital rationing occurs when a companychooses not to fund all positive NPV
projects.The company typically sets an upper limiton the total amount of capital
expenditures that it will make in theupcoming year.
(More...)
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Reason: Companies want to avoid the directcosts (i.e., flotation costs) and the indirectcosts of issuing new capital.Solution: Increase the cost of capital byenough to reflect all of these costs, and thenaccept all projects that still have a positiveNPV with the higher cost of capital.
(More...)
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Reason: Companies dont have enoughmanagerial, marketing, or engineering staff
to implement all positive NPV projects.
Solution: Use linear programming to
maximize NPV subject to not exceeding theconstraints on staffing.
(More...)
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Reason: Companies believe that the projects managers forecast unreasonably high cash flow
estimates, so companies filter out the worstprojects by limiting the total amount of projectsthat can be accepted.Solution: Implement a post-audit process and tiethe managers compensation to the subsequentperformance of the project.