capital budgeting session

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.

capital budgeting session

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