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DrakeDRAKE UNIVERSITY
Fin 200
NPV IRR and Capital Budgeting
DrakeDrake University
Fin 200Capital Budgeting
Expenditures on projects that have a life greater than one year
Long - Term Plans and lost flexibility
DrakeDrake University
Fin 200Independent Projects
Two projects are considered independent if undertaking one of them does not prevent us from considering the otherThe main question we will ask is whether or not a project is “acceptable.”
DrakeDrake University
Fin 200Mutually Exclusive Projects
Two projects are considered to be mutually exclusive when undertaking one project will preclude the other from being accepted.The criteria that causes this should be something other than cost.Ranking Mutually Exclusive Projects need accept / reject then rank the projects Timing of Cash Flows, Size of competing
investments, Scarce Resources
DrakeDrake University
Fin 200
Project Valuation vs.. Security Valuation
Estimate the future cash flows
Determine the appropriate interest rate
Find the PV of the positive cash flows
Compare the PV to the cost
DrakeDrake University
Fin 200What Cash Flow?
The incremental changes to cash flow that result from the project.
DrakeDrake University
Fin 200Incremental Cash Flow
Cash flow changes that result from a particular projectRelevant Cash Outflows Increase Cash outflow Elimination of cash inflow Investment in Assets
Relevant Cash Inflow Increase in cash inflow Elimination of cash outflow Liquidation of assets
DrakeDrake University
Fin 200
Capital Budgeting Decision Tools
Net Present ValuePayback Period and Discounted PaybackInternal Rate of Return & Modified IRRProfitability Index and Modified Profitability index
DrakeDrake University
Fin 200Net Present Value
The sum of the PV of the positive cash flows minus the PV of negative cash flows and the initial cost
or
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1tt
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CFCost Initial
r)(1
CFNPV
DrakeDrake University
Fin 200NPV Accept or Reject
If the NPV is positive the PV of the benefits is greater than the PV of the cost -- You should accept the project (The value of the firm will increase if the project is accepted)If the NPV is negative, The PV of the benefits is less than the PV of the cost -- You should reject the project (The value of the firm would decrease if the project is accepted)
DrakeDrake University
Fin 200NPV Example
Assume a project cost of capital of 10% Year Cash Flow Present Value
0 -1,000 -1,000.00 1 1,000 909.90 2 -2,000 -1,652.89 3 3,000 2,253.94
NPV = 510.14
DrakeDrake University
Fin 200Calculator
HP 10B -1,000 <CFj>
1,000 <CFj>
-2,000 <CFj>
3,000 <CFj>
10 <I/Y> <NPV>
DrakeDrake University
Fin 200The Required Return
What interest rate should be used to discount the cash flows?
The project cost of capital WHY?
DrakeDrake University
Fin 200NPV
Note, as in the case of our bond and stock valuation models there will be an inverse relationship between the required return and the NPV.A lower Cost of Capital increases the NPV of the project (And the value of the firm)
DrakeDrake University
Fin 200Special Case
What if the project is expected to return cash flows that grow at a constant rate forever and the only outlay is at the beginning of the project?Use the constant growth formula (Stock Valuation)
00 I
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g)(1CFNPV
DrakeDrake University
Fin 200Internal Rate of Return
The IRR is the required return that makes the NPV of a project equal to zero.If IRR is greater than the hurdle rate (the project cost of capital) Accept the projectIF IRR is less than the hurdle rate (the project cost of capital) Reject the project
DrakeDrake University
Fin 200IRR and NPV
IRR and NPV will always provide the same accept / reject decision WHY????IRR is the rate that makes NPV zeroIf: Project cost of capital < IRR accept the project, this also implies a
positive NPV (inverse relationship)
If Project Cost of Capital > IRR reject the project , this also implies a
negative NPV
DrakeDrake University
Fin 200IRR Benefits
IntuitiveMeasure of risk compared to WACC
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Fin 200IRR Problems
Ignores size and amount of wealth created
Ignores project life
It is possible to have multiple IRR’s
DrakeDrake University
Fin 200Multiple IRR’s
Time Cash Flow 0 -100 1 275 IRR = 7.4% and 67.6% 2 -180
Time Cash Flow 0 100 1 -275 IRR = 7.4% and 67.6% 2 180
DrakeDrake University
Fin 200Multiple IRR’s vs. NPV
Time Cash Flow 0 -100 1 275 NPV @ 15% = $3 2 -180
Time Cash Flow 0 100 1 -275 NPV @ 15% = -$3 2 180
DrakeDrake University
Fin 200Multiple IRR’s
An easy check for Multiple IRR’s
Mathematically the largest number of IRR’s that is possible equals the number of sign changes in the cash flow stream
DrakeDrake University
Fin 200Modified IRR
The discount rate that makes the PV of the projects costs equal the PV of the terminal value of the projectTerminal Value = the FV of the positive Cash flows compounded at the cost of capital
DrakeDrake University
Fin 200
Example Cost of Capital = 10%
Time Cash Flow PV FV0 -1000 -10001 500 665.502 400 484.003 -150 -112.694 500 500.00
-1,112.69 1,649.50
1112.69 = 1649.50/(1+MIRR)4 MIRR = 10.34%
DrakeDrake University
Fin 200Payback Period
Intuition: Measures length of time it takes for the firm to payback the original investment.Simple example:
Cost = 100,000 Cash Flow = 20,000 a year
Payback = Cost / Cash Flows = 100,000 / 20,000 = 5 years
DrakeDrake University
Fin 200Payback Period
Most problems do not work out even….
You need to look at the cumulative cash flow and compare to the initial cost.
DrakeDrake University
Fin 200Calculating Payback Period
Calculate the cumulative cash flow (total cash flow received)
Calculate the Remaining Cost (Total Cost - Cumulative Cash Flow) Repeat 1 and 2 until remaining cost is less
than zero In last positive year divide remaining cash
flow by yearly cash flow in next year Calculate total payback
DrakeDrake University
Fin 200
Example: Initial Cost = 100,000
Yearly CumulativeRemaining
YR Cash Flow Cash Flow Cash Flow1 40,000 40,000 60,0002 30,000 70,000 30,0003 25,000 95,000 5,000
4 20,000 115,000 -15,000
Payback = 3 + 5,000/20,000 = 3.25
DrakeDrake University
Fin 200Payback Period: Benefits
Easy to Understand and Interpret
Reject / Accept based on a Minimum payback
Provides measure of risk
DrakeDrake University
Fin 200Payback Period Weaknesses
Ignores Time Value of Money
Ignores all cash flows after the payback
DrakeDrake University
Fin 200Discounted Payback Period
Attempts to account for time value of money by evaluating the yearly cash flows in their present value.
DrakeDrake University
Fin 200
Calculating Discounted Payback Period
Calculate the PV of each cash flow Calculate the cumulative present value of the
cash flow s(total cash flow received) Calculate the Remaining Cost
(Total Cost - Cumulative PV Cash Flow) Repeat 1 and 2 until remaining cost is less than
zero In last positive year divide remaining cash flow
by yearly cash flow in next year Calculate total payback
DrakeDrake University
Fin 200Initial Cost=100,000 r = 10%
Yearly PV Cumul Remaining
YR CF CF CF CF1 40,000 36,364 36,364 63,636 2 30,000 24,793 61,157 38,8433 25,000 18,783 79,940 20,060
4 20,000 13,660 93,600 6,4005 15,000 9,314 102,914 -2,914
Payback = 4 + 6400/9314 = 4.687
DrakeDrake University
Fin 200Discounted Payback
Weakness: Still ignores cash flows after paybackStrengths: Accounts for time value of money, easy to understand and calculate, risk measureAccept / Reject -- Set Minimum payback and compare
DrakeDrake University
Fin 200Profitability Index
Measures the value created per dollar invested
00
1t
t
I
NPV1
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CF
PI
n
t
DrakeDrake University
Fin 200PI
If the PI is greater than 1 accept the project (NPV is positive)If the PI is less than 1 reject the project (NPV is negative)If PI = 1.45 it would imply that the project will produce $1.45 for each $1 invested.
DrakeDrake University
Fin 200Modified PI
The basic PI does not account for the possible future costs, modified PI attempts to do this:
sCommitment Future0 PVI
NPV1PI
DrakeDrake University
Fin 200Modified PI
Same Accept Reject decision as regular PI
DrakeDrake University
Fin 200Mutually Exclusive
NPV provides the best ranking when comparing between mutually exclusive investments, The rest can produce inconsistent rankings
DrakeDrake University
Fin 200Example
Project Initial Cost YR1 CF YR2 CF A 1,000,000 1,000,000 0 B 1,200,000 1,119,000 312,000 C 900,000 195,000 970,000 D 1,100,000 980,000 345,000
Compare the different methods for both 7%and 12% (in Class)
DrakeDrake University
Fin 200Comparison of results
NPV PIDiscounted
Paback Pay IRR
A (65,420.56) 0.9346 1.0000 0.0000B 122,307.28 1.1023 1.5512 1.2468 0.1604C 129,478.56 1.1439 1.8472 1.7268 0.1521D 117,224.21 1.1066 1.6110 1.3478 0.1610
A (107,142.86) 0.8929 1.0000 0.0000B 51,831.63 1.0433 1.7916 1.2468 0.1604C 47,385.20 1.0527 1.9387 1.7268 0.1521D 50,031.89 1.0455 1.8181 1.3478 0.1610
0.07
0.12
DrakeDrake University
Fin 200IRR vs. NPV revisited
Investment Cost YR 1 IRRA 10,000 12,000 20%B 15,000 17,700 18%
NPV@12% NPV@16% A 714 344.82B 803.50 258.60
NPV@14% 526.31579 for both
DrakeDrake University
Fin 200On the Graph
14%
526.32
18% 20%
2,000
2,700
DrakeDrake University
Fin 200Quick Review
Method Accept RejectPayback Payback < cutoff
Payback>cutoffDisc. Payback Same as PaybackNPV NPV > 0 NPV < 0IRR IRR > WACC IRR < WACCMIRR MIRR >WACC MIRR < WACCPI PI > 1 PI < 1MPI MPI > 1 MPI < 1
DrakeDrake University
Fin 200Summary
Use NPV as the first ruleThe other criteria can provide secondary informationWhich Criteria is most often used by managers?