drake drake university fin 200 npv irr and capital budgeting

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


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.”


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


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


Fin 200What Cash Flow?

The incremental changes to cash flow that result from the project.


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


Fin 200

Capital Budgeting Decision Tools

Net Present ValuePayback Period and Discounted PaybackInternal Rate of Return & Modified IRRProfitability Index and Modified Profitability index


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

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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)


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


Fin 200Calculator

HP 10B -1,000 <CFj>

1,000 <CFj>

-2,000 <CFj>

3,000 <CFj>

10 <I/Y> <NPV>


Fin 200The Required Return

What interest rate should be used to discount the cash flows?

The project cost of capital WHY?


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)


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)

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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


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


Fin 200IRR Benefits

IntuitiveMeasure of risk compared to WACC


Fin 200IRR Problems

Ignores size and amount of wealth created

Ignores project life

It is possible to have multiple IRR’s


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


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


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


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


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%


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


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.


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


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


Fin 200Payback Period: Benefits

Easy to Understand and Interpret

Reject / Accept based on a Minimum payback

Provides measure of risk


Fin 200Payback Period Weaknesses

Ignores Time Value of Money

Ignores all cash flows after the payback


Fin 200Discounted Payback Period

Attempts to account for time value of money by evaluating the yearly cash flows in their present value.


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


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


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


Fin 200Profitability Index

Measures the value created per dollar invested

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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.


Fin 200Modified PI

The basic PI does not account for the possible future costs, modified PI attempts to do this:

sCommitment Future0 PVI

NPV1PI


Fin 200Modified PI

Same Accept Reject decision as regular PI


Fin 200Mutually Exclusive

NPV provides the best ranking when comparing between mutually exclusive investments, The rest can produce inconsistent rankings


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)


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


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


Fin 200On the Graph

14%

526.32

18% 20%

2,000

2,700


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


Fin 200Summary

Use NPV as the first ruleThe other criteria can provide secondary informationWhich Criteria is most often used by managers?

drake drake university fin 200 npv irr and capital budgeting

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