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NPV IRR and Capital Budgeting

NPV IRR and Capital Budgeting. Capital Budgeting. Expenditures on projects that have a life greater than one year Long - Term Plans and lost flexibility. Independent Projects. Two projects are considered independent if undertaking one of them does not prevent us from considering the other

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NPV IRR and Capital Budgeting

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  1. NPV IRR and Capital Budgeting

  2. Capital Budgeting • Expenditures on projects that have a life greater than one year • Long - Term Plans and lost flexibility

  3. Independent Projects • Two projects are considered independent if undertaking one of them does not prevent us from considering the other • The main question we will ask is whether or not a project is “acceptable.”

  4. Mutually 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

  5. 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

  6. What Cash Flow? • The incremental changes to cash flow that result from the project.

  7. Incremental Cash Flow • Cash flow changes that result from a particular project • Relevant 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

  8. Capital Budgeting Decision Tools • Net Present Value • Payback Period and Discounted Payback • Internal Rate of Return & Modified IRR • Profitability Index and Modified Profitability index

  9. Net Present Value • The sum of the PV of the positive cash flows minus the PV of negative cash flows and the initial cost or

  10. NPV 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)

  11. NPV 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

  12. Calculator • HP 10B • -1,000 <CFj> • 1,000 <CFj> • -2,000 <CFj> • 3,000 <CFj> • 10 <I/Y> • <NPV>

  13. The Required Return • What interest rate should be used to discount the cash flows? • The project cost of capital WHY?

  14. NPV • 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)

  15. Special 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)

  16. Internal 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 project • IF IRR is less than the hurdle rate (the project cost of capital) Reject the project

  17. IRR and NPV • IRR and NPV will always provide the same accept / reject decision WHY???? • IRR is the rate that makes NPV zero • If: 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

  18. IRR Benefits • Intuitive • Measure of risk compared to WACC

  19. IRR Problems • Ignores size and amount of wealth created • Ignores project life • It is possible to have multiple IRR’s

  20. Multiple 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

  21. Multiple 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

  22. Multiple 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

  23. Modified IRR • The discount rate that makes the PV of the projects costs equal the PV of the terminal value of the project • Terminal Value = the FV of the positive Cash flows compounded at the cost of capital

  24. Example Cost of Capital = 10% Time Cash Flow PV FV 0 -1000 -1000 1 500 665.50 2 400 484.00 3 -150 -112.69 4 500 500.00 -1,112.691,649.50 1112.69 = 1649.50/(1+MIRR)4 MIRR = 10.34%

  25. Payback 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

  26. Payback Period • Most problems do not work out even…. • You need to look at the cumulative cash flow and compare to the initial cost.

  27. Calculating 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

  28. Example: Initial Cost = 100,000 Yearly Cumulative Remaining YR Cash Flow Cash Flow Cash Flow 1 40,000 40,000 60,000 2 30,000 70,000 30,000 3 25,000 95,000 5,000 4 20,000 115,000 -15,000 Payback = 3 + 5,000/20,000 = 3.25

  29. Payback Period: Benefits • Easy to Understand and Interpret • Reject / Accept based on a Minimum payback • Provides measure of risk

  30. Payback Period Weaknesses • Ignores Time Value of Money • Ignores all cash flows after the payback

  31. Discounted Payback Period • Attempts to account for time value of money by evaluating the yearly cash flows in their present value.

  32. 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

  33. Initial Cost=100,000 r = 10% Yearly PV Cumul Remaining YR CF CF CF CF 1 40,000 36,364 36,364 63,636 2 30,000 24,793 61,157 38,843 3 25,000 18,783 79,940 20,060 4 20,000 13,660 93,600 6,400 5 15,000 9,314 102,914 -2,914 Payback = 4 + 6400/9314 = 4.687

  34. Discounted Payback • Weakness: Still ignores cash flows after payback • Strengths: Accounts for time value of money, easy to understand and calculate, risk measure • Accept / Reject -- Set Minimum payback and compare

  35. Profitability Index • Measures the value created per dollar invested

  36. PI • 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.

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

  38. Modified PI • Same Accept Reject decision as regular PI

  39. Mutually Exclusive • NPV provides the best ranking when comparing between mutually exclusive investments, The rest can produce inconsistent rankings

  40. Example • ProjectInitial CostYR1 CFYR2 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)

  41. Comparison of results

  42. IRR vs. NPV revisited Investment Cost YR 1 IRR A 10,000 12,000 20% B 15,000 17,700 18% NPV@12% NPV@16% A 714 344.82 B 803.50 258.60 NPV@14% 526.31579 for both

  43. On the Graph 2,700 2,000 526.32 14% 18% 20%

  44. Quick Review Method Accept Reject Payback Payback < cutoff Payback>cutoff Disc. Payback Same as Payback NPV NPV > 0 NPV < 0 IRR IRR > WACC IRR < WACC MIRR MIRR >WACC MIRR < WACC PI PI > 1 PI < 1 MPI MPI > 1 MPI < 1

  45. Summary • Use NPV as the first rule • The other criteria can provide secondary information • Which Criteria is most often used by managers?

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