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CapitalBudgeting Payback Net present value (NPV) Internal rate of return (IRR) Profitability index (PI) Modified internal rate of return (MIRR)

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**What Is capital budgeting?**

Analysis of potential additions to fixed assets. Long-term decisions; involve large expenditures. Very important to firm’s future.

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Steps 1. Generate ideas. 2. Estimate CFs (inflows & outflows). 3. Assess riskiness of CFs. 4. Determine k = WACC (adj.). 5. Find NPV and/or IRR. 6. Accept if NPV > 0 and/or IRR > WACC.

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**An Example of Mutually Exclusive Projects**

BRIDGE VS. BOAT TO GET PRODUCTS ACROSS A RIVER.

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Normal Project Cost (negative CF) followed by a series of positive cash inflows. Nonnormal Project One or more outflows occur after inflows have begun. Most common: Cost (negative CF), then string of positive CFs, then cost to close project. Nuclear power plant, strip mine.

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**Inflow (+) or Outflow (-) in Year**

1 2 3 4 5 N NN - + + + + + N - + + + + - NN - - - + + + N + + + - - - NN - + + - + - NN

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**What is the payback period?**

The number of years required to recover a project’s cost, or how long does it take to get our money back?

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**Payback for Project L (Long: Most CFs in out years)**

1 2 2.4 3 CFt -100 10 60 80 Cumul -100 -90 -30 50 PaybackL = /80 = years.

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**Project S (Short: CFs come quickly)**

1 1.6 2 3 CFt -100 70 50 20 Cumul -100 -30 20 40 PaybackS = /50 = 1.6 years. Payback is a type of breakeven analysis.

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Strengths of Payback Provides an indication of a project’s risk and liquidity. Easy to calculate and understand. Weaknesses of Payback Ignores the TVM. Ignores CFs occurring after the payback period.

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**Discounted Payback: Uses discounted **

rather than raw CFs. Apply to Project L. 2.7 1 2 3 10% CFt -100 10 60 80 PVCFt -100 9.09 49.59 60.11 Cumul -100 -90.91 -41.32 18.79 Disc. payback = /60.11 = 2.7 years. Recover invest. + cap. costs in 2.7 years.

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**Net Present Value (NPV)**

Sum of the PVs of inflows and outflows. n t=0 CFt (1 + k)t NPV = If one expenditure at t = 0, then n t=1 CFt (1 + k)t NPV = CF0.

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**What is Project L’s NPV? Project L: 18.78 = NPVL NPVS = $19.98. 1 2 3**

1 2 3 10% 9.09 49.58 60.11 18.78 = NPVL NPVS = $19.98. 10 60 80

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**Calculator Solution Enter in CFLO for L: = 18.78 = NPVL. -100 10 60 80**

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**Rationale for the NPV Method**

NPV = PV inflows - Cost = Net gain in wealth. Accept project if NPV > 0. Choose between mutually exclusive projects on basis of higher NPV. Adds most value.

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**Using NPV method, which project(s) should be accepted?**

If Projects S and L are mutually exclusive, accept S because NPVS > NPVL . If S & L are independent, accept both; NPV > 0. Note that NPVs change as cost of capital changes.

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**Internal Rate of Return (IRR)**

1 2 3 CF0 CF1 CF2 CF3 Cost Inflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0.

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**( ) NPV: Enter k, solve for NPV. CF k NPV ๅ + 1 .**

= ๅ + 1 . IRR: Enter NPV = 0, solve for IRR.

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**Enter CFs in CFLO, then press IRR:**

What is Project L’s IRR? 1 2 3 IRR = ? 10 60 80 PV1 PV2 PV3 Enter CFs in CFLO, then press IRR: 0 = NPV IRRL = 18.13%. IRRS = 23.56%.

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**Rationale for the IRR Method**

If IRR > WACC, then the project’s rate of return is greater than its cost--some return is left over to boost stockholders’ returns. Example: WACC = 10%, IRR = 15%. Profitable.

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**IRR Acceptance Criteria**

If IRR > k, accept project. If IRR < k, reject project.

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**Using IRR method, which project(s) should be accepted?**

If S and L are independent, accept both. IRRs > k = 10%. If S and L are mutually exclusive, accept S because IRRS > IRRL . Note that IRR is independent of the cost of capital, but project acceptability depends on k.

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**Define Profitability Index (PI)**

PV of inflows PV of outflows PI =

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**Calculate each project’s PI.**

Project L: $ $ $60.11 $100 PIL = = 1.19. Project S: $ $ $15.03 $100 PIS = = 1.20.

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**PI Acceptance Criteria**

If PI > 1, accept. If PI < 1, reject. The higher the PI, the better the project. For mutually exclusive projects, take the one with the highest PI. Therefore, accept L and S if independent; only accept S if mutually exclusive.

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**Managers prefer IRR to NPV. Can we give them a better IRR?**

Yes, modified IRR (MIRR) is the discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC. Thus, MIRR forces cash inflows to be reinvested at WACC.

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**MIRR for Project L (k = 10%):**

1 2 3 10% 10.0 60.0 80.0 -100.0 10% 66.0 12.1 10% MIRR = 16.5% 158.1 -100.0 $158.1 (1+MIRRL)3 $100 = TV inflows PV outflows MIRRL = 16.5%

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**Why use MIRR rather than IRR?**

MIRR correctly assumes reinvestment at opportunity cost = k. MIRR also avoids problems with nonnormal projects. Managers like rate of return comparisons, and MIRR is better for this than IRR.

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**When there are nonnormal CFs, use MIRR:**

1 2 -800,000 5,000,000 -5,000,000 PV 10% = -4,932, TV 10% = 5,500, MIRR = 5.6%

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Accept Project P? NO. Reject because MIRR = 5.6% < k = 10%. Also, if MIRR < k, NPV will be negative: NPV = -$386,777.

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