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## CapitalBudgeting

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**CapitalBudgeting**• Payback • Net present value (NPV) • Internal rate of return (IRR) • Profitability index (PI) • Modified internal rate of return (MIRR)**What Is capital budgeting?**• Analysis of potential additions to fixed assets. • Long-term decisions; involve large expenditures. • Very important to firm’s future.**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.**An Example of Mutually Exclusive Projects**BRIDGE VS. BOAT TO GET PRODUCTS ACROSS A RIVER.**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.**Inflow (+) or Outflow (-) in Year**0 1 2 3 4 5 N NN - + + + + + N - + + + + - NN - - - + + + N + + + - - - NN - + + - + - NN**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?**Payback for Project L(Long: Most CFs in out years)**2.4 0 1 2 3 CFt -100 10 60 80 Cumul -100 -90 -30 0 50 PaybackL = 2 + 30/80 = 2.375 years.**Project S (Short: CFs come quickly)**1.6 0 1 2 3 CFt -100 70 50 20 Cumul -100 -30 0 20 40 PaybackS = 1 + 30/50 = 1.6 years. Payback is a type of breakeven analysis.**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.**Discounted Payback: Uses discounted**rather than raw CFs. Apply to Project L. 2.7 0 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 = 2 + 41.32/60.11 = 2.7 years. Recover invest. + cap. costs in 2.7 years.**Net Present Value (NPV)**Sum of the PVs of inflows and outflows. n t=0 CFt (1 + k)t NPV = ๅ . If one expenditure at t = 0, then n t=1 CFt (1 + k)t NPV = ๅ - CF0.**What is Project L’s NPV?**Project L: 0 1 2 3 10% -100.00 9.09 49.58 60.11 18.78 = NPVL NPVS = $19.98. 10 60 80**Calculator Solution**Enter in CFLO for L: -100 10 60 80 10 CF0 CF1 CF2 CF3 I NPV = 18.78 = NPVL.**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.**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.**Internal Rate of Return (IRR)**0 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.**CF**n t = NPV . ๅ t ( ) 1 + k t = 0 NPV: Enter k, solve for NPV. IRR: Enter NPV = 0, solve for IRR.**What is Project L’s IRR?**0 1 2 3 IRR = ? -100.00 10 60 80 PV1 PV2 PV3 Enter CFs in CFLO, then press IRR: 0 = NPV IRRL = 18.13%. IRRS = 23.56%.**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.**IRR Acceptance Criteria**• If IRR > k, accept project. • If IRR < k, reject project.**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.**Define Profitability Index (PI)**PV of inflows PV of outflows PI = .**Calculate each project’s PI.**Project L: $9.09 + $49.59 + $60.11 $100 PIL = = 1.19. Project S: $63.64 + $41.32 + $15.03 $100 PIS = = 1.20.**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.**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.**MIRR for Project L (k = 10%):**0 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%**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.**When there are nonnormal CFs, use MIRR:**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%**Accept Project P?**NO. Reject because MIRR = 5.6% < k = 10%. Also, if MIRR < k, NPV will be negative: NPV = -$386,777.