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## Should we build this plant?

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**The Basics of**Capital Budgeting Should we build this plant?**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. Estimate CFs (inflows & outflows). 2. Assess riskiness of CFs. 3. Determine k = WACC (adjusted). 4. Find NPV, IRR, MIRR, etc. 5. Accept if NPV > 0, IRR > WACC, etc.**What is the difference between independent and mutually**exclusive projects? Projects are: independent, if the cash flows of one are unaffected by the acceptance of the other. mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.**An Example of Mutually Exclusive Projects**BRIDGE vs. BOAT to get products across a river.**Normal Cash Flow Project:**Cost (negative CF) followed by a series of positive cash inflows. One change of signs. Nonnormal Cash Flow Project: Two or more changes of signs. 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 + + + - - - N - + + - + - 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: Large CFs in later years)**0 1 2 3 CFt -100 10 60 80 -30 Cumulative -100 -90 50 2 + 30/80 = 2.375 years PaybackL =**Project S (Short: CFs come quickly)**0 1 2 3 CFt 70 20 -100 50 Cumulative -100 20 40 -30 1 + 30/50 = 1.6 years PaybackL =**Strengths of Payback:**1. Provides an indication of a project’s risk and liquidity. 2. Easy to calculate and understand. Weaknesses of Payback: • 1. Ignores the TVM. • Ignores CFs occurring after the payback period. • Subjective**Discounted Payback: Uses discounted**rather than raw CFs. 0 1 2 3 10% CFt -100 10 60 80 PVCFt -100 9.09 49.59 60.11 Cumulative -100 -90.91 -41.32 18.79 Discounted payback 2 + 41.32/60.11 = 2.7 years = Recover invest. + cap. costs in 2.7 years.**What’s Project L’s NPV?**Project L: 0 1 2 3 10% -100.00 10 60 80 9.09 49.59 60.11 NPVS = $19.98. 18.79 = NPVL**Calculator Solution**Enter in CFLO for L: -100 10 60 80 10 CF0 CF1 CF2 CF3 I NPV = 18.78 = NPVL**Rationale for the NPV Method**NPV = PV inflows – Cost = Net gain in wealth. Accept project if NPV > 0. Choose between mutually exclusive projects on basis of higher NPV. Adds most value.**Using NPV method, which project(s) should be accepted?**• If Projects S and L are mutually exclusive, accept S because NPVs > NPVL . • If S & L are independent, accept both; NPV > 0.**Internal Rate of Return: IRR**0 1 2 3 CF0 CF1 CF2 CF3 Cost Inflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0.**NPV: Enter k, solve for NPV.**IRR: Enter NPV = 0, solve for IRR.**What’s Project L’s IRR?**0 1 2 3 IRR = ? -100.00 10 60 80 PV1 PV2 PV3 0 = NPV Enter CFs in CFLO, then press IRR: IRRL = 18.13%. IRRS = 23.56%.**Find IRR if CFs are constant:**0 1 2 3 IRR = ? -100 40 40 40 INPUTS 3 -100 40 0 9.70% N I/YR PV PMT FV OUTPUT Or, with CF keys, enter CFs and press IRR = 9.70%.**Q. How is a project’s IRR**related to a bond’s YTM? A. They are the same thing. A bond’s YTM is the IRR if you invest in the bond. 0 1 2 10 IRR = ? ... -1134.2 90 90 1090 IRR = 7.08% (use TVM or CF keys).**Rationale for the IRR Method**If IRR > WACC, then the project’s rate of return is greater than its cost--some return is left over to boost stockholders’ returns. Example: WACC = 10%, IRR = 15%. Profitable.**IRR Acceptance Criteria**• If IRR > k, accept project. • If IRR < k, reject project.**Decisions on Projects S and L per IRR**• If S and L are independent, accept both. IRRs > k = 10%. • If S and L are mutually exclusive?**Construct NPV Profiles**Enter CFs in CFLO and find NPVL and NPVS at different discount rates: NPVL 50 33 19 7 (4 NPVS 40 29 20 12 5 k 0 5 10 15 20 (4)**NPV ($)**k 0 5 10 15 20 NPVL 50 33 19 7 (4) NPVS 40 29 20 12 5 60 . 50 . Crossover Point = 8.7% 40 . . 30 . . S 20 . IRRS = 23.6% . . L 10 . Discount Rate (%) . 0 5 15 20 23.6 10 -10 IRRL = 18.1%**NPV and IRR always lead to the same accept/reject decision**for independent projects: NPV ($) IRR > k and NPV > 0 Accept. k > IRR and NPV < 0. Reject. k (%) IRR**Mutually Exclusive Projects**k < 8.7: NPVL> NPVS , IRRS > IRRL CONFLICT NPV L k > 8.7: NPVS> NPVL , IRRS > IRRL NO CONFLICT IRRS S % k 8.7 k IRRL**To Find the Crossover Rate**1. Find cash flow differences between the projects. See data at beginning of the case. 2. Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68%, rounded to 8.7%. 3. Can subtract S from L or vice versa, but better to have first CF negative. 4. If profiles don’t cross, one project dominates the other.**Two Reasons NPV Profiles Cross**1. Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high k favors small projects. 2. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If k is high, early CF especially good, NPVS > NPVL.**Reinvestment Rate Assumptions**• NPV assumes reinvestment at k (opportunity cost of capital). • IRR assumes reinvest at IRR. • Reinvest at opportunity cost, k, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.**Managers like rates--prefer IRR to NPV comparisons. Can we**give them a better IRR? Yes, MIRR is the discount rate that causes the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at the project’s required rate of return.**MIRR for Project L (k = 10%)**0 1 2 3 10% -100.0 10.0 60.0 80.0 10% 66.0 12.1 10% -100.0 158.1 MIRR = 16.5% PV outflows TV inflows MIRRL = 16.5%**To find TV with HP 10B, enter in CF’s:**CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80 I = 10 NPV = 118.78 = PV of inflows. Enter PV = -118.78, N = 3, I = 10, Press FV = 158.10 = FV of inflows. Enter FV = 158.10, PV = -100, N = 3. Press I = 16.50% = MIRR.**Why use MIRR versus IRR?**MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs. Managers like rate of return comparisons, and MIRR is better for this than IRR.**Project P: NPV and IRR?**0 1 2 k = 10% -800 5,000 -5,000 Enter CFs in CFLO, enter I = 10. NPV = -386.78 IRR = ERROR. Why?**We got IRR = ERROR because there**are 2 IRRs. Nonnormal CFs--two sign changes. Here’s a picture: NPV Profile NPV IRR2 = 400% 450 0 k 100 400 IRR1 = 25% -800**Logic of Multiple IRRs**1. At very low discount rates, the PV of CF2 is large & negative, so NPV < 0. 2. At very high discount rates, the PV of both CF1 and CF2 are low, so CF0 dominates and again NPV < 0. 3. In between, the discount rate hits CF2 harder than CF1, so NPV > 0. 4. Result: 2 IRRs.**Could find IRR with calculator:**1. Enter CFs as before. 2. Enter a “guess” as to IRR by storing the guess. Try 10%: 10 STO IRR = 25% = lower IRR Now guess large IRR, say, 200: 200 STO IRR = 400% = upper IRR**When there are nonnormal CFs and more than one IRR, 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.