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## Chapter 10: The Basics of Capital Budgeting: Evaluating Cash Flows

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**Chapter 10: The Basics of Capital Budgeting: Evaluating**Cash Flows • Overview and “vocabulary” • Methods • Payback, discounted payback • NPV • IRR, MIRR • Profitability Index • Unequal lives • Economic life**What is capital budgeting?**• Analysis of potential projects. • Long-term decisions; involve large expenditures. • Very important to firm’s future.**Steps in Capital Budgeting**• Estimate cash flows (inflows & outflows). • Assess risk of cash flows. • Determine r = WACC for project. • Evaluate cash flows.**Digression:**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 Project**Nonnormal Project**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. n.b. Assumes CF’s occur evenly over the year.**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**Weaknesses of Payback**c(2). 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.**c(3):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 = If one expenditure at t = 0, then n t=1 CFt (1 + k)t NPV = +CF0.**NET PRESENT VALUE**• NPV = CF0 + CF1/(1+k) + CF2/(1+k)2 + ... + CFn/(1+k)n**What is Project L’s NPV?**Project L: (Beware use of comp. fns) 0 1 2 3 10% -100.00 10 60 80**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.**d(2) Rationale for the NPV Method**• If NPV = 0, project breaks even; • recovers cost of investment • investors earn required rate of return (i.e. opportunity cost of capital) • If NPV > 0; • investors get above, plus additional $.**CONSIDER PROJECT L:SUM OF undiscounted CF’s = 150**• Investors get $100 back • Cover their 10% cost of capital; • and have $18.79 left over. • Who does this $18.79 belong to? • Stockholders.**Rationale for the NPV Method**NPV = PV inflows - PV of 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, ? • If S & L are independent, ?**Using NPV method, which project(s) should be accepted?**• If Projects S and L are mutually exclusive,….. • If S & L are independent, accept….. • What happens to the NPV as the cost of capital changes?**e(1) What is the Internal Rate of Return (IRR)**0 1 2 3 CF0 CF1 CF2 CF3 Cost Inflows**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 . 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 0 = NPV**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%.**e(2) How is a project’s IRR related to a bond’s YTM?**0 1 2 10 IRR = ? -1134.2 90 90 1090**How is a project’s IRR related to a bond’s YTM?**They both measure percentage (rate of) return. A bond’s YTM is its IRR. 0 1 2 10 IRR = ? -1134.2 90 90 1090 IRR = 7.08% (use TVM or CFLO).**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, ………. • If S and L are mutually exclusive, accept…………. • What effect does a change in the cost of capital have on the IRR?**Define Profitability Index (PI)**PV of inflows PV of outflows PI = . PI measures a project’s “bang for the buck”.**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 $100 PIS = = 1.20.**PI Acceptance Criteria**• If PI > 1, accept.If PI < 1, reject. • The higher the PI, the better the project. • For mutually exclusive projects, take the one with the highest PI. Therefore, accept L and S if independent; only accept S if mutually exclusive. • Any problems with using PI?**g(1) Construct NPV Profiles**Enter CFs in CFLO and find NPVL and NPVS at different discount rates: NPVL 50 33 19 7 (4) NPVS 40 29 20 12 5 k 0 5 10 15 20**NPV ($)**NPVL 50 33 19 7 (4) NPVS 40 29 20 12 5 k 0 5 10 15 20 50 40 Crossover Point = 8.7% 30 20 S IRRS = 23.6% 10 L 0 Discount Rate (%) 5 10 15 20 23.6 Vertical intercept horizontal intercept crossover point -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**g(2) Mutually Exclusive Projects**NPV k < 8.7: NPVL > NPVS , IRRS > IRRL CONFLICT L k > 8.7: NPVS > NPVL , IRRS > IRRL NO CONFLICT S IRRs % k 8.7 k IRRL**To Find the Crossover Rate**1. Find cash flow differences between the projects. 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.