4 An Example of Mutually Exclusive Projects BRIDGE VS. BOAT TO GETPRODUCTS ACROSS A RIVER.
5 Normal ProjectCost (negative CF) followed by a series of positive cash inflows.Nonnormal ProjectOne 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.
6 Inflow (+) or Outflow (-) in Year 12345NNN-+++++N-++++-NN---+++N+++---NN-++-+-NN
7 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?
8 Payback for Project L (Long: Most CFs in out years) 122.43CFt-100106080Cumul-100-90-3050PaybackL = /80 = years.
9 Project S (Short: CFs come quickly) 11.623CFt-100705020Cumul-100-302040PaybackS = /50 = 1.6 years.Payback is a type of breakeven analysis.
10 Strengths of PaybackProvides an indication of a project’s risk and liquidity.Easy to calculate and understand.Weaknesses of PaybackIgnores the TVM.Ignores CFs occurringafter the payback period.
11 Discounted Payback: Uses discounted rather than raw CFs. Apply to Project L.2.712310%CFt-100106080PVCFt-1009.0949.5960.11Cumul-100-90.91-41.3218.79Disc.payback= /60.11 = 2.7 years.Recover invest. + cap. costs in 2.7 years.
12 Net Present Value (NPV) Sum of the PVs of inflows and outflows.nt=0CFt(1 + k)tNPV = If one expenditure at t = 0, thennt=1CFt(1 + k)tNPV = CF0.
14 Calculator Solution Enter in CFLO for L: = 18.78 = NPVL. -100 10 60 80
15 Rationale for the NPV Method NPV = PV inflows - Cost= Net gain in wealth.Accept project if NPV > 0.Choose between mutuallyexclusive projects on basis ofhigher NPV. Adds most value.
16 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.
17 Internal Rate of Return (IRR) 123CF0CF1CF2CF3CostInflowsIRR is the discount rate that forcesPV inflows = cost. This is the sameas forcing NPV = 0.
18 ( ) NPV: Enter k, solve for NPV. CF k NPV ๅ + 1 . =ๅ+1.IRR: Enter NPV = 0, solve for IRR.
19 Enter CFs in CFLO, then press IRR: What is Project L’s IRR?123IRR = ?106080PV1PV2PV3Enter CFs in CFLO, then press IRR:0 = NPVIRRL = 18.13%.IRRS = 23.56%.
20 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.
22 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.
23 Define Profitability Index (PI) PV of inflowsPV of outflowsPI =
25 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.
26 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.
27 MIRR for Project L (k = 10%): 12310%10.060.080.0-100.010%66.012.110%MIRR = 16.5%158.1-100.0$158.1(1+MIRRL)3$100 =TV inflowsPV outflowsMIRRL = 16.5%
28 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.
29 When there are nonnormal CFs, use MIRR: 12-800,0005,000,000-5,000,000PV 10% = -4,932,TV 10% = 5,500,MIRR = 5.6%
30 Accept Project P?NO. Reject becauseMIRR = 5.6% < k = 10%.Also, if MIRR < k, NPV will be negative: NPV = -$386,777.