IFM12 Ch12 Tool Kit - A 16 17 B C D E F Cash Flows and...

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Fig ure 12-1 Cash Flows and Selected Evaluation Measures for Projects S and L (Millions of Dollars) Panel A: Inputs for Project Cash Flows and Cost of Capital, r INPUTS: r = 10% Initial Cost and Expected Cash Flows Year 0 1 2 3 4 Project S −$10,000 $5,300 $4,300 $1,874 $1,500 Project L −$10,000 $1,900 $2,700 $2,345 $7,800 Panel B: Summary of Selected Evaluation Measures Project S Project L Net present value, NPV $804.38 $1,048.02 Internal rate of return, IRR 14.69% 13.79% Modified IRR, MIRR 12.15% 10.19% Profitability index, PI 1.08 1.10 Payback 2.21 3.39 Discounted payback 3.21 3.80 12-3 Net Present Value (NPV) Fig ure 12-2 Finding the NPV for Projects S and L (Millions of Dollars) INPUTS: r = 10% Initial Cost and Expected Cash Flows Year 0 1 2 3 4 Project S ### $5,300 $4,300 $1,874 $1,500 ### ### ← ← ← ← ← ← ← ← ← ### ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ### ← ← ← ← ← ← ← ← ← ← ← ← ←← ← ← ← ← ← ← ← ←← $804.38 Initial Cost and Expected Cash Flows Year 0 1 2 3 4 Project L ### $1,900 $2,700 $2,345 $7,800 $1,048.02 12-4 Internal Rate of Return (IRR) Fig ure 12-3 Finding the IRR for Projects S and L (Millions of Dollars) INPUTS: Initial Cost and Expected Cash Flows Year 0 1 2 3 4 Project S ### $5,300 $4,300 $1,874 $1,500 ### ### ← ← ← ← ← ← ← ← ← ← ### ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← 867.07 ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← $0.00 IRR = r = 14.69% Value of r that makes NPV = 0. Initial Cost and Expected Cash Flows Year 0 1 2 3 4 Project L ### $1,900 $2,700 $2,345 $7,800 13.79% A Potential Problem with IRR: The Possibility of Multiple IRRs Suppose Project M has the following cash flows: INPUTS: Year 0 1 2 Project M -1.60 10 -10 r NPV 0% -$1.600 5% -$1.146 7% -$0.989 10% -$0.774 13% -$0.582 15% -$0.466 17% -$0.358 20% -$0.211 25% $0.000 = IRR #1 = 25% 30% $0.175 40% $0.441 50% $0.622 60% $0.744 70% $0.822 80% $0.869 90% $0.893 95% $0.898 97% $0.899 98% $0.900 99% $0.900 100% $0.900 101% $0.900 102% $0.900 103% $0.899 102% $0.900 105% $0.899 110% $0.894 120% $0.879 130% $0.857 150% $0.800 160% $0.767 180% $0.696 200% $0.622 250% $0.441 300% $0.275 350% $0.128 400% $0.000 = IRR #2 = 400% 450% -$0.112 500% -$0.211 Fig ure 12-4 Graph for Multiple IRRs: Project M (Millions of Dollars) A Potential Problems When Using the IRR to Evaluate Mutually Exclusive Projects The IRR and NPV can leading to conflicting decisions when choosing among mutually exclusive projects. NPV IRR Project S $804.38 14.69% Project L $1,048.02 13.79% Year 0 1 2 3 4 Project S ### $5,300 $4,300 $1,874 $1,500 Project L # 1,900 2,700 2,345 7,800 $0 $3,400 $1,600 -$471 -$6,300 IRR = Δ 12.274% NPV Profiles for Projects S and L Cost of Capita 0% $2,974.00 $4,745.00 5% 1,800.73 2,701.28 ### 804.38 1,048.02 Crossover = 12.274% 399.91 399.91 ### 145.90 0.00 ### 0.00 -227.16 ### -$789.35 -$1,423.03 Fig ure 12-5 NPV Profiles for Projects S and L (Millions of Dollars) Crossovers are caused by timing differences and size differences as shown below. r = 10% Year Project 0 1 2 NPV IRR Sooner ### $1,020 $120 $26 12.7% Later ### $120 $1,120 $35 12.0% $0 $900 −$1,000 11.1% r = 10% Year Project 0 1 2 NPV IRR Smaller ## $12 $112 $13 18.4% Larg er ### $120 $1,120 $35 12.0% ## −$108 −$1,008 11.3% 12-5 Modified Internal Rate of Return (MIRR) Fig ure 12-6 Finding the MIRR for Projects S and L INPUTS: r = 10% Initial Cost and Expected Cash Flows Year 0 1 2 3 4 Project S −$10,000 $5,300 $4,300 $1,874 $1,500 → → $2,061 → → → → → $5,203 → → → → → → → → → → $7,054 −$10,000 Terminal Value of Positive CF (TV) = $15,819 Calculator: N = 4, PV = −10000, PMT = 0, FV = 15819. Press I/YR to g et: 12.15% 12.15% 12.15% Year 0 1 2 3 4 Project L −$10,000 $1,900 $2,700 $2,345 $7,800 For Project L, using the MIRR function:

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