# 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: