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CHAPTER 7 Discounted Cash Flow Techniques 7-1 McGraw-Hill/Irwin Copyright © 2007 The McGraw-Hill Companies, Inc. All rights reserved. TABLE 7-1 Cash Flows for Container-Loading Pier ($ millions) Year 0 1 2 3 4 5 6 7 8 9 10 Cash flow ($40) 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 17 7-2 FIGURE 7-1 Cash Flow Diagram for Container-Loading Pier 7.5 17 1 40 7-3 2 3 4 5 6 7 8 9 10 Calculator Conventions PMT FV … 0 PV 7-4 1 2 3 4 … n Using a Calculator to Find the Present Value of a $2 million, 4-year Annuity, Discounted at 15% Input: Output: 7-5 4 15 ? n i PV -5.71 2 PMT -FV $5,710,000 Today is Equivalent to $2 million a Year for 4 Years When the Interest Rate is 15 % BeginningEnd-of of-Period Interest at -Period Year Principal 15% Principal 1 $5,710,000 $856,500 $6,566,500 2 4,566,500 684,975 5,251,475 3 3,251,475 487,721 3,739,196 4 1,739,196 260,879 2,000,075 Withdrawal $2,000,000 2,000,000 2,000,000 2,000,000 Note: The $75 remaining in the account after the last withdrawal is due to round-off error in the present value tables. 7-6 TABLE 7-2 NPV of Container Pier at Different Discount Rates Discount Rate NPV ($ millions) 10% 12% $9.75 5.44 IRR = 15% 18% 7-7 -4.48 FIGURE 7-2 NPV of Container Pier at Different Discount Rates NPV ($ millions) 50 40 30 20 IRR 10 0 -10 -20 0 4 8 12 16 Discount rate (%) 7-8 20 24 TABLE 7-3 Calculating Container Pier’s Estimated NPV, IRR, and BCR with a Computer Spreadsheet A B C D E F G H 1 ESTIMATED ANNUAL CASH FLOWS ($ millions) 2 Year 0 1 2 3 4 5 6 3 Cash flow ($40) 7.5 7.5 7.5 7.5 7.5 7.5 4 5 Discount rate: 10% 6 Equation 7 Net present value (NPV): =NPV(C5,C3:L3) + B3 8 Benefit Cost Ratio (BCR): =NPV(C5,C3:L3)/-B3 9 Internal Rate of Return (IRR): =IRR(B3:L3,0.12) 7-9 I 7 7.5 J 8 7.5 Answer $9.75 1.24 15% K 9 7.5 L 10 17 TABLE 7-4 Division Financial Analysis of New Line of Cellular Telephones ($ millions) Plant & equipment Increased working caital Preliminary engineering Excess capacity Total Investment Total salvage value Sales Cost of sales Gross profit Interest expense Allocated expenses Selling & administrative expenses Total operating expenses 7-10 1 0 Year $ $ 2 3 $ 15 $ 15 157 $ 68 89 120 52 68 (30) (14) (2) 0 (46) $ 60 $ 26 34 82 $ 35 47 5 0 10 14 4 0 13 17 140 $ 60 80 4 0 22 26 5 4 3 0 25 28 3 0 19 22 TABLE 7-4 (Continued) Operating income Depreciation 20 3 29 3 54 3 61 3 46 3 Income before tax Tax at 40 percent Income after tax $ 17 7 10 $ 26 11 16 $ 51 20 30 $ 58 23 35 $ 43 17 26 (46) $ 10 $ 16 $ 30 $ 35 $ 41 Free cash flow $ Net present value @ 15% Benefit cost ratio $ Internal rate of return Totals may not add due to rounding. 7-11 35 1.76 37% The Two-Step Treatment of Depreciation when Calculating Aftertax Cash Flow (ATCF) Operating income 7-12 $20 Less Depreciation Profit before tax 3 17 Less Tax at 40% Income aftertax 7 10 Plus Depreciation Aftertax cash flow 3 $13 Calculating the Investment in Working Capital Year New phone sales Working capital @ 20% of sales 0 1 2 3 4 5 $0 $60 $82 $140 $157 $120 0 12 16 28 1 24 0 12 4 12 3 -7 Change in working capital Recovery of working capital Total working capital investment 7-13 24 $0 $(12) $(4) $(12) $(3) $31 TABLE 7-5 Revised Financial Analysis of New Line of Cellular Telephones ($ millions) Year Assumptions Increased working capital Preliminary engineering Excess capacity Interest expense Allocated expenses Plant & equipment Increased working capital Preliminary engineering Excess capacity Total costs Total salvage value Sales Cost of sales Gross profit 7-14 0 1 2 3 4 5 20 percent of sales, full recovery at end of year 5 Already spent, sunk cost $20 million cost of new capacity year 2, $2 million annual depreciation Subsumed in discount rate Variable allocated costs equal to 14% of sales $ $ (30) 0 0 (12) (30) $ $ (12) $ 60 $ 26 34 (4) (20) (24) $ 82 $ 35 47 (12) 15 31 (3) 14 (12) $ 140 $ 60 80 (3) $ 60 157 $ 68 89 120 52 68 TABLE 7-5 (Continued) Year 0 1 2 3 4 5 Interest expense Allocated expenses Selling & administrative expenses Total operating expenses 0 8 10 18 0 11 13 25 0 20 22 42 0 22 25 47 0 17 19 36 Operating income Depreciation 16 3 22 3 38 5 42 5 32 5 Income before tax Tax at 40 percent Income after tax Add back depreciation 13 5 8 $ 3 19 8 11 $ 3 33 13 20 $ 5 37 15 22 $ 5 27 11 16 5 $ 11 $ 14 $ 25 $ 27 $ 21 (30) $ (1) $ (10) $ 13 $ 24 $ 82 $ After tax cash flow Free cash flow $ Net present value @ 15% $ Benefit cost ratio 1.76 Internal rate of return 30% Totals may not add due to rounding. 7-15 25 FIGURE 7A-1 Cash Flow Diagrams for Alternative Service Station Designs $100,000 1 2 3 4 5 6 7 $522,000 Inexpensive option 7-16 8 9 10 FIGURE 7A-1 (Continued) $195,000 1 2 3 4 5 6 $1.1 million Expensive option 7-17 7 8 9 10 TABLE 7A-1 Figures of Merit for Service Station Designs Inexpensive option Expensive option 7-18 NPV at 10% BCR at 10% IRR $92,500 1.18 14% 98,200 1.09 12 TABLE 7A-2 Four Independent Investment Opportunities under Capital Rationing (Capital budget =$200,000) Investment A 7-19 Initial Cost NPV at BCR at 12% 12% $200,000 $10,000 IRR 1.05 14.4% B 120,000 8,000 1.07 15.1 C 50,000 6,000 1.12 17.6 D 80,000 6,000 1.08 15.5 FIGURE 7A-2 Capital Budgeting Decision Tree Use NPV, IRR, or BCR Rank by NPV Mutually exclusive Rank by NPV over common investment horizon No fractional projects Accept bundle of investments with highest NPV Accept bundle of investments with highest NPV over common horizon Accept bundle of investments with highest NPV Rank by BCR 7-20