120000 Depreciation expense 50000 Increase in net income 70000 On initial

120000 depreciation expense 50000 increase in net

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120,000 Depreciation expense 50,000 Increase in net income $ 70,000 On initial investment 14% On average investment: Average investment $ 250,000 Book rate of return 28% (3) NPV: Present value of net cash inflows $ 678,000 Initial investment (500,000) Net present value (NPV) = $ 178,000 (4) PV Payback period: Present value payback period in years 6.12 or 6 years and 2 months
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(5) IRR Present Net 12% Value Cumulative Cash Discount of Net Cash Year Inflow Factor Cash Inflow Flow 0 $ (500,000) $ (500,000) $ (500,000) 1 120,000 0.893 107,160 (392,840) 2 120,000 0.797 95,640 (297,200) 3 120,000 0.712 85,440 (211,760) 4 120,000 0.636 76,320 (135,440) 5 120,000 0.567 68,040 (67,400) 6 120,000 0.507 60,840 (6,560) 7 120,000 0.452 54,240 47,680 8 120,000 9 120,000 10 120,000 Present Value of net cash inflows: At 20% $ 503,040 At 25% 428,520 Difference in present value with 5% difference in discount rate $ 74,520 Estimated Internal rate of return (IRR), based on interpolation = 20.20% Formula or,IRR = 20.18% =IRR(D57:D67,0.1) (6) MIRR = modified internal rate of return; using the built-in formula in Excel, we have: Net Cash Year Inflow 0 $ (500,000)### 1 $ 120,000 - 2 $ 120,000 - 3 $ 120,000 - 4 $ 120,000 - 5 $ 120,000 - 6 $ 120,000 - 7 $ 120,000 - 8 $ 120,000 ## 9 $ 120,000 ## 10 $ 120,000 ## Formula MIRR = 15.46% =MIRR(E82:E92,I16,I16)
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Problem 12-48: Basic Capital-Budgeting Techniques; Uneven Net Cash Inflows with Taxes and MACRS; Spreadsheet Application Background Pre-tax Pre-tax Net Cash Net Cash Year Flow Year Flow 1 $ 50,000 6 $ 300,000 2 80,000 7 270,000 3 120,000 8 240,000 4 200,000 9 120,000 5 240,000 10 40,000 Purchase price of machine $ 500,000 Expected useful life in years 10 Percentage used to evaluate capital investments 12% Combined tax rate 30% Required Solution Savings or Net Net Cumulative 1) Net (Expense) After-tax After-tax Net After-tax Cash Depreciation Taxable on Income Income Cash Cash Year Inflow Expense Income Tax (Loss) Flow Flow 0 (500,000) (500,000) ($500,000) 1 50,000 (50,000) - - - 50,000 ($450,000) 2 80,000 (50,000) 30,000 (9,000) 21,000 71,000 ($379,000) 3 120,000 (50,000) 70,000 (21,000) 49,000 99,000 ($280,000) 4 200,000 (50,000) 150,000 (45,000) 105,000 155,000 ($125,000) 5 240,000 (50,000) 190,000 (57,000) 133,000 183,000 $58,000 6 300,000 (50,000) 250,000 (75,000) 175,000 225,000 7 270,000 (50,000) 220,000 (66,000) 154,000 204,000 8 240,000 (50,000) 190,000 (57,000) 133,000 183,000 9 120,000 (50,000) 70,000 (21,000) 49,000 99,000 10 40,000 (50,000) (10,000) 3,000 (7,000) 43,000 Totals (500,000) 1,160,000 (348,000) 812,000 Payback period in years 4.68 2)Book (accounting) rate of return: Average net income of the investment period $ 81,200 Book rate of return on intitial investment 16.24% Book rate of return on average investment 32.48%
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3)Net present value (NPV): Present Cumulative Net After-tax 12% Value PV of Net Cash Discount of Net After-tax After-tax Year Inflow Factor Cash Inflow Cash Flows 0 ($500,000) 1.000 $ (500,000) $ (500,000) 1 $ 50,000 0.893 44,650 $ (455,350) 2 71,000 0.797 56,587 $ (398,763) 3 99,000 0.712 70,488 $ (328,275) 4 155,000 0.636 98,580 $ (229,695) 5 183,000 0.567 103,761 $ (125,934) 6 225,000 0.507 114,075 $ (11,859) 7 204,000 0.452 92,208 $ 80,349 8 183,000 0.404 73,932 9 99,000 0.361 35,739 10 43,000 0.322 13,846 Total $ 703,866 NPV = $ 203,866 or, using the built-in function, NPV = $ 203,781 (difference is due to rounding) 4)Present value payback period:as indicated in the above schedule, the present value payback period is “6-plus” years; this is the time it takes for the PV of future cash inflows to equal the initial investment outlay of $500,000. 5)Internal rate of return (IRR): Present Present Net After-tax 18% Value 20% Value Cash Discount of Net Discount of Net Year Inflow Factor Cash Inflow Factor Cash Inflow 1 $ 50,000 0.847 $ 42,350 0.833 $ 41,650 2 71,000 0.718 50,978 0.694 $ 49,274 3 99,000 0.609 60,291 0.579 $ 57,321 4 155,000 0.516 79,980 0.482 $ 74,710 5 183,000 0.437 79,971 0.402 $ 73,566 6 225,000 0.370 83,250 0.335 $ 75,375 7 204,000 0.314 64,056 0.279 $ 56,916 8 183,000 0.266 48,678 0.233 $ 42,639 9 99,000 0.225 22,275 0.194 $ 19,206 10 43,000 0.191 8,213 0.162 $ 6,966 Total $ 540,042 $ 497,623 PV of net cash inflows at 18% $ 540,042 PV of net cash inflows at 20% 497,623 Difference in PV with 2% difference in discount rate $ 42,419 Internal rate of return 19.89% or, IRR = 19.88%
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6) Modified internal rate of return (MIRR) Net After-tax Cash Year Inflow 0 ($500,000) 1 $ 50,000 Formula 2 $ 71,000 Using the built-in function, MIRR = 15.90% =MIRR(E112:E122,M17,M17) 3 $ 99,000 4 $ 155,000 5 $ 183,000 6 $ 225,000 7 $ 204,000 8 $ 183,000 9 $ 99,000 10 $ 43,000
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