12-10 Elgin Restaurant Supplies is analyzing the purchase of manufacturing equipment that will cost $20,000. The annual cash inflows for the next three years will be Year Cash flow $10000 9.000 6,500 a. Determine the internal rate of return using interpolation b. With a cost of capital of 12 percent should the machine be purchased? Solution Elgin restaurant Supplies a. Step 1 average the inflows $10000 9.000 6500 $25500÷3=$8,500 Step 2 Divide the inflows by the assumed annuity in Step 1 Investment $20000 2.353 Annuity 8,500 Step 3 Go to Appendix d for the 1 st approximation. The value in Step 2(for n=3)falls between 13% and 14% Step 4 Try a first approximation of discounting back the inflows Because the inflows are biased toward the early years, we will use the higher rate of 14% S-431 CopyrightC2005 by The McGraw-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-431 12-10. Elgin Restaurant Supplies is analyzing the purchase of manufacturing equipment that will cost $20,000. The annual cash inflows for the next three years will be: Year Cash Flow 1 ....................................... $10,000 2 ....................................... 9,000 3 ....................................... 6,500 a. Determine the internal rate of return using interpolation. b. With a cost of capital of 12 percent, should the machine be purchased? Solution: Elgin Restaurant Supplies a. Step 1 Average the inflows. $10,000 9,000 6,500 $25,500 ÷ 3 = $8,500 Step 2 Divide the inflows by the assumed annuity in Step 1. 2.353 8,500 $20,000 Annuity Investment = = Step 3 Go to Appendix D for the 1st approximation. The value in Step 2 (for n = 3) falls between 13% and 14%. Step 4 Try a first approximation of discounting back the inflows. Because the inflows are biased toward the early years, we will use the higher rate of 14%
12-10. Continued Year Cash Flow PVE at 14% Present value $10,000 877 $8.770 9.000 769 6.921 6.500 675 4388 20.079 Step 5 Since the NPv is slightly over $20,000, we need to try a higher rate. We will try 15% Year Cash Flow PVE at 15% Present value $10000 870 $8,700 9.000 756 6804 3 6.500 658 4.277 $19,781 Because the nPv is now below $20000. we know the irr is between 14% and 15%. We will interpolate $20079PV@14%$20,079 PⅤ@14% 19781.PV@15%-20000.Cost $298 $79 14%+($79/$298)(1%)=265 14%+265(1%)=14.265%IRR The irR is 14.265% CopyrightC 2005 by The McGray-Hill Companies, Inc. S-432
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-432 12-10. Continued Year Cash Flow PVIF at 14% Present Value 1 $10,000 .877 $ 8,770 2 9,000 .769 6,921 3 6,500 .675 4,388 $20,079 Step 5 Since the NPV is slightly over $20,000, we need to try a higher rate. We will try 15%. Year Cash Flow PVIF at 15% Present Value 1 $10,000 .870 $ 8,700 2 9,000 .756 6,804 3 6,500 .658 4,277 $19,781 Because the NPV is now below $20,000, we know the IRR is between 14% and 15%. We will interpolate. $20,079...............PV @ 14% –19,781...............PV @ 15% $ 298 $20,079 ...............PV @ 14% –20,000...............Cost $ 79 14% + ($79/$298) (1%) = .265 14% + .265 (1%) = 14.265% IRR The IRR is 14.265%
12-10. Continued If the student skipped from 14% to 16%, the calculations to find the IRR would be as follows Year Cash Flow PVIF at 16% PresentⅤ Value $10000 862 $8620 9.000 743 6.687 6.500 641 4.167 $19,474 $20079……PV@14%$20,079…PV@14% 19474 PV@16%-20000 Cost $605 $79 14%+($79/$605)(2%)=131(2%) 14%+(131)(2%)=14.262% This answer is very close to the previous answer. the difference is due to rounding b. Since the IrR of 14.265%(or 14.262%)is greater than the cost of capital of 12%, the project should be accepted S-433 Copyright C2005 by The McGra-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-433 12-10. Continued If the student skipped from 14% to 16%, the calculations to find the IRR would be as follows: Year Cash Flow PVIF at 16% Present Value 1 $10,000 .862 $ 8,620 2 9,000 .743 6,687 3 6,500 .641 4,167 $19,474 $20,079...............PV @ 14% –19,474...............PV @ 16% $ 605 $20,079 ...............PV @ 14% –20,000...............Cost $ 79 14% + ($79/$605) (2%) = .131 (2%) 14% + (.131) (2%) = 14.262% This answer is very close to the previous answer, the difference is due to rounding. b. Since the IRR of 14.265% (or 14.262%) is greater than the cost of capital of 12%, the project should be accepted
12-11 Aerospace Dynamics will invest $110,000 in a project that will produce the following cash flows. The cost of capital is 11 percent. Should the project be undertaken? (Note that the fourth year's cash flow is negative Year Cash flow 36000 44.000 Solution: Aerospace Dynamics Year Cash FlOw PVIF at 11% Present Value $36,000 901 $32,436 44.000 812 35,728 38.000 731 27,778 (44,000 659 (28,96) 5 81000 593 48033 Present value of inflows $114,979 Present value of outflows 110.000 Net present value $4,979 The net present value is positive and the project should be undertaken CopyrightC 2005 by The McGray-Hill Companies, Inc. S-434
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-434 12-11. Aerospace Dynamics will invest $110,000 in a project that will produce the following cash flows. The cost of capital is 11 percent. Should the project be undertaken? (Note that the fourth year's cash flow is negative.) Year Cash Flow 1 ....................................... $36,000 2 ....................................... 44,000 3 ....................................... 38,000 4 ....................................... (44,000) 5 ....................................... 81,000 Solution: Aerospace Dynamics Year Cash Flow PVIF at 11% Present Value 1 $36,000 .901 $ 32,436 2 44,000 .812 35,728 3 38,000 .731 27,778 4 (44,000) .659 (28,996) 5 81,000 .593 48,033 Present value of inflows $114,979 Present value of outflows 110,000 Net present value $ 4,979 The net present value is positive and the project should be undertaken
12-12 The Horizon Company will invest $60,000 in a temporary project that will generate the following cash inflows for the next three years Year Cash Flow $15 25.000 40.000 The firm will be required to spend $10,000 to close down the project at the end of the three years. If the cost of capital is 10 percent, should the investment be undertaken? Solution Horizon Company Present Value of Inflows Year Cash Flow X PVIe at 10% Present Value $15000 $13.635 25.000 826 20.650 40.000 751 30040 5 Present value of outflows 0$60000 1.000 $60.000 3 10.000 751 7510 67,510 Present Value of inflows $64.325 Present value of outflows 67510 Net present value ($3,185) The net present value is negative and the project should not be undertaken Note, the $10.000 outflow could have been subtracted out of the $40,000 inflow in the third year and the same answer would result S-435 Copyright C2005 by The McGra-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-435 12-12. The Horizon Company will invest $60,000 in a temporary project that will generate the following cash inflows for the next three years. Year Cash Flow 1 ....................................... $15,000 2 ....................................... 25,000 3 ....................................... 40,000 The firm will be required to spend $10,000 to close down the project at the end of the three years. If the cost of capital is 10 percent, should the investment be undertaken? Solution: Horizon Company Present Value of Inflows Year Cash Flow x PVIF at 10% Present Value 1 $15,000 .909 $13,635 2 25,000 .826 20,650 3 40,000 .751 30,040 $64,325 Present Value of Outflows 0 $60,000 1.000 $60,000 3 10,000 .751 7,510 $67,510 Present Value of inflows $64,325 Present Value of outflows 67,510 Net present value ($ 3,185) The net present value is negative and the project should not be undertaken. Note, the $10,000 outflow could have been subtracted out of the $40,000 inflow in the third year and the same answer would result