IE343_HW6_Solutions

IE343_HW6_Solutions - Homework Assignment #6 Solutions...

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Unformatted text preview: Homework Assignment #6 Solutions PURDUE UNIVERSITY IE 343: Engineering Economics Fall 2010 Instructor: A. Capponi Homework Assignment #6 Assigned: 01 Oct 2010 Due: 08 Oct 2010 Missing name on the top of each page submitted – 2 Not stapled together – 2 Not completed on the correct template – 10 Problem 1 (15 points) Find the internal rate of return of a two-year investment that, for an initial payment of $1,000, generates a revenue of $500 at the end of the first year, and a revenue of $300 at the end of the second year. 500 300 0 1 2 1000 The present worth of this investment as a function of the interest rate i is given by () Let equation ( ) . In order to find the internal rate of return i, we need to find to solve the second order which may be rewritten as thus yielding and Since i > -1, then x > 0. Therefore, the solution is . IE 343 – Homework Assignment #6 Solutions – Page 1 Homework Assignment #6 Solutions Problem 5-46 (15 points) A small company purchased now for $23,000 will lose $1,200 each year the first four years. An additional invested $8,000 in the company during the fourth year will result in a profit of $5,500 each year from the fifth year through the fifteenth year. At the end of 15 years, the company can be sold for $33,000. 33000 5500 5500 5500 5500 5500 5500 5500 5500 5500 5500 5500 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1200 1200 1200 1200 8000 23000 a. Determine the IRR. () (| (| ) (| ) (| To find the solution to the equation Excel. We will use both methods. () , we can either do linear interpolation or use If we linearly interpolate, we obtain ( ) ( )( | ) ) Using linear interpolation, we obtain that the internal rate of return i is given by ( ) IE 343 – Homework Assignment #6 Solutions – Page 2 ) Homework Assignment #6 Solutions A more accurate answer can be obtained using Excel, which yields i = 10.01%. b. Calculate the FW if MARR = 12%. ( ( ) (| (| ) ) (| (| )( | ) ) c. Calculate the ERR when . All net cash outflows discounted to the present: (| ) (| ) All net cash inflows compounded to period N: (| ) Solve for ERR: (| (| ) ) IE 343 – Homework Assignment #6 Solutions – Page 3 ) Homework Assignment #6 Solutions Problem 5-49 (10 points) An hospital plans to invest $14,000 in a portable medical fluoroscope. The estimated cash outflows and inflows are shown below. What is the simple payback period for this proposed investment? EOY 0 1 2-7 8-12 12a a Expected Cast Flow -10,000 -4,000 3,000 6,000 4,000 Recover of working capital For simple payback, simply add each additional year’s cost/income until a positive Year End value is achieved. 0 1 2 3 4 Cumulative Net Cash Flow -10,000 -14,000 -11,000 -8,000 -5,000 5 6 -2,000 1,000 Year The payback period, to the nearest year, is six years. Notice that the cash flows occurring after the payback period are ignored. Thus, payback period is 6 years. IE 343 – Homework Assignment #6 Solutions – Page 4 Homework Assignment #6 Solutions Problem 5-55 (15 points) The International Parcel Service has installed a new radio frequency identification system to help reduce the number of packages that are incorrectly delivered. The capital investment in the system is $65,000, and the projected annual savings are tabled below. The system’s market value at the EOY five is negligible, and the MARR is 18% per year. 46000 EOY 1 2 3 4 5 40000 Savings 25,000 30,000 30,000 40,000 46,000 30000 30000 25000 0 a. What is the FW of this investment? ( ) ( ) ( ) ( ) ( ) ) ( ) ) ( ( 65000 , so this investment is acceptable. b. What is the IRR of the system? () ( ) ( ( Using Excel, we find acceptable. ) ( ( ) ) ) > MARR=18%. Thus the investment is IE 343 – Homework Assignment #6 Solutions – Page 5 1 2 3 4 5 Homework Assignment #6 Solutions c. What is the discounted payback period for this investment? Discounted Payback Period Method Period Net Cash Flow PW of Cash Flow Cumulative PW through year k 0 -65,000 -65,000.00 1 25,000 21,187.50 -43,812.50 2 30,000 21,546.00 -22,266.50 3 30,000 18,258.00 -4,008.50 4 40,000 20,632.00 16,623.50 5 46,000 20,106.60 36,730.10 The discounted payback period, to the nearest year, is 4 years. Notice that the cash flows occurring after the payback period are ignored. Thus, payback period is 4 years. IE 343 – Homework Assignment #6 Solutions – Page 6 Homework Assignment #6 Solutions Problem 5-66 (15 points) A piece of new equipment has been proposed by engineers to increase the productivity of a certain manual welding operation. The investment cost is $25,000, and the equipment will have a market (salvage) value of $5,000 at the end of its expected life of five years. Increased productivity attributable to the equipment will amount to $8,000 per year after extra operating costs have been subtracted from the value of the additional production. Create a single spreadsheet that calculated PW, FW, AW, IRR, and ERR for the proposed investment. Assume that per year. Does your recommendation change if the MARR decreases to 18%? Increases to 22%? 5000 8000 0 25000 IE 343 – Homework Assignment #6 Solutions – Page 7 8000 8000 8000 8000 1 2 3 4 5 Homework Assignment #6 Solutions The original recommendation is unchanged for a MARR =18%. However, the recommendation does change for MAR = 22% (which is greater than the IRR of the project’s cash flows). Note that ERR is unaffected by changes in the MARR. This is because 1) the reinvestment rate was assumed to remain at 20%, and 2) there was only a single net cash outflow occurring at t=0. IE 343 – Homework Assignment #6 Solutions – Page 8 ...
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This note was uploaded on 09/19/2011 for the course IE 343 taught by Professor Vincent,g during the Spring '08 term at Purdue.

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