IE343_HW7_Solutions

# IE343_HW7_Solutions - Homework Assignment #7 Solutions...

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Unformatted text preview: Homework Assignment #7 Solutions PURDUE UNIVERSITY IE 343: Engineering Economics Fall 2010 Instructor: A. Capponi Homework Assignment #7 Assigned: 15 Oct 2010 Due: 22 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) Sugar Spice, a cook factory, needs a new cookie cutter machine. They have narrowed their choices to three different types of machines, which are presented below A B C Cost \$50,000 \$22,000 \$15,000 Annual Net Income \$5,093 \$2,077 \$1,643 Each alternative has a useful life of 20 years with no salvage value. If the MARR is 6%, which alternative should be selected, if any? We first need to determine which of the alternative is attractive. To this purpose, we compute the internal rate of return of each and compare it to MARR. We have -\$50,000 + \$5,093 (P|A, i, 20) = 0. Using Excel, i = 8% for Alternative A. -\$22,000 + \$2,077 (P|A, i, 20) = 0. Using Excel, i = 7% for Alternative B. -\$15,000 + \$1,643 (P|A, i, 20) = 0. Using Excel, i = 9% for Alternative C. Thus, all alternatives are attractive since they are all greater than 6%. As discussed in class, the IRR cannot be used to rank investment, but an incremental analysis is needed. We first rank alternatives based on the cost of the initial investment. This produces the ranking of C < B < A. The alternative C is the base alternative. We compare alternative C and B. The incremental investment leads to extra revenues The IRR of this incremental investment is the rate i such that ( ) ( ) ( ) As 2.14% < MARR, then alternative C remains the winner and the most attractive up to this point. IE 343 – Homework Assignment #7 Solutions – Page 1 Homework Assignment #7 Solutions We next compare alternative C and A. The incremental investment leads to extra revenues The IRR of this incremental investment is the rate i such that ( ) ( ) ( ) As 7.56% > MARR, then the extra investment of \$35,000 in alternative A is justified, as it leads to attractive incremental revenues, yielding a rate of return of 7.56%. Thus, the winner is A. Choose alternative A. IE 343 – Homework Assignment #7 Solutions – Page 2 Homework Assignment #7 Solutions Problem 2 (10 points) Textbook Problem 6-5 Which mutually exclusive design (if any) should be chosen from the designs listed here? A 10-year study period is to be used, and the MARR is 10% per year. All market values are negligible. Design A Design B Design C Capital investment \$170,000 \$330,000 \$300,000 Annual receipts 114,000 147,000 130,000 Annual expenses 70,000 79,000 64,000 Use the FW method. Confirm your recommendation, using the PW and AW methods. USING FUTURE WORTH ( ) ( )( )( ) ( )( )( ) ( ( ) ) ) ( ( ( ) ( ) ) ( ( USING PRESENT WORTH ( ) ( ( )( ( )( )( ) ) )( ) ) )( )( ) ) ) )( )( ) ( ) ) ( ) ) ( ( ( ) ) ( ( ( ) ( ( ( ) )( ( ( ( )( ) ( ( USING ANNUAL WORTH ( ) ( ( ( ) ) ( ( ) ) ) ) ) ) ) Therefore, all methods, FW, PW, and AW, choose Design C IE 343 – Homework Assignment #7 Solutions – Page 3 Homework Assignment #7 Solutions Problem 3 (15 points) Textbook Problem 6-18 A stem cell research project requires expensive specialized laboratory equipment. For this purpose, three pieces of equipment and their associated cash flows (listed below) are under consideration. One piece of equipment must be selected, and the laboratory’s MARR is 15% per year. Equipment EOY A B C 0 -\$136,500 -\$84,000 -\$126,000 1 – 4 -\$12,500 -\$31,500 -\$15,500 5 -\$15,000 -\$31,500 -\$15,500 a. Use the PW method to rank-order the economic attractiveness of the three projects. ( ) ( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ( ( ) ( ) ) ) ( ( ) ) So the rank-order is C>A>B. (C is the best one.) b. Determine the interest rate at which the laboratory would be indifferent between Equipment B and Equipment C. This means that the PW or AW of Equipment B and Equipment C are equivalent. USING PRESENT WORTH ( ) ( ( ) ( USING ANNUAL WORTH ( ) ) ( ( ) ( ) ( ( ) ( ) ) ( ) ) ( ( ) ) Using Excel, we get, i’=26.19%. If the MARR > 26.19%, select Equipment B. If the MARR < 26.19%, select Equipment C. IE 343 – Homework Assignment #7 Solutions – Page 4 ) Homework Assignment #7 Solutions Problem 4 (15 points) Textbook Problem 6-24 Two mutually exclusive harvesting combines are being considered for purchase by a wheat farmer. He must buy a new combine now. Information relevant to his comparison of the alternatives is summarized below. Deere FMC Capital investment \$240,000 \$200,000 Market value at end of service life \$80,000 \$20,000 Annual fuel and maintenance expenses \$5,000 \$10,000 Service life 12 years 12 years Use the IRR method to determine the better machine to purchase. The farmer’s MARR is 12% per year. Based on the incremental analysis method, savings in annual expenses of \$5,000 are achieved by selecting the ‘Deere’ option, which comes at an additional investment cost of \$40,000 and a loss of \$60,000 of market value at the end of the service life. Therefore, select Deere as the basis for incremental IRR. The present worth of this incremental investment is given by ( ( ( ) ) ) ( ( ( ( ) ) ) ( ( ) ) ) Using Excel, you can solve using IRR. This will result in i = 14.3%. Since i = 14.3% > 12%. Therefore, the Deere option is better. Additional solution – not asked for… This can also be confirmed by simply computing the PW for both options, using the MARR = 12%. ( ) ( ( ) ( ( ( ) ) ) ) ( ) ( ( ) ( ) ) IE 343 – Homework Assignment #7 Solutions – Page 5 Homework Assignment #7 Solutions Problem 5 (15 points) Textbook Problem 6-28 Consider the following EOY cash flows for two mutually exclusive alternatives (one must be chosen): Machine X Machine Y Capital investment \$6,000 \$14,000 Annual expenses \$2,500 \$2,400 Useful life 12 years 18 years Market value at end of useful life \$0 \$2,800 The MARR is 5% per year. a. Determine which alternative should be selected if the repeatability assumption applies. USING ANNUAL WORTH Machine X () ( Machine Y () ) ( ( ) ( ) ( ) ( ) ) USING PRESENT WORTH (with study period equal to list common multiple = 36) Machine X () ( )( )) ( ) ( ( ) ( ) ( ) ( ( ( ( ) ( Machine Y () ) )( )( ) ) ( ( ( )( )( ( ) ) ( ) ) ) ( ( )) ( ) ) ) ( )) ( ( ) ( ( ( (( ( ) ) ( )( ) ( ( ) ) ) ( )( ( ) ( ) ) Therefore, both AW or PW select Alternative X. IE 343 – Homework Assignment #7 Solutions – Page 6 ) ) ( ( ) ) Homework Assignment #7 Solutions b. Determine which alternative should be selected if the analysis period is 18 years, the repeatability assumption does not apply, and a machine can be leased for \$8,000 per year after the useful life of either machine is over. USING ANNUAL WORTH Machine X ( ) ( ( Machine Y () ( ) ) ( )( )( ) ( ( )( ) ) ( ) USING PRESENT WORTH Machine X () ( Machine Y () ( ( ( ) ( ( )( ) )( ( ) )( ( ( ) ) ) Or ( ) ( ) ) ( ) ) ) ( ) ) For PW or AW, select Alternative Y IE 343 – Homework Assignment #7 Solutions – Page 7 ...
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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 University-West Lafayette.

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