ARAB ACADEMY FOR SCIENCE AND TECHNOLOGY College: Engineering and Technology Department: Industrial and Management Engineering
Course Code: NE 364 Course Title: Engineering Economy
Tutorial Exercise Workbook
Name
No
Table of Contents
1. Preface 2. Assessment Sheet 3. Introduction and Course ILO's 4. Student Instructions 5. Exercises 6. Study Problems 7. Recommended References 8. Remarks and Notes
1.
Preface
Engineering economy-what is it, and why it is important? The initial reaction of many engineering students to these questions is "money matters will be handled by someone else. It is not something I need to worry about" In reality, any engineering project must be not only physically realizable, but also economically affordable. For example a child's tricycle could be built with an aluminum frame or a composite frame. Some may argue that because the composite frame. Some may argue that because the composite frame will be stronger and lighter, it is a better choice. However, there is not much of a market for thousand dollar tricycle! One might suggest that this argument is ridiculously simplistic and that common sense will dictate choosing aluminum for the framing material. Although the scenario is an exaggeration, it reinforces the idea that the economic factors of a design weigh heavily in the design process, and that engineering economy is an integral part of that process, regardless of the engineering discipline. Engineering without economy, makes no sense at all.
2.
Assessment Sheet Exercise
Date
Mark A
Mark B
Signature
3.
Introduction and Course ILO's
A measurable quantity is a property of phenomenon, bodies or substances that can be defined qualitatively or expressed quantitatively
This workbook is designed to act as a guideline to the student register for Engineering Economy Course (NE-364). Concerning lectures and tutorials required for achieving the ILO’s of the course as stated below BASIC INFORMATION
II- PROFESSIONAL INFORMATION 1- Overall Aims of Course The aim of this course is to provide students with the basic knowledge and theoretical background related to economy and cost analysis in addition to conducting comparing alternatives into systems engineering. 2- Intended Learning Outcomes of Course (ILOs) A- Knowledge and Understanding
B- Intellectual Skills
C- Professional and Practical Skills
D- General and Transferable Skills
3. Student Assessment
1
Any formative only assessments
4. Student Instructions
•
Part of the sheet or some examples will be solved during the tutorial session.
•
Student has to complete an assignment during the tutorial time and a mark “A” will be given on this assignment.
•
The rest of the tutorial sheet will be completed by the student during the week and will be given mark “B” on the next tutorial session.
•
The student is evaluated on his tutorial attendance and the some of marks “A” and “B”.
5.
Exercises
2 4 3
Uniform Series
6
-
7th Week Exam
7
4
Arithmetic Gradient
8
5
Nominal and Effective Interest Rates
9
6
Applications of Money-time Relationships (Pw,Fw,Aw)
10
-
Revision
11
-
12th Week Exam
12
7
Comparing Alternatives (Pw,Fw,Aw)
13
-
Depreciation and Revision
14
Sheet #1 1. A company produces circuit boards used to update outdated computer equipments. The fixed cost is $ 42,000 per month, and the variable cost is $53 per circuit board. The selling price per unit is p = $150 – 0.02D. Maximum output of the plant is 4,000 units per month. a) b) c) d)
Determine optimum demand for this product. What is the maximum profit per month? At what volumes does breakeven occur? What is the company's range of profitable demand?
2. Company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately D = 780 – 10p units. (D is the demand or quantity sold per month, and p is the price per dollars.) The fixed cost is $800 per month, and the variable cost is $30 per unit produced. What number of units, D*, should be produced per month and be sold to maximum net profit? Also, determine D'1 and D'2.
3. A large wood products company is negotiating a contract to sell plywood overseas. The fixed cost that can be allocated to the production of plywood is $900,000 per month. The variable cost per thousand board feet is $131.50. The price charged will be determined by p = $600 – (0.05) D per 1,000 board feet. a) For this situation determine the optimal monthly sales volume for this product and calculate the profit (or loss) at the optimal volume. b) What is domain of profitable demand during a month?
4. A plant has a capacity of 4,100 hydraulic pumps per month. The fixed cost is $ 504,000 per month. The variable cost is $166 per pump, and the sales price is $328per pump. (Assume that sales equal output volume.) What is the breakeven point in number of pumps per month? What percentage reduction will occur in the breakeven point if fixed costs are reduced by 18% and unit variable costs by 6%?
5. Suppose that the ABC Corporation has a production (and sales) capacity of $1,000,000 per month. Its fixed costs—over a considerable range of volume—are $350,000 per month, and the variable costs are $0.50 per dollar of sales. a) What is the annual breakeven point volume (D')? b) What would be the effect on D' of decreasing the variable cost per unit by 25% if the fixed costs thereby increased by 10%? c) What would be the effect on D' if the fixed costs were decreased by 10% and the variable cost per unit were increased by the same percentage?
6. A plant operation has fixed costs of $2,000,000 per year, and its output capacity is 100,000 electrical appliances per year. The variable cost is $40 per unit, and the product sells for $90 per unit. a) Construct the economic breakeven chart. b) Compare annual profit when the plant is operating at 90% of capacity with the plant operation at 100% capacity. Assume that the first 90% of capacity output is sold at $90 per unit and that the remaining 10% of production is sold at $70 per unit.
Sheet #2 1. What lump-sum amount of interest will be paid on a $10,000 loan that was made on August 1, 2005, and repaid on November 1, 2009, with ordinary simple interest at 10% per year?
2. Draw a cash-flow diagram for $10,500 being loaned out at an interest rate of 12% per year over a period of six years. How much simple interest would be repaid as a lump-sum amount at the end of the sixth year?
3. What is the future equivalent of $1,000 invested at 8% simple interest per year for 2.5 years? a) b) c) d) e)
$1,157. $1,188. $1,200. $1,175. $1,150.
4. Jim loans Juanita $10,000 with interest compounded at a rate of 6% per year. How much money will Juanita owe Jim if she repays the entire loan at the end of five years?
5. If you want to withdraw $50,000 at the end of four years, how much should you deposit now in an account that pays12% interest compounded annually?
6. Ashlea purchased 100 shares of Microsoft at a price of $25 per share. She hopes to double her investment. How long will she have to wait if the stock price increases at a rate of 10% per year?
7. A homeowner purchased a home in 1995 for $189,500. Eleven years later the home was sold for $240,000. What compounded annual interest rate was realized by the homeowner?
Sheet #3 1. How much money can be withdrawn at the end of five years from your savings account if you make an annual contribution of $5,000 to your savings account at the end of each year for five years? Assume that your savings account earns an interest rate of 8% annually.
2. A future amount of $150,000 is to be accumulated through annual payments, A, over 20 years. The last payment of A occurs simultaneously with the future amount at the end of year 20. If the interest rate is 9% per year, what is the value of A?
3. A person wishes to accumulate $5,000 over a period of 15 years so that a cash payment can be made for a new roof on a summer cottage. To have this amount when it is needed, annual payments will be made into a savings account that earns 8% interest per year. How much must each annual payment be? Draw a cash flow diagram.
4. What equal annual payment series is required in order to repay a present amount of $25,000 in eight years at 10% interested compound annually?
5. If $25,000 is deposited now into a savings account that earns 6% per year, what uniform annual amount could be withdrawn at the end of each year for 10 years so that nothing would be left in the account after the 10th withdrawal?
6. It is estimated that a certain piece of equipment can save $22,000 per year in labor and materials cost. The equipment has an expected life of five years and no market value. If the company must earn a 15% annual return on such investments, how much could be justified now for the purchase of this piece of equipment? Draw a cash-flow diagram from the company's viewpoint.
7. Suppose that installation of Low-Loss thermal windows in your area is expected to save $350 a year on your home heating bill for the next 18 years. If you can earn 8% per year on other investments, how much could you afford to spend now for these windows?
8. How much should be deposited each year for 12 years if you wish to withdraw $309 each year for five years, beginning at the end of the 14th year? Let i = 8% per year.
9. Suppose that you have $10,000 cash today and can invest it at an interest rate of 10% compounded each year. How many years will it take you to become a millionaire?
10. Maintenance costs for a small bridge with an expected 50-year life are estimated to be $1,000 each year for the first 5 years, followed by a $10,000 expenditure in the year 15 and a $10,000 expenditure in year 30. If i = 10% per year, what is the equivalent uniform annual cost over the entire 50-year period?
11. You purchase special equipment that reduces defects by $10,000 per year on an item. This item is sold on contract for the next five years. After the contract expires, the special equipment will save approximately $3,000 per year for five years. You assume that the machine has no market value at the end of 10 years. How much can you afford to pay for this equipment now if you require a 20% annual return on your investment? All cash flows are end-of-year amounts.
12. What lump sum of money must be deposited into a bank account at the present time so that $500 per month can be withdrawn for five years, with the first withdrawal scheduled for six years from today? The interest rate is 3 / 4% per month. (Hint: Monthly withdrawals begin at the end of the month 72.)
13. Solve for the value of Z in the accompanying figure, so that the left cash-flow diagram is equivalent to the right one. Let i = 8% per year.
14. A woman arranges to repay a $1,000 bank loan in 10 equal payments at a 10% effective annual interest rate. Immediately after her third payment, she borrows another $500; also she talks the banker into letting her repay the remaining debt of the first loan and the entire amount of the second loan in 12 equal payments. The first of these 12 payments would be made one year after she receives the $500. Compute the amount of each of the 12 payments.
Sheet #4 1. If $10,000 now is equivalent to 4Z at the end of year two, 3Z at the end of year three, 2Z at the end of year four, and Z at the end of year five, what is the value of Z when i= 8% per year? Use a uniform gradient amount (G) in your solution.
2. In the accompanying diagram, Figure 4.1, what is the value of K on the left-hand cash-flow diagram that is equivalent to the right-hand cash flow diagram? Let i= 12% per year.
Figure 4.1
3. Calculate the future equivalent at the end of 2005, at 8% per year, of the following series of the cash flows in Figure 4.2. Use uniform gradient amount (G) in your solution.
Figure 4.2
4. Suppose that the parents of a young child decide to make annual deposits into savings account, with the first deposit being made on the child's 5th birthday and the last deposit being made on the 15th birthday. Then, starting on the child's 18th birthday, the withdrawals as shown will be made. If the effective annual interest rate is 8% during this period of time, what are the annual deposits in year 5 through 15? Use uniform gradient amount (G) in your solution. (See Figure 4.3).
Figure 4.3
Sheet #5 1. Compute the effective annual interest rate in each of these situations: a. 10% nominal interest, compounded semiannually. b. 10% nominal interest, compounded quarterly. c. 10% nominal interest, compounded weekly.
2. Sixty monthly deposits are made into an account paying 6% nominal interest compounded monthly. If the objective of these deposits is to accumulate $100,000 by the end of the fifth year, what is the amount of each deposit? a. $1,9230. b. $1,478. c. $1,667. d. $1,430.
e. $1,695.
3. What extra semiannual expenditure for five years would be justified for the maintenance of a machine in order to avoid an overhaul costing $3,000 at the end of five years? Assume nominal interest at 8% compounded semiannually.
4. Determine the current amount of money that must be invested at 12% nominal interest, compounded monthly, to provide an annuity of $10,000 (per year) for 6 years, starting 12 years from now. The interest rate remains constant over this entire period of time.
5. Find the present equivalent value of the following series of payments: $100 at the end of each month for 72 months at a nominal rate of 15% compounded monthly.
6. You have used your credit card to purchase automobile tires for $340. Unable to make payments for 11 months, you then write a letter of apology and enclose a check to pay your bill in full. The credit card company's nominal interest rate is 16.5% compounded monthly. For what amount should you write the check?
7. What is the principle remaining after 20 monthly payments have been made on a $20,000 fiveyear loan? The annual interest rate is 12% nominal compounded monthly. a. $10,224.
b. $13,333.
d. $16,073.
e. $17,094.
c. $14,579.
Sheet#6 1. You are faced with making a decision on a large capital investment proposal. The capital investment amount is $640,000. Estimated annual revenue at the end of each year in the eight-year study period is $180,000. The estimated annual year-end expenses are $42,000 starting in year one. These expenses begin decreasing by $4,000 per year at the end of year four and continue decreasing through the end of year eight. Assuming a $20,000 market value at the end of year eight and a MARR = 12% per year, answer the following questions: a) What is the PW of this proposal? b) What is your conclusion about the acceptability of this proposal?
2. Evaluate machine XYZ on the basis of the PW method when the MARR is 12% per year. Pertinent cost data are as follows: Machine XYZ Investment cost
$13,000
Useful life
15 years
Market value
$3,000
Annual operating expenses
$100
Overhaul cost-end of 5th year
$200
Overhaul cost-end of 10th year
$550
3. Determine the PW, FW, and AW of the following engineering project when the MARR is 15% per year. Is the project acceptable? Proposal A Investment cost
$10,000
Expected life
5 years
Market(salvage) value
-$1,000
Annual receipts
$8,000
Annual expenses
$4,000
4. Your uncle has almost convinced you to invest in his peach farm. It would require a $10,000 initial investment on your part. He promises you revenue (before expenses) of $1,800 per year the first year, and increasing by $100 per year thereafter. Your share of the estimated annual expenses is $500. You are planning to invest for 6 years. Your uncle has promised to buy out your share of the business at that time for $12,000. You have decided to set a personal MARR of 15% per year. Use the PW method to determine the profitability of this investment project. Include a cash flow diagram.
Sheet#7 1. Four mutually exclusive alternatives are being evaluated, and their costs and revenues are itemized in the following table: Mutually Exclusive Alternative 1
2
3
4
Capital investment
$100,000
$152,000
$184,000
$220,000
Annual revenues less expenses
15,200
31,900
35,900
41,500
Market value (end of useful life)
10,000
0
15,000
20,000
Useful life (years)
10
10
10
10
If the MARR is 15% per year, and the analysis period is 10 years, use the PW method to determine which alternatives are economically acceptable and which one should be selected. If the total capital investment budget available is $200,000, which alternative should be selected?
2. The Consolidated Oil Company must install antipollution equipment in a new refinery to meet federal clean-air standards. Four design alternatives are being considered, which will have capital investment and annual operating expenses as shown in the following table: Alternative Design D1
D2
D3
D4
$600,000
$760,000
$1,240,000
$1,600,000
Power
68,000
68,000
120,000
126,000
Labor
40,000
45,000
65,000
50,000
Maintenance
660,000
600,000
420,000
370,000
Taxes and insurance
12,000
15,000
25,000
28,000
Capital investment Annual expenses:
Assuming a useful life of 10 years for each design, no market value, a desired MARR of 10% per year, and an analysis period of 10 years, determine which design should be selected on the basis of the PW method. Confirm your selection by using the FW and AW methods.
3. The following cash-flow estimates have been developed for two small, mutually exclusive investment alternatives, what is the AW of both Alternatives, and which Alternative should be selected? The MARR=12% per year.
4. Three mutually exclusive design alternatives are being considered. The estimated cash flows for each alternative are given next. The MARR is 20% per year. At the conclusion of the useful life, the investment will be sold.
A decision-maker can select one of these alternatives or decide to select none of them. Make a recommendation, using the PW method.
5. Three mutually exclusive alternatives are being considered for the production equipment at a tissue paper factory. The estimated cash flows for each alternative are given here. (All costs are in thousands).
Which equipment alternative, if any, should be selected? The firm's MARR is 20% per year.
6. A piece of production equipment is to be replaced immediately because it no longer meets quality requirements for the end product. The two best alternatives are a used piece of equipment (E1) and a new automated model (E2). The economic estimates for each are shown in the accompanying table. The MARR is 15% per year. Which Alternative is preferred?
7. A company is considering constructing a plant to manufacturing a proposed new product. The land costs $300,000 the building costs $600,000 the equipment costs $250,000 and $100,000 additional working capital is required. It is expected that the product will result in sales of $750,000 per year for 10 years, at which time the land can be sold for $400,000, the building for $350,000, and the equipment for $50,000. All of the working capital would be recovered at the end of year 10. The annual expenses for labor, materials, and all other items are estimated to total $475,000. If the company requires a MARR of 15% per year on projects of comparable risk, determine if it should invest in the new product line. Use the PW method.
6. Study Problems 7. A large work area can be illuminated satisfactorily by either one of two methods. By using incandescent lighting, the initial cost is low ($10,000) but the operating costs are relatively high ($12.50 per hour). The other lighting system utilizes fluorescent lamps having a high initial cost $25,000) but relatively low operating costs ($4.25 per hour). Only one year (8,760 hours) is to be used in deciding between these two types of lighting. Furthermore, the number of hours of operation during the year (H) must be considered in making the decision. What value of H makes the costs of both types of lighting the same? 8. Draw a cash-flow diagram for a $10 000 loan payable in 5 years. Knowing that the simple interest rate is 12% per year, how much would be repaid as a lump-sum at the end of the fifth year
9. The annual fixed costs for a plant are $ 100,000 and the variable coats are $ 140,000 at 70% utilization of available capacity with net sales of $ 280,000. What is the breakeven point in units of production if the selling price per unit is $40? Also calculate the available capacity of the plant. 10. Draw a cash-flow diagram for $10,500 being loaned out at an interest rate of 12% per year over a period of six years. How much simple interest would be repaid as a lump-sum amount at the end of the sixth year? 11. A company is considering investing $10,000 in a heat exchanger. The heat exchanger is estimated to produce a net income (after expenses) of $2,000 per year. The company plans to sell the heat exchanger after 5 years of operations. What should the market value (of the heat exchanger) be at the end of the 5th year to justify the investment, knowing that the company expects to earn 15% annual return on investment?
12. What is the present worth of a series of EOY (end of year) payments of $1,200 each for 10 years, knowing that the interest rate is 15% compounded monthly?
13. You can buy a machine for $100,000 that will produce a net income after operating expenses of $10,000 per year. If you plan to keep the machine for FOUR years, what must the market value be at the end of four years to justify the investment? It is recommended to make a 15% annual return on your investment. Draw a cash flow diagram. 14. Find the present equivalent value of the following series of payments $100 at the end of each month for 72 months at a nominal rate of 15% compounded monthly. 15. It is estimated that a certain piece of equipment can save $22,000 per year in labor and materials cost. The equipment has an expected life of five years and no market value. If the company must earn a 15% annual return on such investments, how much spending could be
justified now for the purchase of this piece of equipment? Draw a cash-flow diagram from the company's viewpoint. 16. You are faced with making a decision on a large capital investment proposal. The capital investment amount is $640,000. Estimated annual revenue at the end of each year in the eightyear study period is $180,000. The estimated annual year-end expenses are $42,000 starting in year one. These expenses begin decreasing by $4,000 per year at the end of year four and continue decreasing through the end of year eight. Assuming a $20,000 market value at the end of year eight and a MARR = 12% per year. What is your decision based on PW for such proposal. 17. A new electric saw for cutting small pieces of lumber in a furniture manufacturing plant has a cost basis of 4000 pounds and a ten year depreciable life. The estimated SV of the saw is Zero at the end of 10 years. Determine the annual depreciation amounts, using the straight- line method. Also what is the book value of the saw at the end of year Five?
7. Selected References
1. AU, T., and T.P. Au. Engineering Economics for capital Investment Analysis, 2nd ed. (Boston: Allyn and Bacon, 1992). 2. Barish, N. N., and S. Kaplan. Economic Analysis for Engineering and Managerial Decision Making (New York: McGraw Hill 1978). 3. Blank, L.T., and A. J. Tarquin. Engineering Economy, 5th ed. (New York: McGraw Hill 2001).
8. Remarks and Notes ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… …………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… …………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… …………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… …………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………….
