PART I : ENGINEERING ECONOMY 1. INTEREST FORMULAS 1. What will be the amount accumulated by each of these present investments? a. LE 8,000 in 8 years at 12% compounded annually. b. LE 2,500 in 43 years at 8% compounded annually. 2. What is the present value of these future payments? a. LE 5,500 6 years from now at 10% compounded annually. b. LE 1,700 12 years from now at 9% compounded annually. 3. What is the present value of the following series of prospective payments? a. LE 3,500 a year for 8 years at 9% compounded annually. b. LE 1,000 a month for 4 years at 10% compounded annually. 4. What is the accumulated value of each of the following series of payments? a. LE 500 at the end of each year for 12 years at 8% compounded annually. b. LE 1,400 at the end of each quarter for 10 years at 10% compounded annually. 5. What equal series of payments must be paid into a sinking fund to accumulate the following amounts? a. LE 9,000 in 5 years at 9 % compounded annually when payments are annual. b. LE 15,000 in 8 years at 11% compounded annually when payments are annual. 6. What equal series of payments are necessary to repay the following present amounts? a. LE 5,000 in 5 years at 12% compounded annually with annual payments. b. LE 16,000 in 8 years at 10% compounded annually with semiannual payments. 7. What effective annual interest rate corresponds to the following? a. Nominal interest rate of 10% compounded semiannually. b. Nominal interest rate of 8% compounded monthly. 8. What lump-sum amount of interest will be paid on a $10,000 loan that was made on January 1, 1999, and repaid on January 1, 2004, with simple interest rate at 10% per year? 9. Compare the interest earned by $9,000 for five years at 8% simple interest per year with the interest earned by the same amount for five years at 8% compound annually. Explain the difference occurs. Draw the cash flow diagram. 10. A future amount, F, is equivalent to $1,500 now with six years separate the amounts and the annual interest rate is 12%. What is the value of F? 11. What amount would need to be paid each January 1 into savings account if at the end of 15 years (15 payments) you desired $10,000? Annual interest rate is 7%. (Note: The last payment will coincide with the time of the $10,000 balance.) - 1-
12. A proposed product modification to avoid production difficulties requires an immediate expenditure of $14,000 to modify certain dies. What annual savings must be realized to recover this expenditure in five years with interest at 10% per year? 13. A small company wants to deposit a single amount of money now, so that it will have enough to purchase a new machine costing $50,000 five years from now. If the money can be deposited into an account, which earns interest at 10% per year, what is the amount that must be deposited? 14. Suppose that annual income from a rental property is expected to start at $1,200 per year and decrease at a uniform amount of $40 each year for the 15-year expected life of the property. The investment cost is $8,000 and interest rate is 9% per year. Is this a good investment? Assume that the investment occurs at time zero (now) and the annual income is first received at the end of year one. 15. 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. 16. 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 15th year? Let i = 8% per year. 17. Suppose that $400 is deposited each year into a bank account that pays interest annually (i= 10%). If 12 payments were made into the account, how much would be accumulated in this fund by the end of the twelfth year? The first payment occurs at time zero (now). 2. COMPARISON OF ALTERNATIVES Use where applicable the present worth, equivalent annual payment, payback period and return on investment to make a decision on the economic justification in the following cases. 1. Four alternatives are being evaluated, and their costs and revenues are itemized in the table below. If the MARR is 12% per year, use the PW, FW and AW methods to determine which alternative is economically selected. Alternative A B C D Capital investment - $100,000 - $ 152,000 - $ 184,000 - $ 220,000 Annual revenues less expenses 15,200 31,900 35,900 41,500 Market value 10,000 0 15,000 20,000 Useful life (years) 10 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 table below. Assuming a useful life of 10 years for each design, no market value, and a desired MARR of 12% per year, determine which design should be selected based on the PW, FW and AW methods. Confirm your selection by using the IRR method. - 2-
Alternative design D1 D2 D3 D4 Capital investment - $ 600,000 - $ 760,000 - $ 1,240,000 - $ 1,600,000 Annual expenses: 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 3. Two pumps are being considered for a certain service of 25 years. The Toltec pump has a firstcost of L.E 5,000 and an estimated annual cost of L.E 3,200 for electric energy used for pumping purposes. The Mandan pump has a first cost of L.E 3,800. Because it is less efficient its annualcosts for pumping energy will be L.E 140 higher than those of the Toltec pump. Estimated annualincome taxes will be L.E 42 higher with the Toltec pump. It is anticipated that there will be no other cost differences and no salvage values. What is the prospective after-tax rate of return on the extra investment required to purchase the Toltec pump? 4. Two mutually exclusive proposals are Projects X and Y. Project X requires a present investment of L.E 250,000. Estimated annual receipts for 25 years are L.E 88,000; estimated annual disbursements other than income taxes are L.E 32,000; estimated annual income taxes are L.E 24,000. Project Y requires a present investment of L.E 325,000. Estimated annual receipts for 25 years are L.E 100,000; estimated annual disbursements other than income taxes are L.E 40,000;estimated annual income taxes are L.E 23,500. Each project is estimated to have a L.E 50,000 salvage value at the end of 25 years. Assuming an after-tax i of 11%, make the necessary calculations to determine whether to recommend Project X, Project Y, or neither. Make a specific recommendation and explain why you made it. 5. A front-end loader can be had for L.E 10,000 under either of two plans. a. Borrow L.E 10,000 at bank and repay in equal annual installments over five-year period at 8 percent on unpaid balance. b. Borrow L.E 2,000 down payment and repay the L.E 2,000 in equal annual payments over five years at 12 percent. Pay off remaining L.E 8,000 balance owed dealer at L.E 2,000 per year for five years. 3. Depreciation Use (a) straight-line depreciation; (b) sum-of-years-digits depreciation; and (c) 8% sinking fund method of depreciation 1. A central air-conditioning unit is purchased for L.E 25,000 and it has an expected life of 10 years. The salvage value for the unit at that time is expected to be L.E 4,000. What will be the book value at the end of 7 years. Filters costing L.E 1,000 per set are used to separate particles from hot gases being discharged into the air. These filters must be replaced every 2,500 hours. If the plant operates 24 hours per day, days per month, what is the depreciation charge per month for these filters? - 3-
2. A real estate company purchased an office building to be used as rental property. The total price was $700,000, of which $100,000 was the appraised value of the land. The building had an estimated remaining life of 20 years, with an estimated salvage value of zero. After having owned the property for 10 years, the company received an offer of $500,000 for it, of which $200,000 was the appraised value of the land. Find the book value of the property at the end of 10 years. The company had received net receipts after all disbursements for maintenance, property taxes, insurance, and so on, of $120,000 a year for the 10 years. Find the true rate of return earned on the original investment if the property is now sold for $500,000. 3. At the start of 1990, K.Brown, a certified public accountant, purchased a minicomputer for use in his private accounting practice. Its first cost was $25,000. He believed that it would have an economic life of 6 years with a net salvage value of $4,000. What depreciation expense would he have recorded for the third year and what would have been the book value at the end of the third year. 4. INFLATION IN ECONOMIC ANALYSIS 1. A certain bond is purchased at $1000 with a maturity life of 3 years. The bond provides $150 per year, for an inflation rate of 10%. If the bond can be purchased at the end of its life for $1000, what is the real interest rate? 2. A client expects to depoit $1000 per year for ten years (first deposit at EOY 1, last deposit at EOY 10) into an account that pays interest compounded at 8% per year. If the inflation is estimated at 5% per year find the real interest rate in terms of compound increase in buying power. 3. A home buyer purchased a house for $70,000. he pays $10,000 down and gets a $60,000 mortgage at 10% and 30 years pay out period. If the inflation occurs at 8%, what is the real interest rate? 4. A young engineer on his twenty-third birthday decides to start saving (investing) toward building up a retirement fund. He feels that $300,000 worth of buying power in terms of today s dollars will be adequate to see through his sunset years starting at his sixty-third birthday. a. If the inflation rate is estimated to be 7% for the investing period, how much the investment be worth on his sixty-third birthday? b. If his rate of return from savings is estimated at 12% and he expects to make annual end of year deposits (first deposit on his twenty-third birthday and the last on his sixty-third birthday), what the annual deposit must be? c. What is the real interest rate? 5. EVALUATION OF REPLACEMENTS 1. A machine was purchased 3 years ago for L.E 12,000. Its present value is L.E 5,000 and its operating expenses are expected to continue at L.E 1,000 a year. A secondhand machine costing L.E 2,000 is available but its operating expenses are expected to be L.E 1,600 per year. It is anticipated that the machines will be in service for 6 more years with L.E 1,000 salvage value for - 4-
the present machine and zero for the second-hand machine. Using the rate-of-return approach and a minimum attractive rate of return of 12%, find the best course of action. 2. Two years ago a centrifugal pump driven by a direct-connected induction motor was purchased to meet a need for a flow of 2,000 gallons of water per minute for an industrial process. The unit cost L.E 2,300 and had an estimated salvage value of L.E 400 at the end of 6 years of use. It consumed electric power at the rate of 47 kw and was used 12 hours per day for 300 days a year. The process for which the water is required has been changed and in the future a flow of only 800 gallons per minute is needed 3 hours per day for 300 days a year. At the decreased flow both pump and motor are relatively inefficient and the current consumption is 36 kw. A new unit of a capacity conforming to future needs will cost L.E 1,350. This unit will have an estimated life of 8 years with estimated salvage value of L.E 200. Its current consumption will be 19kw. The present unit can be sold for L.E 700. The original estimates of useful life and salvage value are still believed to be reliable. Insurance, taxes, and maintenance are estimated at 6% of the original cost for both units. The cost of power is L.E 0.022 per kwt-hr and MRR 10%. a.should the old unit be retained or should the new unit be purchased? b. At what number of hours per day for 300 days a year with a requirement of 800 gallons of water per minute will the future equivalent annual cost of the two units be equal? 3. A grain elevator requires additional capacity for the grinding of feed. Two plans for securing this capacity are to be compared. Plan A. Replace the existing centrifugal bar mill with a patent feed grinding mill manufactured by the XYZ Company. This XYZ mill will provide 3 times the present capacity. Plan B. Continue the present centrifugal bar mill in service and supplement it by another similar mill of like capacity. This will provide double the present capacity, which appears to be adequate for all needs. The existing centrifugal bar mill cost $4,000 5 years ago. Straight-line depreciation has been charged on the books against it based on an estimated life of 15 years. It has a present net realizable value of $1,000. A new similar mill will cost $5,100. The XYZ mill has a first cost installed of $9,500. It is estimated that the maintenance cost of the existing centrifugal bar mill will average at least $250 a year in the future. A new centrifugal bar mill with somewhat improved design can be maintained for about $175 a year, it is believed. The XYZ mill is expected to have an annual maintenance cost of $200. Energy requirements for a centrifugal bar mill of this capacity are 23 kw.hr per hour of operation. It is expected that if two such mills are operated, each will operate about 1,200 hours per year. Because of its greater capacity, the XYZ mill will grind the same total amount of feed as the other two in 800 hours per year. Its energy requirements are 41 kw-hr per hour of operation. Energy is purchased for 4.3 cents per kw-hr. Labor costs and taxes will be practically unaffected by the choice of plan. Make a comparison of equivalent annual costs for Plans A and B assuming a 10-year remaining life for the present mill and a 10- year life for both new mills with zero terminal salvage values for all. Use MMR of 25%. - 5-
4. A furniture manufacturer is considering the installation of an automatic boring machine to replace two machines that now provide the same total capacity. The proposed machine will cost $27,500 ready to operate. If acquired, it will be depreciated for accounting and tax purposes by the years-digits item method assuming a 10-year life and zero salvage value. Annual disbursements for its operation are estimated as follows: Direct labor will be one operator at $400 per week for 48 weeks per year. Labor extras are 30% of direct labor cost. Power will be 4,000 kw-hr per year at 5~ per kw-hr. Annual repairs and supplies are estimated at $600. Insurance total 3% of first cost. The two present machines cost $8,000 each and are 5 years old. Straight-line item depreciation has been used for accounting and tax purposes assuming a 15-year life and zero terminal salvage value. Their present realizable value is $2,000 each. Annual expenditures are: Direct labor is two operators at $250 per week each for 48 weeks per year. Labor extras are 30% of direct labor cost. Power is 2,500 kw-hr per machine per year at 5c. per kw-hr. Annual repairs and supplies are $400 per machine. Property taxes and insurance total 3% of first cost. Assuming a 20% MRR, compute the before-tax annual cost of extending service of the defenders for 10 more years. Compare this with the annual cost of the challenger over a 10-year service life. Assume zero salvage values for both defender and challenger at the end of the 10 years. 6. B/C analysis 1. A new road is under consideration for connecting two municipalities in the Smoky Mountains by a more direct route. The existing route is 25 mi long and has an annual maintenance cost of L.E 4,800 per mile. Every ten years major maintenance and resurfacing costs an additional L.E 1,000,000, and one is due at the present time. The new direct route will be just 15 mi long and will cost L.E 15,000,000. Annual maintenance is estimated at L.E 3,200 per mile, and major maintenance and resurfacing every ten years is expected to cost L.E 520,000. The average speed on the existing route is 45 mph, whereas the new route should sustain 55 mph average. The average annual traffic is estimated at 800,000 vehicles per year of which 20 percent are commercial. Traffic is expected to increase at about 40,000 vehicles per year until reaching capacity at 2,000,000 vehicles per year. The cost of time for commercial traffic is estimated at L.E 12.00 per hour and for noncommercial traffic at L.E 3.00 per hour. Time charges do not include vehicle operating costs which are estimated on the existing route at L.E 0.30 per mile for commercial traffic and L.E 0.12 per mile for noncommercial. Operating cost on the new route is 10 percent less per mile. The anticipated life of both proposals is 40 years, with zero salvage value for - 6-
both. Using I = 7 percent, compare the B/C using the modified and the conventional methods. 2. Assume that a new direct route from Alexandria to Rosetta is proposed with two alternate alignments. The data on each alternative are given in the table below. The anticipated life of the road is 25 years, with a value at the end of that time estimated at 50 percent of the cost new. Use the modified B/C to determine which is the best alternative. Use i = 7 percent. Anticipated traffic on either of the new alignments is estimated at 4,000,000 vehicles per year the first year, increasing by 500,000 vehicles per day until reaching capacity at 10,000,000 vehicles per day. Traffic on the existing route is currently 1,200,000 vehicles per day and growing by 100,000 vehicles per day. 3. A water supply flood control project is proposed for a certain river valley in central Florida. There is a question as to the location of the dam, and the number of alternate sites has been narrowed down to two, site A and site B. Estimates of the costs associated with each of these sites are listed below. The funds to construct the project are available from bonds bearing interest at 6 percent. The anticipated life of the project at either site is 40 years, and no salvage value is expected. Use the modified B/C to reach a recommendation on which alternative is best. PART II : ENGINEERING COST ANALYSIS I. MATERIAL AND LABOR COST 1. In a cement company, material ledger sheet for calcium carbonate is as follows: Date Qty./ton Price(x 100), L.E. 2/1/2003 200 10 1/4 300 12 2/8 100 11 3/1/2004 400 13 4/1 300 14-7-
You are required to calculate the issue price using FIFO, LIFO and weighted average methods for the following issues: a. 400 ton on 1/10/2003 b. 200 ton on 2/1/2004 2. Calculate labor earnings using piece rate, Halsey plan, and Rowan plan of remuneration, given; For a 7 hr shift, normal rate of production 42 shafts, for which.an operator is paid L.E 20. The actual rate of production during same period is 54 shaft. 3. In the above plan, using high piece-rate system, calculate labor earnings if: guaranteed rate at 85% of nominal production. 110% from normal pay for 100-120% of nominal production 120% from normal pay for 120-140% of nominal production 150% from normal pay for more than 140% of nominal production II. DISTRIBUTION OF OVERHEADS Department XYZ makes two products, Alpha and Beta. The departmental budgeted overheads for XYZ are 12,000, and the budgeted production is Alpha 2000 units, Beta 800 units. The estimated prime cost of Alpha and Beta was calculated thus: Alpha Material 24 lb of code 989 at 0.25 = 6 17 lb of code 281 at 0.20 = 3.4 Labor 6 hrs (of which 2 hrs are 25 hrs (of which 10 hrs are Beta on a machine) at 0.40.hr= 2.4 on a machine) at 0.20. hr= 5 Total 8.4 8.4 Calculate, using at least three different methods, overhead recovery rates and show the overhead for 1 unit of Alpha and also 1 unit of Beta. III. BREAK-EVEN ANALYSIS 1. The cost sheet for a cassette recorder is as follows : Materials Labor 110 L.E 130 L.E Variable Expenses 80 L.E Fixed Expenses 60 L.E The number of sets made and sold is 50,000, and unit selling price is L.E.500 Draw the break-even chart Calculate the number of sets to be produced and sold if the price is reduced by LE. 20 in order to give the same profit? Draw the corresponding B.E. chart. 2. The cost per unit (L.E) of the three products A, B and C of a concern is as follows: A B C Direct Materials 10 8 9 Direct Labor 6 7 6-8-
Variable Expenses 4 5 3 Fixed Expenses 3 3 2 Total Cost 23 23 20 Profit 9 7 6 Selling Price 32 30 26 No. of units produced 10,000 5,000 8,000 Production arrangements are such that if one product is given up, the production of the others can be raised by 50%. It is proposed that C should be given up because the contribution in that case is lowest, do you agree? 3. A factory is currently working to 50% capacity and produces 10,000 units. Estimate the profits of the company when it works to 60% and 80% capacities. At 60% capacity selling price falls by 2%, and at 80% capacity the selling price falls by 5% accompanied by a similar fall in prices of raw materials. The cost at present per unit is: Materials 100 Labor 30 Overheads 50 (60% fixed) The selling price is LE 200 per unit 4. A chemical company, manufacturing wall paints, is considering expanding its operations to meet expected demand, through operating 2.or 3 shifts. If selling price is L.E 100 per 10 litre can, variable cost L.E 5/litre and other cost data are as follows : Shift capacity (litre) fixed cost (L.E) I 100 000 200 000 II 200 000 250 000 III 300 000 325 000 Calculate break-even volume(s) and find the corresponding factor of safety. IV. VARIANCE ANALYSIS 1. MUD is prepared by mixing M, U and D (standard prices 1, 2 and 3 a ton respectively) in the proportions of 1:1:3. A standard loss of 20% is allowed. Last period 1100 tons of M costing 1000, 1000 tons of U costing 2200, and 2900 tons of D costing 8888 were processed to give 3815 tons of MUD. Find the variances. 2. Extract from the following data all overhead variances: Budgeted production 50 lots Fixed overhead absorption rate 3 per hour Actual and budgeted variable overheads 7500 Standard hours per lot 100 hours Actual production 60 lots - 9-
Actual fixed overheads 14,500 Actual hours worked 5600 hours 3. A foundry producing castings of a standard alloy uses standard costs. The standard mixture is as follows: 40% material A at 300 per ton 30% material B at 100 per ton 10% material C at 420 per ton 20% scrap metal of this alloy It is expected that from each charge there will be a 5% loss in melt, 35% returned to scrap stock (runners, heads, etc.) and 60% will be good castings. Scrap is credited and charged at the standard average cost of the metal mixture. In a certain period the following materials are purchased and used: 380 tons material A at 310 per ton 330 tons material B at 110 per ton 90 tons material C at 420 per ton 200 tons scrap metal at standard price From this material, 608 tons of good castings are produced, and 340 tons of scrap metal are returned to scrap metal stock. Prepare a statement of the standard metal costs, and show variances from standard. V. BALANCE SHEET Given the financial data of the following firm for the fiscal year 1/7/2002 to 30/6/2003, prepare for i. Income (profit/loss) statement ii. Balance sheet iii. Calculate, using all indicators, * Liquidity * Efficient use of Assets * Leverage (financing) * Profitability XYZ Company Interest expense 4,750 Depreciation 66,000 Accrued expenses 7,900 Cash 225,000 Common Stock 289,000 Long-Term Debt 334,000 Cost of Goods sold 297,000 Net Sales 573,000 Inventory 99,300 Accounts payable 102,000 Taxes 50,500 General and admin. Expenses 79,000 Accumulated Depreciation 263,000 Buildings and Equipment 895,000 Prepaid expenses 14,500 Notes payable 75,000 Taxes payable 53,000 Accounts receivable 153,000 Retained earnings 262,900-10-
VI. COST ESTIMATING PRODUCTION COST COMPARISON (1) Shells 60 mm long of the shape and dimensions given in the figure are to be produced in big numbers from brass 70/30 of density 8.53 gm/cc. Two processes (A and B) have been suggested for drawing the shells to the final shape. They differ from each other in the shape of initial material. Process A: Uses brass rods 60 mm diameter, and 6 m long. Process B: Uses coined brass strips 10 mm thick and 130 mm wide. Operation sequence for each process is as follows: Process A (starting from rods) Shearing from rod on shearing press (no process scrap). Cold forging into cup on forging press. Soft annealing. Ironing to first shell in a simple die on a drawing press. Soft annealing. Ironing to final shell in 3-stages die on drawing press. Trimming of edge on a trimming press. Process B (starting from strip) Combined blanking and cupping from strips on drawing press (process scrap is present). Redrawing to first shell on a drawing press. Tool cost : Process A 1. Shearing at no cost. 2. Forging tools 40 L.E 3. Tools for simple die 20 L.E 4. Tools for 3 stage die 30 L.E 5. Trimming tools 10 L.E Other data Brass 70/30 costs L.E 500/ton. Scrap cost L.E 300/ton. Press Labor costs L.E 15/8 hrs.day/man. Production of shells 2000 part/8 hrs.day. Overheads amount to 30% of Labor cost.. Soft annealing.ironing to final shell in 3- stages die on a drawing press. Trimming of edge on a trimming press Process B 1. Combined blanking/cupping tools 30 L.E 2. Redrawing tools 20 L.E. 3. Tools for 3-stage die 30 L.E. 4. Trimming tools 10 L.E Annealing costs 5 L.E./ 1000 part/annealed (including furnace Labor). Allow 5 mm in shell height for final trimming and chose the best arrangement of blanks in process B - 11-
Required: 1. Calculate the manufacturing cost in each case if 100,000 parts are to be produced. 2. Find the production volume, which makes the 2 processes beak-even. PRODUCTION COST COMPARISON (2) Details of a job contract between a department manager and a machine shop are as follows : Basic Salary L.E. 2500 per month Housing Allowance 20% of Salary Transportation 10% of Salary Medical Insurance L.E. 250 per month Gratuity 20 days Salary per year Annual Vacation 1 month per year, with Salary Sick leave 10 days/year, with salary Accident Insurance 3% of Basic Salary The company follows a five day week, 8 hours per 5 days. The department manager is scheduled to work overtime 1 hour on normal days and 2 hours on Thursday paid at 150% the normal salary. Nonchargeable hours (tea breaks, washing, changing clothes etc.) are estimated at 6% of the time. The company provides the following fringe benefits. Subsidized meal at 6 L.E although the actual cost is 12 L.E The company provides 2 pairs of shoes, 1 pair of work suit per year costing L.E.900 The company pays 15 days bonus on each Eid vacation. Based on the given data : 1. Calculate the total net working hours per year. 2. Calculate the total amount of expenditure/year 3. What is the gross hourly rate. 4. The company has 5 department managers at the moment. However, the company is considering hiring another department manager to reduce the overtime work. Calculate the total cost under the two circumstances and find out which is more economical. - 12-