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SOLVED PROBLEMS INENGINEERING ECONOMY & ACCOUNTING Submitted by: MICHAEL ERNIE F. RODRIGUEZ BS Electrical Engineering – 4 Submitted to: ENGR. IAN D. VALDEZTAMON Instructor IE 41: Engineering Economy & Accounting SIMPLE INTEREST COMPOUND INTEREST 1. A man borrowed P10,000.00 from his friend and 4. A man is expecting to receive P450,000.00 at the agrees to pay at the end of 90 days under 8% end of 7 years. If money is worth 14% simple interest rate. What is the required amount? compounded quarterly, how much is it worth at present? 2. What is the principal amount if the amount of 5. Mr. Adam deposited P120,000.00 in a bank who interest at the end of 21/2 year is P4500 for a offers 8% interest compounded quarterly. If the simple interest of 6% per annum? interest is subject to a 14% tax, how much will he receive after 5 years? 3. How long must a P40,000 note bearing 4% 6. A person invests P4500 to be collected in 8 years. simple interest run to amount to P41,350.00? Given that the interest rate on the investment is 14.5% per year compounded annually, what sum will be collected in 8 years? ORDINARY ANNUITY DEFERRED ANNUITY 7. A contractor bought a concrete mixer at 10. On the day his grandson was born, a man P120,000.00 if paid in cash. The mixer may also deposited to a trust company a sufficient amount be purchased by installment to be paid within 5 of money so that the boy could receive five years. If money is worth 8%, determine the annual payments of P10,000 each for his college amount of each annual payment, if all payments tuition fees, starting with his 18th birthday. are made at beginning of each year. Interest at the rate of 12% per annum was to be paid on all amounts of deposit. There was also a provision that the grandson could elect to withdraw no annual payments and receive a single lump amount on his 25th birthday. The grandson chose this option. a. How much did the boy receive as the single payment? b. How much did the grandfather deposit? 8. A man is left with an inheritance from his father. He has an option to receive P2 M at the end of 10 years, however he wishes to receive the money at the end of each year for 5 years. If interest rate is 8%, how much would he receive every year? 11. If P10,000 is deposited each year for 9 years, how much annuity can a person get annually from the bank every year for 8 years starting 1 year after the 9th deposit is made. Cost of money is 14% 9. What is the accumulated value of a payment of P 12. A debt of P40,000, whose interest rate is 15% 6,000 every six months for 16 years with interest compounded semiannually, is to be discharged at 7% compounded semiannually? by a series of 10 semiannual payments, the first payment to be made 6 months after consummation of the loan. The first 6 payments will be P6,000 each, while the remaining 4 payments will be equal and of such amount that the final payment will liquidate the debt. What is the amount of the last 4 payments? ANNUITY DUE PERPETUITY 13. A man bought an equipment costing P60,000 16. If money is worth 8%, determine the present payable in 12 quarterly payments, each value of a perpetuity of P1,000 payable annually, installment payable at the beginning of each with the first payment due at the end of 5 years? period. The rate of interest is 24% compounded quarterly. What is the amount of each payment? 14. A certain property is being sold and the owner 17. What amount of money invested today at 15% received two bids. interest can provide the following scholarships: The first bidder offered to pay P400,000 each P30,000 at the end of each year for 6 years; year for 5 years, each payment is to be made at P40,000 for the next 6 years and P50,000 the beginning of each year. The second bidder thereafter? offered to pay P240,000 first year, P360,000 the second year and P540,000 each year for the next 3 years, all payments will be made at the beginning of each year. If money is worth 20% compounded annually, which bid should the owner of the property accept? 18. P25,000 is deposited in a savings account that pays 5% interest compounded semi-annually. Equal annual withdrawals are to be made from the account beginning one year from now and continuing forever. Determine the maximum amount of equal annual withdrawals. 15. What is the annuity due having the following data? Annual payment = P12,000 Number of years = 6 years Interest rate = 12% compounded annually STRAIGHT LINE DEPRECIATION SINKING FUND METHOD 19. An equipment costing P250,000 has an estimated 22. An equipment costing P250,000 has an estimated life of 15 years with a book value of P30,000 at life of 15 years with a book value of P30,000 at the end of the period. Calculate the depreciation the end of the period. Compute the depreciation charge and its book value after 10 years. charge and its book value after 10 years, assuming i = 8%. 20. An engineer bought an equipment for P500,000. 23. A broadcasting corporation purchase an Other expenses including installation amounted equipment for P53,000 and paid P1,500 for to P30,000. At the end of its estimated useful life freight and delivery charges to the job site. The of 10 years, the salvage value will be 10% of the equipment has a normal life of 10 years with a first cost. What is the book value after 5 years? trade-in value of P5,000 against the purchase of a new equipment at the end of the line. Determine the annual depreciation cost. Assume interest at 6-1/2% compounded annually. 21. A machine costs P 8,000.00 and an estimated life 24. A firm bought an equipment for P56,000. Other of 10 years with a salvage value of P500.00. expenses including installation amounted to What is its book value after 8 years? P4,000. The equipment is expected to have a life of 16 years with a salvage value of 10% of the original cost. Determine the book value at the end of 12 years at 12% interest. SUM OF THE YEARS DIGIT METHOD CAPITALIZED COST 25. An equipment costing P250,000 has an estimated 28. Determine the capitalized cost of an equipment life of 15 years with a book value of P30,000 at costing P2M with an annual maintenance of the end of the period. Compute the depreciation P200,000.00 if money is worth 20% per annum. charge and its book value after 10 years. 26. An asset is purchased for P120,000.00. Its 29. At 6%, find the capitalized cost of a bridge whose estimated economic life is 10 years, after which cost is P200M and life is 20 years, if the bridge it will be sold for P12,000.00. Find the must be partially rebuilt at a cost of P100M at the depreciation for the first year. end of each 20 years. 27. An asset is purchased for P9,000.00. Its 30. An item is purchased for P100,000.00. Annual estimated life is 10 years, after which it will be costs are P18,000.00. Using 8%, what is the sold for P1,000.00. Find the book value during capitalized cost of perpetual service? the third year. 31. A company uses a type of truck which costs P2M, 34. The purchase of a motor for P6000 and a with life of 3 years and a final salvage value of generator for P4000 will allow a company to P320,000. How much could the company afford produce its own energy. The configuration can be to pay for another type of truck for the same assembled for P500. The service will operate for purpose, whose life is 4 years with a final salvage 1600 hours per year for 10 years. The value of P400,000, if money is worth 4%? maintenance cost is P300 per year and the cost to operate is P0.85 per hour for fuel and other related cost. Using straight-line depreciation, what is the annual cost in the operation? There is P400 in salvage value for the system at the end of 10 years. 32. A new engine was installed by a textile plant at a cost of P300,000 and projected to have a useful life of 15 years. At the end of its useful life, it is estimated to have a salvage value of P30,000. Determine its capitalized cost if interest is 18% compounded annually. 35. Given: First Cost = P50,000 Salvage Value = P2,000 Annual maintenance = P6,000 Economic life = 5 years Compute for the annual cost. ANNUAL COST 33. A community wishes to purchase an existing 36. A printing machine is bought at P1.5 million and utility valued at P500,000 by selling 5% bonds is estimated to have a salvage value of P100,000 that will mature in 30 years. The money to retire after 500,000 copies. The annual cost of renting the bond will be raised by paying equal annual the space for the business is P80,000, power cost amounts into a sinking fund that will ern 4%. per copy is P1.50, and maintenance and paper What will be the total annual cost of the bonds cost per copy is P4.00. The expected annual until they mature? production of the machine is 100,000 copies. Annual interest is 15%. Compute for the total annual cost. 37. Determine the annual cost of CICC that requires 40. An investor pays P1,100,000 for a mine which P480M to construct, P25M per year to maintain will yield a net income of P200,000 at the end of and with a book value of P50M after 20 years, if each year for 10 years and then will become interest rate is 18%. useless. He accumulates a replacement fund to recover his capital by annual investments at 4.5%. At what rate (%) does he receive interest on his investment at the end of each year? CAPITAL RECOVERY 38. A mine is purchased for P1,000,000.00 and it is 41. Machine cost = $15,000; Life = 8 years; Salvage anticipated that it will be exhausted at the end of Value = $3,000. What minimum cash return 20 years. If the sinking-fund rate is 4%, what would the investor demand annually from the must be the annual return from the mine to realize operation of this machine if he desires interest a return of 7% on the investment? annually at the rate of 8% on his investment and accumulates a capital replacement fund by investing annual deposits at 5%? 39. A syndicate wishes to purchase an oil well which, 42. A company must relocate one of its factories in estimates indicate, will produce a net income of three years. Equipment for the loading duck is P2M per year for 30 years. What should the being considered for purchase. The original cost syndicate pay for the well if, out of this net P20,000, the salvage value after three years is income, a return of 10% of the investment is P8,000. The company’s rate of return (i) on desired and a sinking fund is to be established at money is 10%. Determine the capital recovery 3% interest to recover this investment. rate per year. BONDS 46. A man wants to make 14% nominal interest compounded semi-annually on a bond 43. A P100,000, 6% bond, pays dividend semi- investment. How much should the man be annually and will be redeemed at 110% on July willing to pay now for a 12%. P10,000-bond that 1, 1999. Find its price if bought on July 1, 1996, will mature in 10 years and pays interest semi- to yield an investor 4%, compounded semi- annually? annually. 47. Mr. Romualdo bought a bond having a face value of P1,000 for P970. The bond rate was 14% 44. A man paid P110,000 for a P100,000 bond that nominal and interest payments were made to him pays P4,000 per year. In 20 years, the bond will semi-annually for a total of 7 years. At the end of be redeemed for P105,000. What net rate of the seventh year, he sold the bond to a friend at a interest will the man obtain on his investment? price that resulted a yield of 16% nominal on his investment. What was the selling price? 45. A man wants to make 14% nominal interest BREAK-EVEN ANALYSIS compounded semi-annually on a bond investment. How much should the man be 48. XYZ Corporation manufactures bookcases that it willing to pay now for a 12%, P10,000 bond that sells for P65.00 each. It costs XYZ P35,000.00 will mature in 10 years and pays interest semi- per year to operate its plant. This sum includes annually? rent, depreciation charges on equipment, and salary payments. If the cost to produce one bookcase is P50.00, how many cases must be sold each year for XYZ to avoid taking a loss? 49. A Company that manufactures electric motors 52. The annual maintenance cost of a machine is has a production capacity of 200 motors a month. P70,000. If the cost of making a forging P56 and The variable costs are P150.00 per motor. The its selling price is P125 per forged unit. Find the average selling price of the motors is P275.00. number of units to be forged to break even. Fixed costs of the company amount to P20,000.00 per month which includes taxes. What is the number of motors that must be sold each month to break even? 50. Determine the break-even point in terms of number of units produced per month using the following data: (the costs are in pesos per unit) Selling price per unit P600 Total monthly overhead expenses P428,00 Labor cost P115 Cost of materials P76 Other variable cost P2.32 51. The cost of producing a small transistor radio set consists of P23.00 for labor and P37.00 for materials. The fixed charges in operating the plant are P100,000 per month. The variable cost is P1.00 per set. The radio set can be sold for P75.00 each. Determine how many sets must be produced per month to break-even.