Principles of Engineering Economic Analysis, 6th Edition   solutions manual by John A. White, Kenneth E. Case, David B. Pratt

NOTES - CHAPTER 2 SOLUTIONS
FOLLOWING ARE SOME THOUGHTS ABOUT THE PROBLEMS AND SOLUTIONS IN THIS CHAPTER THAT MAY BE OF HELP TO FACULTY AND STUDENTS.
1	THIS IS, PERHAPS, THE MOST CRITICAL CHAPTER IN THE BOOK IN THAT IT DEALS WITH THE "TIME VALUE OF MONEY (TVM)," A FUNDAMENTAL CONCEPT USED THROUGHOUT THE REST OF THE BOOK.
2	THERE ARE 180 BASE PROBLEMS, MANY WITH MULTIPLE PARTS, AND MULTIPLE SOLUTIONS FOR MANY OF THOSE PARTS ARE PRESENTED IN THIS SOLUTION MANUAL
3	THERE ARE FIVE DIFFERENT METHODS THAT ARE SEEN MULTIPLE TIMES IN THESE SOLUTIONS.  THEY INCLUDE USE OF (1) SIMPLE AND COMPOUND INTEREST FORMULAS, (2) INTEREST TABLES SUCH AS THOSE IN APPENDICES A AND B, AS WELL AS "ELECTRONIC" INTEREST TABLES (SEE ITEM 5 BELOW), (3) USE OF MYRIAD EXCEL FUNCTIONS, (4) SEARCH PROCEDURES USING EXCEL'S "SOLVER" AND "GOAL SEEK" TOOLS, AND (5) BRUTE FORCE TABULAR APPROACHES
4	THE COMPOUND INTEREST FORMULAS ARE OFTEN THE MOST ONEROUS TO USE, GIVEN THAT THEY REPRESENT THE FUNDAMENTAL MATHEMATICS OF TVOM.
5	THE INTEREST TABLES REPRESENT THE MOST COMMON APPROACH USED HERETOFORE IN "ENGINEERING ECONOMY" COURSES; THEY USUALLY VASTLY SIMPLIFY THE MATHEMATICS INVOLVED BY INCORPORATING ONE OR MORE COMPOUND INTEREST FORMULAS INTO A SINGLE TABULATED "FACTOR" AVAILABLE IN APPENDICES A AND B.  SINCE THE INTEREST TABLES ARE FOR ONLY A FINITE (ALTHOUGH VERY LARGE) SET OF INTEREST RATES (i AND j) AND TIME HORIZONS (n), THEY MAY NOT BE AVAILABLE FOR A SPECIFIC SET OF i, j, OR n NEEDED.  "ELECTRONIC" INTEREST TABLES ARE AVAILABLE, AND HAVE BEEN USED WHEN UNAVAILABLE TABULATED VALUES OF i, j, AND/OR n HAVE BEEN NEEDED.  PLEASE SEE NOTES 13 AND 14 BELOW FOR MORE DETAIL ON THE USE OF "ELECTRONIC" INTEREST TABLES.
6	PROBLEMS 25, 63, 92, 123, AND 146 ASK FOR THE DEVELOPMENT OF CERTAIN INTEREST FACTORS SUCH AS ARE PRESENTED IN THE INTEREST TABLES.  THESE SERVE TO CONVINCE THE STUDENT THAT THERE IS NO "MAGIC" INVOLVED IN THE INTEREST TABLES.  IN ADDITION, THE FORMULAS USED IN DEVELOPING THE INTEREST FACTORS HAVE BEEN VERY USEFUL TO THE AUTHORS IN "COPY AND PASTE" OPERATIONS IN THE DEVELOPMENT OF THE CHAPTER 2 SOLUTIONS.
7	THE EXCEL FUNCTIONS HAVE NOT TRADITIONALLY BEEN WIDELY USED IN TEACHING "ENGINEERING ECONOMY."  THEY HAVE, HOWEVER, BEEN USED IN THE WORLD OF FINANCE.  THE EXCEL FUNCTIONS ARE WELL DESIGNED, AND PROVIDE A VERY PRECISE TOOL FOR USE IN SOLVING A WIDE ARRAY OF PROBLEMS INVOLVING TVM.  BEWARE!  FOR THE NOVICE, THESE EXCEL FUNCTIONS MAY APPEAR CONFUSING, COMPLEX, AND NOT WORTH THE TIME TO LEARN.  THEY ARE, HOWEVER, QUITE STRAIGHTFORWARD AND CONSISTENT, ONCE ONE GETS PAST THE INITIAL TRIALS OF LEARNING SOMETHING NEW.  THEY ARE LIKELY TO BE YOUR FAVORITE METHOD OF PROBLEM SOLUTION IF YOU USE THEM TO SOLVE OR CHECK YOUR SOLUTIONS IN THIS CHAPTER.
8	SOMETIMES, YOU WILL NEED TO SOLVE FOR A MONETARY VALUE, AN INTEREST RATE, A TIME INTERVAL, A GRADIENT, OR WHATEVER, NEEDED TO MATCH OTHER PARAMETERS OF A PROBLEM (E.G., WHAT INTEREST RATE MAKES AN INVESTMENT OF $100 WORTH $150 IN THREE YEARS).  WHILE IT IS OFTEN POSSIBLE AND CONVENIENT TO USE ANALYTICAL APPROACHES (E.G., ALGEBRA), SOMETIMES THESE SOLUTIONS ARE DIFFICULT AND CUMBERSOME (ANALYTICALLY INTRACTABLE OR NEARLY SO).  SEARCH PROCEDURES CAN BE VERY HANDY IN THESE CASES.  EXCEL PROVIDES "SOLVER" AND "GOAL SEEK," BOTH OF WHICH RECEIVE SOME USE IN THE SOLUTIONS FOR CHAPTER 2.  THE AUTHORS HAVE FOUND SOLVER TO BE QUITE ROBUST AND ACCURATE FOR THE PROBLEMS OF CHAPTER 2.  GOAL SEEK, ALTHOUGH CLOSE, IS NOT QUITE AS CONSISTENT.  BOTH ARE EASY TO USE.
9	THE "BRUTE FORCE" TABULAR APPROACH CAN BE VERY USEFUL WHEN A PROBLEM IS VERY COMPLEX AND DIFFICULT TO KEEP IN MIND WHILE ATTEMPTING TO USE AN INTEREST TABLE APPROACH OR AN EXCEL FUNCTION APPROACH.  IN THESE INSTANCES, IT IS OFTEN USEFUL TO SIMPLY LIST THE ENTIRE SET OF CASH FLOWS, PERIOD BY PERIOD.  THEN, OFTEN AN NPV FUNCTION OR AN FV-PLUS-NPV FUNCTION OR A PMT-PLUS-NPV FUNCTION CAN BE EASILY USED ON THE TABLE.  THE BRUTE FORCE TABULAR APPROACH ALSO HAS THE ADVANTAGE THAT THE ENTIRE PATTERN OF CASH FLOWS CAN BE SEEN AND UNDERSTOOD.  BE CAREFUL!  ACTUALLY, MOST PROBLEMS CAN BE SOLVED USING THE BRUTE FORCE APPROACH - IN FACT, IT IS QUITE COMMONLY USED IN INDUSTRY!  FOR NOW, WHILE LEARNING THIS MATERIAL, USE THE BRUTE FORCE APPROACH ONLY AS A LAST RESORT OR AS A PROBLEM CHECK AS HAS BEEN DONE IN THESE SOLUTIONS.  TO USE THE BRUTE FORCE APPROACH ALONE IN CHAPTER 2 IS TO NOT LEARN THE OTHER APPROACHES.
10	IN THIS CHAPTER, WITH MULTIPLE APPROACHES USED IN SOLVING MANY PROBLEMS, THERE ARE OFTEN SLIGHTLY DIFFERENT SOLUTIONS ACHIEVED.  THESE ARE NOT WRONG!  USUALLY, IF NOT ALWAYS, THE INTEREST FORMULA APPROACH AND THE EXCEL FUNCTION APPROACH WILL BE PRECISELY THE SAME BECAUSE THERE IS VIRTUALLY NO ROUND OFF ERROR WITHIN THE COMPUTER.  THE INTEREST TABLE APPROACH WILL BE SLIGHTLY DIFFERENT, DUE TO THE PRESENTATION OF INTEREST FACTORS TO FIVE PLACES AFTER THE DECIMAL IN MOST CASES.  MANY TABLES USE ONLY FOUR PLACES.  EVEN WITH FIVE PLACES, THERE WILL BE SOME MINOR DISCREPANCIES WHEN COMPARED TO THE EVEN MORE PRECISE APPROACHES.  NOTE THAT SUCH DIFFERENCES ARE ALMOST ALWAYS INCONSEQUENTIAL BECAUSE THE ESTIMATES REQUIRED IN ECONOMIC EVALUATIONS ARE USUALLY ONLY APPROXIMATIONS ANYWAY.
11	EVEN THOUGH MANY PROBLEMS HAVE MULTIPLE PARTS, IT IS NOT INTENDED THAT ALL PARTS OF A PROBLEM NECESSARILY BE ASSIGNED AND WORKED.  IN MANY CASES, THE LEARNING THAT TAKES PLACE CAN BE ACHIEVED BY WORKING ONLY ONE OR TWO PARTS.  SEE, FOR EXAMPLE, PROBLEM 79.
12	WHILE MULTIPLE APPROACHES ARE OFTEN USED HEREIN TO SOLVE A PROBLEM, KEEP IN MIND THAT THERE ARE AN INFINITE (LITERALLY) NUMBER OF WAYS A TVM PROBLEM CAN BE SET UP AND SOLVED.  TRANSLATION - THE SOLUTIONS PRESENTED HEREIN ARE QUITE DIRECT IN THEIR APPROACH, BUT NOT THE ONLY APPROACH.
13	WHEN A SOLUTION MAKES USE OF BOTH INTEREST TABLES AND EXCEL FUNCTIONS, THE ANSWERS WILL OFTEN BE SOMEWHAT DIFFERENT DUE TO ROUNDOFF ERROR IN THE BOOK TABLES.  IN GENERAL, THE EXCEL FUNCTIONS CARRY MANY PLACES WITHIN THE COMPUTER, THEREBY MAKING THEM "EXACT" (REMEMBER, SINCE MOST THINGS IN ENGINEERING ECONOMIC ANALYSIS ARE ESTIMATED, IT IS SOMEWHAT LUDICROUS TO REFER TO MANY SOLUTIONS AS "EXACT").  SOMEWHERE IN BETWEEN THE PRECISION OF EXCEL FUNCTIONS AND THE BOOK'S TABLES ARE "ELECTRONIC" INTEREST TABLES.  A SEPARATE WORKSHEET WITH ELECTRONIC INTEREST TABLES IS AVAILABLE ON THE BOOK WEB SITE.  USING THAT WORKSHEET, THE USER MAY SELECT THE NUMBER OF PLACES FOLLOWING THE DECIMAL TO USE.  HERE IS THE PROTOCOL FOLLOWED IN THE SOLUTIONS TO CHAPTER 2:
	a	IF THE VALUES OF i, j, AND n NEEDED ARE AVAILABLE IN THE BOOK'S TABLES, THEY ARE USED HEREIN TO EMULATE THE PROCEDURE USED BY SOMEONE USING THEM, THIS IS THE TRADITIONAL APPROACH TO ENGINEERING ECONOMIC ANALYSIS.  NOTE THAT MOST FACTORS ARE PRESENTED TO 5 PLACES AFTER THE DECIMAL.
	b	IF THE VALUES OF i, j, AND n NEEDED ARE NOT AVAILABLE IN THE BOOK'S TABLES, THE ELECTRONIC TABLES ARE USED.  IN THIS CASE, THE NUMBER OF PLACES AFTER THE DECIMAL MUST BE DECIDED UPON FOR BOTH THE INPUT VALUES OF i AND/OR j AND ALSO FOR THE FACTOR VALUE ITSELF.  HEREIN, 9 PLACES FOLLOWING THE DECIMAL ARE USED IN ALL CASES.  THE REASON FOR 9 PLACES IS THAT THIS NUMBER IS SIMILAR TO THE NUMBER OF PLACES AVAILABLE ON MANY SCIENTIFIC AND FINANCIAL CALCULATORS.
	c	AS A FIRST EXAMPLE, LET'S DETERMINE THE MONTHLY PAYMENT THAT IS EQUIVALENT TO A PRESENT VALUE OF $10,000 IF INTEREST IS 6% NOMINAL, COMPOUNDED MONTHLY OVER A PERIOD OF 24 MONTHS.
		P=	$10,000.00
		n=	24 MONTHS
		r=	6%	NOMINAL COMPOUNDED MONTHLY
		i=	0.500000000%	PER MONTH
		INTEREST TABLE APPROACH:
		A=	=$10,000*(A|P 6%/12,24)
			=$10,000*(A|P 0.5%,24)
			=10000*0.04432
			$443.20	FE-type Sample Questions for PEEA 6e Chapter 1 Chapter 1 The fact that one should not add or subtract money unless it occurs at the same point in time is an illustration of what concept? (a)   time value of money (b)  marginal return (c)   economy of scale (d)  Pareto principle Answer: (a) If a set of investment alternatives contains all possible choices that can be made, then the set is said to be which of the following? (a)   coherent (b)  collectively exhaustive (c)   independent (d)  mutually exclusive Answer: (b) Which of the following examples does not illustrate a cash flow approach? (a)   a payroll manager writes a check to pay a shop worker (b)  a neighbor pays $0.25 to buy a glass of lemonade at a lemonade stand (c)   a hungry teenager pays for snacks with a debit card (d)  a building contractor buys lumber on account at a local lumber yard Answer: (d) The “discounting” in a discounted cash flow approach requires the use of which of the following? (a)   an interest rate (b)  the economic value added (c)   the gross margin (d)  the incremental cost Answer: (a) Risks and returns are generally ______________ correlated. (a)   inversely (b)  negatively (c)   not (d)  positively Answer: (d) Assuming zero incremental costs for the “do nothing” alternative is generally (a)   appropriate (b)  risky (c)   optimistic (d)  realistic Answer: (b) Answering “what if” questions with respect to an economic analysis is an example of which step in the Systematic Economic Analysis Technique? (a)   identifying the investment alternatives (b)  defining the planning horizon (c)   comparing the alternatives (d)  performing supplementary analysis Answer: (d) Which of the following is useful in making a final selection when multiple criteria exist? (a)   four discounted cash flow rules (b)  seven step systematic analysis technique (c)   ten principles of engineering economic analysis (d)  weighted factor comparison method Answer: (d) Time value of money calculations may not be required in an economic evaluation for all of the following reasons except (a)   annual cash flows are proportional to the first year cash flow (b)  inflation is absent (c)   no investment of capital is required (d)  no differences in the cash flows of the alternatives after the first year Answer: (b) If a student’s time value of money rate is 30 percent, then the student would be indifferent between $100 today and how much in one year? (a)   $30 (b)  $100 (c)   $103 (d)  $130 Answer: (d) A bottled mango juice drink must contain at least 17.0% mango juice for proper taste.  The drink is created by blending unprocessed juice from two orchards.  RightRipe Orchard sells unprocessed mango juice that is 12.5% mango juice and 87.5% base liquids.  PureBlend Orchard sells unprocessed juice that is 20.0% mango juice and 80.0% base.  What percentage of unprocessed juice from each orchard is required to exactly meet the 17.0% specification? (a)   40% RightRipe; 60% PureBlend (b)  50% RightRipe; 50% PureBlend (c)   60% RightRipe; 50% PureBlend (d)  Can not be determined from the information given Answer: (a) A printed circuit board is produced by passing through a sequence of three steps.  The scrap rates for steps one through three are 5%, 3%, and 3%, respectively.  If 10,000 good parts are needed, the number that should be started at step one is closest to which of the following? (a)   11,100 (b)  11,140 (c)   11,190 (d)  11,240 Answer: (c) Reconsider the preceding problem assuming that the sequence can be rearranged such that the processing step with the 5% scrap rate occurs last rather than first.  Using this redesigned sequence, the number of parts that should be started will (a)   Increase (b)  Decrease (c)   Be unchanged (d)  Cannot be determined from the information given Answer: (c) FE-type Sample Questions for PEEA 6e Chapter 2 Chapter 2 A deposit of $3,000 is made in a savings account that pays 7.5% interest compounded annually.  How much money will be available to the depositor at the end of 16 years? (a)   $8,877 (b)  $10,258 (c)   $9,542 (d)  $943               Answer: (c) The plan was to leave $5,000 on deposit in a savings account for 15 years at 6.5% interest compounded annually.  It became necessary to withdraw $1,500 at the end of the 5th year.  How much will be on deposit at the end of the 15 year period? (a)   $11,359 (b)  $9,359 (c)   $12,043 (d)  $10,043               Answer: (d) 3.     A child receives $100,000 as a gift which is deposited in a 6% bank account compounded semiannually.  If $5,000 is withdrawn at the end of each half year, how long will the money last? (a)   21.0 years (b)  15.5 years (c)   25.0 years (d)  18.0 years               Answer: (b) 4.     Your company seeks to take over Good Deal Company.  Your company’s offer for Good Deal is for $3,000,000 in cash upon signing the agreement followed by 10 annual payments of $300,000 starting one year later.  The time value of money is 10%.  What is the present worth your company’s offer? (a)   $3,000,000 (b)  $2,281,830 (c)   $4,843,380 (d)  $5,281,830               Answer: (c) 5.     If you want to triple your money at an interest rate of 6% per year compounded annually, for how many years would you have to leave the money in the account? (a)   12 years (b)  19 years (c)   32 years (d)  cannot be determined without knowing the amount invested. Answer: (b) 6.     Let F be the accumulated sum, P the principal invested, i the annual compound interest rate, and n the number of years.  Which of the following correctly relates these quantities? (a)   F = P (1 + in) (b)  F = P (1 + i)n (c)   F = P (1 + n)i (d)  F = P (1 + ni)n-1 Answer: (b) 7.     The maintenance costs of a car increase by $200 each year.  This cash flow pattern is best described by which of the following? (a)   gradient series (b)  geometric series (c)   infinite series (d)  uniform series Answer: (a) 8.     If you invest $5,000 three years from now, how much will be in the account fifteen years from now if i = 10% compounded annually. (a)   $8,053 (b)  $15,692 (c)   $20,886 (d)  $27,800 Answer: (b) 9.     The president of a growing engineering firm wishes to give each of 20 employees a holiday bonus.  How much needs to be deposited each month for a year at a 12% nominal rate, compounded monthly, so that each employee will receive a $2,500 bonus? (a)   $2,070 (b)  $3,840 (c)   $3,940 (d)  $4,170 Answer: (c) 10.  What is the annual interest rate if a simple interest loan of $10,000 for four years charges a total of $2,800 interest?  The loan is repaid with a single payment at the end of year four. (a)   7.0% (b)  28.0% (c)   i such that 12,800 = 10,000 (F|P,i,4) (d)  cannot be determined from the information given Answer: (a) 11.  What is the effective annual interest rate if the nominal annual interest rate is 24% per year compounded monthly? (a)   2.00% (b)  24.00% (c)   26.82% (d)  27.12% Answer: (c) 12.  Under what circumstances are the effective annual interest rate and the period interest rate equal? (a)   Never true (b)  If the number of compounding periods per year is one (c)   If the number of compounding periods per year is infinite (d)  Always true Answer: (b) 13.  Consider the following cash flow diagram.  What is the value of X if the present worth of the diagram is $400 and the interest rate is 15% compounded annually? 200 X X 0 1 2 3 (a)   $246 (b)  $165 (c)   $200 (d)  $146 Answer: (b) 14.  A young engineer calculated that monthly payments of $A are required to pay off a $5,000 loan for n years at i% interest, compounded annually.  If the engineer decides to borrow $10,000 instead with the same n and i%, her monthly payments will be $2A. (a)   TRUE (b)  FALSE (c)   Can not be determined without knowing the value of n and i (d)  Can not be determined without knowing the value of n or i Answer: (a)