principles of engineering economic analysis

ENGR 345-02 Prof. Hatem Elayat Engineering Economy Phone: 2615-3078 LEC UW 8:30-9:45 CP35 / SSE Office Hours: UW, 10:00-11:00 Fall 2012 or by appointment, SSE 2029 Email: [email protected] TA: Irene Fahim, SSE 2004 Office Hrs: UW, 10:00-11:00 am [email protected]

SYLLABUS Course Description & Motivation Engineering Economy involves formulating, estimating, and evaluating economic outcomes of alternatives to realize a specified goal. It presents mathematical and practical methods for evaluating decisions in the design and operation of engineering systems. These methods support the selection and justification of design alternatives, operating policies, and capital expenditure. The topics covered include time value of money, evaluation methods, depreciation and inflation, cost benefit analysis, replacement analysis, and notions on capital budgeting and sensitivity analysis. With the successful completion of this course, you will be able to apply Engineering Economy concepts and tools to select the most economically attractive alternative and to assess the feasibility of engineering or business projects. This course will help you compliment your technical knowledge with the ability to identify the most economically viable avenue to achieve the objectives of your engineering project. It will help you make financially prudent decisions in your day-to-day life. With a combination of lectures, exercises, real life applications, I will introduce the key concepts and guides you through the required steps to use Engineering Economy approaches relevant to you as a future-practicing Engineer. Catalog Course Description Economic and cost concepts, the time value of money, Single, multiple and series of cash, flows, gradients, functional notation, nominal and effective interest rates, continuous compounding, rates of return. Computation and applications, economic feasibility of projects, worth of investments, comparison of alternatives. Replacement, depreciation and break-even analysis. Introduction to risk analysis. Prerequisites MATH 231

Course Objectives The primary goal of this course is to provide the students with the ability to apply economic approaches to evaluate investment opportunities and to assess the feasibility of engineering and business projects. Course Outcomes

With the successful completion of this course you will be able to: 1. Apply the basic concepts of engineering economy as part of a decision making

process. 2. Derive and use the different engineering economy factors. 3. Evaluate investment opportunities and compare between alternatives using single and

combined engineering economy factors. 4. Perform a replacement study considering inflation and indirect cost allocation. 5. Use depreciation and depletion models. 6. Perform breakeven analysis and sensitivity analysis under uncertainty conditions. 7. Utilize spreadsheet functions to perform economic calculations. Text White, Case, Pratt and Agee, 2010, Principles of Engineering Economic Analysis, 5th edition, John Wiley & Sons, Inc. ISBN 978-0-470-11396-7. Software We will use Microsoft Excel to assist in processing and analyzing data for assignments. Use of Computers Students can use their personal computers, iPads, or other computers to which they have access. In addition to using computers, students should have a good engineering calculator (TI 83 or TI 89) to use for some class assignments and quizzes. Course Website: Blackboard Lectures, handouts, assignments, announcements and other information will be available on the course website on Blackboard. The following modules are included on Blackboard:

1. Course outline 2. Lectures 3. Handouts 4. Review problems 5. Assignments 6. Projects

7. Solution to Quizzes & past exams 8. Grades

Email Policy Please include in the subject line the course code ENGR 345 and a concise and clear statement of purpose; otherwise it may be deleted, along with spam messages and messages potentially containing viruses. Lectures I will use overheads during lectures and will put copies on Blackboard. Other details will be given on the board. You should read the material before lecture so that you have some idea of what will be discussed even if you don't understand everything. Please ask questions as I go along. Most of our time will be spent covering more difficult material rather than things you can understand easily. Class lectures definitely will not replace reading the textbook. Handouts, will be posted on Blackboard Course Requirement

1. Six review problem sets are posted on Blackboard and students are expected to complete these sets, which will be reviewed in class.

2. Five spreadsheet assignments are posted on Blackboard and students are expected to complete the assignments and turn them in on the due dates. No late assignments will be accepted.

3. Unannounced quizzes will be given to students at regular intervals. 4. Each student is expected to complete a project and write a report describing the

work done. Students are required to turn in the reports on the due date and give an oral presentation.

5. Two mid-term examinations and a final examination. The dates for these exams are listed below.

Review Problems At the end of every chapter there is a set of review problems, posted on Blackboard, and their solution. The only way you can understand the subject material and do well in this course is by actually solving problems. Hence, it is recommended that you solve the review problems. Not only will this help you to understand the basic concepts but also considerably reduce the amount of time you will need to solve a problem. Both of these will benefit you when taking the examinations. Spreadsheet Assignments Five computer assignments will be given during the semester, and are posted on Blackboard. You must use EXCEL to solve each assignment. Tentative due dates are listed below. Assignments are posted on Blackboard. Assignments will be collected at the

beginning of class on the due date. Please turn in your assignment as you enter class. Students who enter late should turn in their assignment when they arrive, not at the end of the class after any review has taken place. Assignments turned in by students after the due date will not receive any credit unless prior arrangements have been made. Assignment Tentative Due Date 1 October 10, 2012 2 October 21, 2012 3 November 11, 2012 4 November 28, 2012 5 December 12, 2012 Quizzes Unannounced quizzes will be given at regular intervals covering recent material discussed in class. No make up allowed if you miss a quiz. If you miss a class because of illness, notify the department office (2615-3063, 2615-

3153) immediately (same day). If a quiz is given that day, you will be given the quiz at a later date provided: 1. You notified the department about your illness immediately, 2. You provide a medical note from AUC Medical Clinic.

Missing class, because of travel or engagement in AUC activities requires prior instructor written approval one week before that date.

Project Students are divided into groups of 3-4 and are assigned a project were they are expected to use some of the tools learned in this course. The project grade is determined based on: 1. Content 2. Written Report 3. Class Presentation 4. Student participation The report must be type written (3 5 pages). No special cover required. Title sheet stapled to the report is recommended. The report will be graded for writing style as well as analysis, recommendations and conclusions. The outline to be followed is: Executive summary Introduction Analysis Conclusions & recommendations References A 15 minutes power point presentation done as a group: Describe the scope of your analysis - What did you consider?

Results - What is the economic merit of project? Sensitivity/Monte Carlo simulation - What conditions / assumptions effect your results? Recommendations Exams The first midterm examination covers topics discussed in week 1-5. The second midterm examination covers topics discussed in week 6-10. The final examination is comprehensive. Students will be tested on material covered in class. All exams will be closed book and notes. If you miss an exam because of illness, notify the department office (2615-3063,

2615-3153) immediately (same day) & provide a medical note from AUC Medical Clinic before a make-up exam will be allowed. Failure to do so will earn you zero credit on the exam.

If you miss an exam because of travel or other circumstances, prior instructor written approval is required one week before the exam.

Tentative Dates Midterm Exam I will be given on Sunday October 7, 2012. Midterm Exam II will be given on Wednesday November 14, 2012. Final Exam will be given during Final week. Class Participation The student is expected to read the material to be discussed before the class meeting. Several handouts will be distributed in class or posted on Blackboard to supplement the textbook. These handouts will be discussed in class. Each student is responsible for the material discussed and the instructions given in class even if he or she is absent. Always bring your textbook and calculator or iPad to class. Active student participation in class discussions is encouraged. Come to class prepared by reading the material assigned and solving homework problems. Grading Spreadsheet Assignments 10 % Quizzes 10 % Project 10 % Midterm 1 20 % Midterm 2 20 % Final Exam 30 %

The grades in ENGR 345 will be awarded as follows: 90% - 92.99% = A- 93% or better = A 80% 82.99% = B- 83% - 86.99% = B 87% - 89.99% = B+ 70% 72.99% = C- 73% - 76.99% = C 77% - 79.99% = C+ 60% 64.99% = D 65% - 69.99% = D+ below 60% = F Topical Breakdown

Role of engineering economy in the decision making process Nominal and effective interest rates and continuous compounding Derivation of engineering economy factors and use of multiple factors Present worth and capitalized cost evaluation Equivalent uniform annual worth evaluation Rate of return and Minimum attractive rate of return computation Benefit/Cost ratio evaluation Replacement analysis Inflation, cost estimation and indirect cost allocation Depreciation and depletion models Break-even analysis and payback period Minimum attractive rate of return Sensitivity analysis and expected value decisions

Academic Dishonesty

Academic dishonesty is not tolerated at AUC and is subject to academic discipline ranging from a mark of zero on the exam or assignment/quiz to dismissal from the university. Academic Regulations Class policy regarding add, drops, incomplete, absences, cheating, etc. will be in accordance with the university rules and regulations. Students will turn their cell phones off or put them on vibrate mode while in class. They will not answer their phones in class or send text messages. Important Dates September - This class begins Sunday September 2 2012 October

- Deadline to drop courses, October 24, 2012 - Eid El Edha (H) October 25 29, 2012

November - Deadline for withdrawal from the semester (undergraduate) Sunday November 25, 2012

December - Last day of regular classes, Thursday December 13, 2012 - Final Exams, December 15 20, 2012

Summary of Discrete Compounding Interest Factors

(F / P,i,n) = (1+ i)n

(P / F,i,n) = 1(1+ i)n

(P / A,i,n) = (1+ i)n 1

i(1+ i)n

(A / P,i,n) = i(1+ i)n

(1+ i)n 1

(F / A,i,n) = (1+ i)n 1i

(A / F,i,n) = i(1+ i)n 1

(P /G,i,n) = (1+ i)n in 1

i2 (1+ i)n

(A /G,i,n) = 1i

n(1+ i)n 1

P =A11 (1+ j)n (1+ i)n

i j

nA11+ i

i j

i = j

for

ieffective = (1+rm)m 1

Period interest Rate = Nominal Annual interest RateNumber of interest Rates per period

The number of interest periods (n) must be adjusted to match the new frequency

Summary of Continuous Compounding Interest Factors

Bonds P = Vr (P/A, i, n) + F (P/F,i,n) where P = the purchase price of a bond F = the sales price (redemption value) of a bond V = the par or face value of a bond r = the bond rate per interest period i = the yield rate (return on investment or rate of return) per interest period n = the number of interest payments received by the bondholder A = Vr = the interest or coupon payment received

Find Given Factor Symbol P F ern (P / F,r,n)

F P ern

(F / P,r,n)

F A ern 1er 1

(F / A,r,n)

A F er 1ern 1

(A / F,r,n)

P A ern 1

ern (er 1) (P / A,r,n)

ieff = er 1

Effective Interest Rate in Continuous Compounding

Loans 1. Principal outstanding (unpaid principal) at beginning of period k

2. Unpaid principal after making k payments

3. Payoff quantity is the total amount required to payoff the loan at k (including current payment & unpaid balance)

4. Interest in the k-th payment

5. Principal contained in the k-th payment

Capitalized Cost

Annuity

An annuity is an asset that pays a fixed sum each year for a specified number of years. Present value of annuity. To to consider a growth g, then replace A by A/(1+g) and I by (i-g)/1+g) External Rate of Return ERR

= A 1 (1+ i)(n+ k1)

i

Uk = A(P / A,i,n k)

Payoffk = A +Uk = A[1+ (P / A,i,n k)]

Ik = A 1 (1+ i)(n+ k1) = A 1 (P / F,i,n k +1)[ ] = iUk1

Ek = A(1+ i)(n+ k1) = A(P / F,i,n k +1) = A Ik

P = Ai

P = A[1i

1i(1+ i)t

]

Rjtr=0

n

(1+ rt )n t = Cjtt=0

n

(1+ i ' )n t

where

i ' is the ERR

Rjt Positive cash flow for investment j during period t

Cjt Negative cash flow for investment j during period t

rt Reinvestment rate for net positive cash flows occurring in Period t, normally it is MARR

Savings / Investment Ratio SIR

SL Depreciation DB Depreciation Sum of the YearsDigits

Depreciation Dt Dt = (P F)/n Dt = pBt-1 Dt = [{n-(t-1)}(P-F)] /

[n(n+1)/2] Bt Bt = P t[(P = F)/n] Bt = P(1=p)t Bt = F+(P F) [(n-t)(n-

t+1)]/[n(n+1)]

SIRj (i) =Rjt (1+ i)

t

t=0

n

Cjt (1+ i) t

t=0

n

where

SIRj (i)Is the savings / investment ratio for investment Alternative j based on a MARR of i%

Rjt Positive cash flow for investment j during period t

Cjt Negative cash flow for investment j during period t Depreciation

Expected Value: E[X] =

i xi p(xi) or

Variance: Var[X] =

i (xi - E[X]) 2p(xi) or

xf (x)dx

(x E(x))2

f (x)dx

ENGR 345, Dr. Hatem Elayat, AUC

ENGR 345 Projects Guideline Dr. Hatem Elayat

DELIVERABLES Produce a technical report that describes the pertinent aspects of your project. The report should consist of the following sections: 1. Executive Summary A one page description of your overall teams efforts and findings. 2. Introduction -- Overall description of the project (where, when, why, current status, participants, etc.). How you collected data/information (interviews via phone or email or in-person), online material, journals, magazines, public records, etc.) 3. Project Details

- Financial aspects and feasibility planning aspects of the project (optional depends

on availability of information)

- How were the activities planned (this is optional depends on availability of information)

- How was the project monitored and controlled (optional depends on availability of

information) - A review of the project (any specific problems and challenges that were

encountered in the delivery of the project, any successes worth mentioning, etc.) - Project learning: identify any additional lessons that could be learned from this

project for the benefit of future similar projects.

4. Overall discussion. This should be your teams overall critique of the project and how it was managed. Discuss each item provided under Section 3 of the report. Here do not just state what was done (as you did in Section 3) but add your opinion on whether it was done right or wrong and why. This may include finance, evaluation, planning, monitoring and control, planning and organization, how well the project was managed in terms of relevant performance metrics (time delays, work quality, etc.), project learning opportunities made available by the project, and any other points of view you have about the project.

5. Summary and conclusions 6. Acknowledgements (of your data sources especially if they are individuals or

organization you actually communicated with via phone, email, or in person)

7. References (reports, journals, manuals, codes, etc.). Use a consistent style of referencing citation and listing)

8. Appendices or Exhibits. The appendix should include a page showing the

organizational framework (team members, respective tasks, and linkages) used for

ENGR 345, Dr. Hatem Elayat, AUC

your study. You may add the team photo as an appendix.

Formatting specifications for the report preparation:

1. 2,000 to 5,000 words. 2. 1-inch margins 3. Use any font style or size 4. 1.5 spacing

Photos, figures, charts, etc. may be added but should be legible, and captions should be provided. Also, Tables may be provided and table titles should be provided. Kindly edit your report carefully for errors in grammar, sentence structure, etc. Also, please check to ensure that your writing style is coherent, lucid, and technical. Submissions should be in both soft copy and hard copy. ORAL PRESENTATIONS You will have 15 minutes for the presentation. You may present the material you submitted in your report. Use Power Point presentation.

ENGR 345: Engineering Economy Hatem Elayat

Mechanical Engineering Department American University in Cairo AUC

Spreadsheet Assignment 1

This assignment introduces you to basic engineering economy formulas and financial functions that are included with Excel. Refer to lectures Module 2 (Time value of money) posted on Blackboard p. 111 118, for additional detail on some of these functions. You will become familiar with the following functions:

NOMINAL(effect_rate, npery) - computes nominal rate EFFECT(nominal_rate, npery) - computes effective rate RATE(nper,pmt,pv,fv,type,guess) - computes interest rate of an annuity (periodic amounts are the 'pmt' values) PV(rate,nper,pmt,fv,type) - computes present worth value of periodic amounts; does not include any cash flow in year 0 FV(rate,nper,pmt,pv,type) - computes the future worth value of an periodic payments NPV(rate,value1,value2, ...) - computes the PW of some non-uniform stream of cash flows; does not include cash flow in year 0 Use Excel to solve the following problems: Problem 1: Solve the following problems manually and then check your answers with the appropriate financial function in Excel.

NOTE: The financial functions themselves may not be enough to solve the problems. You may need to write equations that use the financial functions.

Part 1 NOMINAL function - What quarterly interest rate is equivalent to an effective annual rate of 8% per year, compounded quarterly?

Part 2 EFFECT function - What effective interest rate per quarter is equivalent to a nominal 12% per year, compounded monthly?

Part 3 RATE function - If $5000 is invested now in a franchise that promises the investment will be worth $10,000 in 3 years, what is the earned rate of return?

Part 4 PV function - How much money can you borrow now if you promise to repay the loan in 10 year-end payments of $3000, starting 1 year from now, if the interest rate is 18% per year?

Part 5 FV function - How much money will you have 12 years from now if your take your Christmas bonus of $2500 each year and buy shares in a stock mutual fund that earns 16% per year?

Part 6 NPV function - For the cash flows shown, calculate the present worth in year 0. Assume i = 14% per year.

Year 1 2 3 4 Cash Flow$ 4000 3200 2400 1600

Problem 2 You borrow $100 for n years & you want to compare the following two rates: - At 10% per year simple interest - At 10% per year compound interest

Plot the amount owed after n years for both simple & compound interest, for n = 1, 2, , 20, and compare on the same graph. (The x-axis should be n = 1, 2, , 20). Discuss the results. Problem 3 You borrow $100 for n years & you want to compare & plot the amount owed after n years at the following compound rates, 5%, , 10%, 15%, & 20%. Plot the amount owed versus n for all rates on the same graph. (The x-axis should be n = 1, 2, , 10). Discuss the results. Problem 4 For the Uniform Series Present Worth Factor (P/A, i, n), plot the following curves for n = 1, 2, 10, and the compound interest i = 0%, 5%, 10%, 15%, & 20% on the same graph. Discuss the results. (The x-axis should be n = 1, 2, , 10)

ENGR 345: Engineering Economy Hatem Elayat Mechanical Engineering Department American University in Cairo AUC


Use Excel to solve the following problems: Problem 1 You are asked to compare the arithmetic and geometric gradient cash flow series. The base amount A1 (an input variable entered by the user, use $1000), the compound interest rate i is 10%, the constant G in the arithmetic series is 10% of A1, the percent change j in the geometric series is 10%, and n = 0, 1, 2, 5. Plot the end of period amount versus the period n for both the arithmetic and geometric series on the same graph. Discuss the results. Problem 2 Ahmad purchased a car for 150,000 EP. The down payment is 15,000; the balance is financed over a 5-year period. Equal monthly payments are made. If the monthly interest rate is 1%, prepare

A. A table showing the month, the interest paid, and the principal contained in each month payment

B. Plot interest paid each month versus the period n = 1, 2, , 60. (The x-axis should be n = 1, 2, , 60). Show on the graph the principal contained in each month payment

Problem 3 Develop a general-purpose spreadsheet to calculate out the balance due, principal payment, and interest payment for each period of the loan. The user inputs to the spreadsheet will be the loan amount, the number of payments per year, the number of years payments are made, and the nominal interest rate. Submit printouts of your analysis of a loan in the amount of $15,000 at 8.9% nominal rate for 36 month and for 60 months of payments. Problem 4 You borrowed $5,000 from a bank, and you have to pay it back in 5 years. Interest is 8%/yr/yr. create the following table and complete for 5 years. year Amount

owed Interest owed

Total owed Principal Payment

Total Payment

1 2 3 4 5 SUM Set up the table to allow the user to change the amount and interest rate charged. Problem 5

Repeat problem 4 and create a similar table if you pay the principal and interest in one payment at the end of 5 years. Problem 6 Repeat problem 4 and create a similar table if you pay interest due at the end of each year and principal in one payment at the end of 5 years.

ENGR 345: Engineering Economy Hatem Elayat

Mechanical Engineering Department American University in Cairo AUC


1. Brock Associates invested $80.000 in a business venture with the following cash flow results. EOY CF $ EOY CF $ EOY CF $ 0 -80,000 3 22,000 6 22,000 1 10,000 4 28,000 7 16,000 2 16,000 5 28,000 8 10,000 IF MARR is 12 % determine the following a. Present worth b. Annual worth c. Future worth d. Internal rate of return e. External rate of return f. Saving/ investment ration g. Payback period without considering the time value of money

2. Shrewd Endeavors, Inc. invested $70.000 in a business venture with the following cash flow results. EOY CF $ EOY CF $ EOY CF $ 0 -70,000 7 14,000 14 7,000 1 20,000 8 13,000 15 6,000 2 19,000 9 12,000 16 5,000 3 18,000 10 11,000 17 4,000 4 17,000 11 10,000 18 3,000 5 16,000 12 9,000 19 2,000 6 15,000 13 8,000 20 1,000 Assuming MARR to be 10 % determine the following a- Present worth b- Annual worth c- Future Worth d- Internal rate of return e- External rate of return f- Saving/ investment ration g- Payback period without considering the time value of money

3. An investment of $20.000 is to be made on a computer that will last for 6 years and have a zero salvage value at that time. Operating, maintenance, and software costs are projected to be $15.000 the first 3 years and $20.000 the last 3 years. The minimum attractive rate of return is specified to be 12%. Determine for this investment the following. a- Present worth b- Annual worth C-Future Worth

4. A utility vehicle is purchased for $30.000, kept for 4 years, and sold for $7500. Annual operating and maintenance costs were $5000. Using a 10% minimum attractive rate of return, determine the following. a-Present worth b-Annual worth c-Future Worth

5. Owners of an economy motel chain are considering building a new 200-unit motel. The present worth cost of building the motel is $8.000.000; the firm estimates furnishings for the motel will cost an additional $800.000 and will require replacement every 5 years. Annual operating and maintenance costs for the facility are estimated to be $800.000. The average rate for a unit is anticipated to be $60/ day. A 15-year planning horizon is used by the firm in evaluating new ventures of this type; a terminal salvage value of 15% of the original building cost is anticipated; furnishings are estimated to have no salvage value at the end of each 5-year replacement interval. Assuming average daily occupancy percentages of 50%, 60%, 70%, 80% for years 1 through 4, respectively, and 90% for the fifth and each remaining year, MARR of 12%, 365 operating days/year, and ignoring the cost of the land, should the motel be built? Base your decision upon the following values. a-Present worth b-Annual worth c-Future Worth d-Internal rate of return e-External rate of return f-Saving/ investment ration

6. A floor control project has a construction cost at t = 0 of $2.000.000, an annual maintenance cost of $50.000, and a major repair at 5-year intervals projected to cost $250.000 with the first such repair occurring at t = 5. If interest is 8% annually, determine the amount of money needed at t = 0 to provide for construction and perpetual upkeep.

7. A distillation column is purchased for $300.000. Operating and maintenance costs for the first year are $30.000. Thereafter, operating and maintenance costs increase by 10% / year over the previous year's costs. At the end of 8 years the column is sold for $50.000. During the life of the investment, revenue was produced that could be related directly to the investment in the column. The revenue the first year was $75.000. Thereafter, revenue increased by $10.000 over the previous year's revenue. Using a MARR of 12%, determine the equivalent annual worth for the investment.

8. What should be entered in cells B11 through B15 to obtain the values for PW, AW, FW, IRR, and SIR using Excel? Determine the values for PW, AW, FW, IRR, and SIR. R/C A B 1 MARR= 0.1 2 3 Time Cash flow 4 0 -$ 25,000.00 5 1 -$5000.00 6 2 $8000.00 7 3 $8000.00 8 4 $8000.00 9 5 $8000.00 10 6 $18000.00 11 PW= 12 AW= 13 FW= 14 IRR= 15 SIR=



1. The PW of a project is uniformly distributed between $2,000 and $7,000. Using Excel, perform a Monte Carlo simulation for 100 observations and calculate the E(PW) and the V(PW). 2. The life of a project has a symmetric triangular distribution with a = 4, and b = 10. Using Excel, perform a Monte Carlo simulation for 100 observations and calculate the E(N) and the V(N). 3. A project is estimated to require an investment of $25,000, have a life of 5 years and 0 salvage value and have an annual net cash flow that can be described by a symmetric triangular distribution with a = $5,000, and b = $12,000. If the minimum required rate of return is 15%. Using Excel, perform a Monte Carlo simulation for 100 observations and construct the distribution of the net PW. Calculate the E(PW) and the V(PW).

4. A certain project requires an investment of $10,000, and is expected to have a net annual receipts minus disbursements of $2,800. The life of the project is 5 years, and the salvage value is normally distributed with a mean of $2,000 and a standard deviation of $1,000. Using Excel, perform a Monte Carlo simulation for 100 observations and construct the distribution of the net PW. Calculate the E(PW) and the V(PW).



1. A high precision programmable router for shaping furniture components is

purchased by Henredon for $190,000. It is expected to last 12 years and have a salvage value of $55,000. Calculate the depreciation and book value in each year: A. Use the straight-line depreciation. B. Use declining-balance depreciation with a rate that insures the book value

equals the salvage value. C. Use double declining balance depreciation. D. Use Sum-of-the years digits depreciation. E. Plot the book value versus time for all four methods on the same graph. (x-

axis is time, for 1 12 years, and y-axis is the book value).

2. A new proposed engineering building at AUC is to contain 10,000,000 square feet. The total cost of the building (TC) is given by the following expression:

TC = (220 + 88X + 2X 2)A where X = number of floors, and A = floor area in ft2 / floor A. Create a table (using Excel) that shows the total building cost, average cost,

and marginal cost for configurations ranging from floor 1 to 12 floors, inclusive.

B. Plot the total cost versus number of floors (1 12). Based on the plot, what is optimal number of floors for the building.

C. Demonstrate using differential calculus that your answer to part B is correct.

ENGR 345, Dr. Hatem Elayat, AUC 1

ENGR 345: Engineering Economy Hatem Elayat Mechanical Engineering Department American University in Cairo - AUC

Review Problems Set 1 Time Value of Money Operations

1) How much money today is equivalent to $10,000 in '12 years, with interest at

10% compounded annually?

2) If $5000 is deposited into a fund paying 8% compounded annually, what sum will

be accumulated at the end of 10 years? What would be the sum accumulated at

the end of 5 years if the fund paid 16% compounded annually? What is suggested

regarding doubling the: interest rate and halving the length of the time period? If

you had $5000 available for investment and the two options were available, which

would you choose if you had to choose one of them? Justify your choice. If you

chose the shorter duration investment, what will you do with your accumulated

monies over the next 5-year period? Should the answer to this question influence

your choice?

3) If a fund pays 12% compounded annually, what single deposit now will

accumulate $12,000 at the end of the tenth year? If the fund pays 6% compounded

annually, what single deposit is required now in order to accumulate $6000 at the

end of the tenth year?

4) Maria deposits $1200, $500, and $2000 at t = 1,2, and 3, respectively. If the fund

pays 8% compounded per period, what sum will be accumulated in the fund at (a)

t = 3 and (b) t = 6?

5) Suppose you wanted to become a millionaire at retirement. If an annual

compound interest rate of 8% could be sustained over a 40-year period, how much

would have to be deposited yearly in the fund in order to accumulate $1 million?

What if the interest rate is 10%?, 12%?

6) Juan deposits $1000 in a savings account that pays 8% compounded annually.

Exactly 2 years later he deposits $3000; 2 years later he deposits $4000; and 4

years later he withdraws all of the interest earned to date and transfers it to a fund

that pays 10% compounded annually. How much money will be in each fund 4

years after the transfer?

7) A debt of $1000 is incurred at t = 0. What is the amount of four equal payments at

t = 1, 2, 3, and 4 that will repay the debt if money is worth 10% compounded per

period?

8) Five deposits of $500 each are made at t = 1, 2, 3, 4, and 5 into a fund. paying 6%

compounded per period. How much will be accumulated in the fund at (a) t = 5,

and B(b) t = 10?

9) What equal annual deposits must be made at t = 2, 3, 4, 5, and 6 in order to

accumulate $25,000 at t = 8 if money is worth 10% compounded annually?


Review Problems Set 2

Time Value of Money Operations

1) John borrows $15,000 at 18% compounded annually; he pays off the loan over

a 5-year period with annual payments. Each successive payment is $700 greater

than the previous payment. How much was the first payment?

2) Solve Problem 1 for the case in which each successive payment is to be 10%

greater than the previous payment.

3) Yavuz wishes to make a single deposit P at t =0 into a fund paying 15%

compounded quarterly such that $1000 payments are received at t = 1, 2, 3, and

4 (periods are 3-month intervals), and a single payment of $7500 is received at t

= 12; What single deposit is required?

4) Dr. Shieh deposits $3000 in a money market fund. The fund pays interest at a

rate of 12% compounded annually. Just 3 years after making the single deposit,

he withdraws one third the accumulated money in his account. Then, 5 years

after the initial deposit, he withdraws all of the accumulated money remaining in

the account. How much does, he withdraw 5 years after his initial deposit?

5) David borrows $25,000 at 8% compounded quarterly. He wishes to repay the

money with 10 equal semiannual Installments. What must be the size of the

payment If the first payment is made 1 year after obtaining the $25,000?

6) Barbara makes four consecutive annual deposits of $2000 in a savings account

that pays interest at a rate of 10% compounded semiannually. How much money

will be in the account 2 years after the last deposit?

7) Mary Lib purchases a house for $250,000; a down payment of $20,000 is made

at the time of purchase; and the balance is financed at 12% compounded

monthly, with monthly payments made over a 10-year period.

a. What is the size of the monthly payments?

b. If the loan period had been 20 years, what would have been the size of the

monthly payments?

8) It is desired to determine the size of the uniform series over the time period [2,

5] that is equivalent to the cash flow profile shown below using an interest rate

of 10%.

9) Given the following cash flows, what single sum at t = 4 is equivalent to the

given data.

Assume i = 15%.

10) Given the cash flow profiles shown below, determine the value of X such that

the two cash flow profiles are equivalent at 20% compounded annually.

EOY CF (A) CF(B)

1

2

3

4

5

6

-$12,000

1,000

4,000

6,000

7,000

5,000

$ -X

7,000

9,000

10,000

10,000

7,000


Review Problems Set 3 Practical Applications

1) At t = 0, Martin borrows $5000 at 6%/period. Twelve equal payments are used

to repay the loan at t = 1, , 12. Determine the amount of interest included in

the fourth payment.

2) Chris and Debbie borrow $10,000 at 7% compounded monthly. The loan is to

be paid off with 48 equal monthly payments. One month after making the

thirtieth payment, they decide to payoff the unpaid balance on the note. How

much should be repaid?

3) Tom and Dale purchase a boat for $150,000; the down payment is $15,000; the

balance is financed over a 10-year period. Equal monthly payments are made.

Determine the amount of interest paid the first month if the monthly interest rate

is 1 %.

4) Dr. Schultz is considering purchasing a bond having a face value of $2500 and

a bond rate of 10% payable semiannually. The bond has a remaining life of 8

years. How much should she pay for the bond in order to earn a return on

investment of 14% compounded semiannually? Assume the bond will be

redeemed for face value.

5) Dr. Ramirez wishes to purchase a bond having a face value of $10,000 and a

bond rate of 15% payable annually. The bond has a remaining life of 8 years. In

order to earn a 20% rate of return on the investment, what amount should be paid

for the bond?

6) Kristin buys a $2000 bond for $2100. The bond has a bond rate of 12% with

bond premiums paid annually. If the bond is kept for 8 years and sold for par

value, determine the equivalent annual yield rate (rate of return) for Kristin's

bond investment.



Comparison of Alternatives

1) Consider the net cash flows (NCF) and salvage values (SV) for each of

Alternatives 1 and 2 having lives of 3 and 5 years, respectively.

Alternative 1 Alternative 2 EOY

NCF1 SV1 NCF2 SV2

0

1

2

3

4

5

-$60,000

35,000

35,000

35,000

$60,000

30,000

10,000

0

-$100,000

30,000

30,000

30,000

30,000

30,000

$100,000

60,000

40,000

25,000

15,000

10,000

2) Alternatives 1, 2, and 3 have lives of 3, 4, and 6 years, respectively. Their net

cash flow (NCF) and salvage value (SV) profiles are as follows:

Alternative 1 Alternative 2 Alternative 3 EOY

NCF1 SV1 NCF2 SV2 NCF3 SV3

0

1

2

3

4

5

6

-$20,000

8,000

8,000

28,000

-

-

-

-

-$40,000

20,000

20,000

20,000

20,000

$40,000

30,000

20,000

10,000

0

-$70,000

30,000

30,000

30,000

30,000

30,000

30,000

$70,000

50,000

30,000

20,000

10,000

5,000

2,000

3) Metal Salvage, Inc. has available three investment proposals A, B, and C,

having the cash flow profiles shown below. Proposals Band C are mutually

exclusive and Proposal C is contingent on Proposal A being chosen.

NCF(A) NCF(B) NCF(C)

Initial investment

Life

Annual receipts

Annual disbursements

Salvage value

$400,000

8 years

$320,000

$230,000

$100,000

$600,000

12 years

$380,000

$240,000

$200,000

$300,000

6 years

$400,000

$400,000

$400,000

4) Consider the following investment decision.

Machine 1 Machine 2

First cost

Estimated life

Estimated annual revenues

Estimated annual operative costs

Estimated salvage value at end of 5 years

$15,000

5 years

$12,000

$6,000

$1,500

$20,000

10 years

$14,000

$8,000

$5,000

5) Two mutually exclusive proposals, each with a life of 5 years, are under

consideration. MARR is 12%. Each proposal has the following cash flow

profile:

EOY NCF (A) NCF (B)

0

1

2

3

4

5

-$30,000

9,300

9,300

9,300

9,300

9,300

-$42,000

12,625

12,625

12,625

12,625

12,625

6) The ABC Company is considering three investment proposals, A, B, and C.

Proposals A and B ate mutually exclusive, and Proposal C is contingent on

Proposal B. The cash flow for the investments over a 10-year planning horizon

are given below. The ABC Company has a budget limit of $1 million for

investments of the type being considered currently. MARR = 15%.

NCF (A) NCF (B) NCF (C)

Initial investment

Planning horizon

Salvage values

Annual receipts

$600,000

10 years

$70,000

$400,000

$800,000

10 years

$130,000

$600,000

$470,000

10 years

$65,000

$260,000

Annual disbursements $130,000 $270,000 $70,000

7) Consider the net cash flows of the following three alternatives. None is

renewable. MARR is 12%.

EOY NCF (1) NCF (2) NCF (3)

0

1

2

3

4

5

-$3,000

1,000

1,500

0

4,000

6,000

-$4,000

4,000

2,000

0

0

0

-$6,000

3,000

3,000

3,000

0

0



Comparison of Alternatives 1-An aluminum extrusion plant manufactures a particular product at variable cost of

$0.04 per unit, including material cost. The fixed costs associated with manufacturing the

product equal $30.000/year. Determine the break- even value for annual sales if the

selling price per unit is (a) $0.40, (b) $0.30, and (c ) $0.20.

2- A manufacturing plant in Michigan has been contracting snow removal at a cost of

$400/day. The past 3 years have produced heavy snowfalls, resulting in the cost of snow

removal being of concern to the plant manager. The plant engineer has found that a snow-

removal machine can be purchased for $25.000; it is estimated to have a useful life of 6

years, and a zero salvage value at that time. Annual costs for operating and maintaining

the equipment are estimated to be $5.000. Determine the break-even value for the number

of days per year that snow removal is required in order to justify the equipment, based on

a MARR of (a) 0%, (b) 10%, and (c) 15%.

3-The motor on a gasfired furnace in a small foundry is to be replaced. Three different

15- horsepower electric motors are being considered. Motor X sells for $2500 and has an

efficiency rating of 90%; motor Y sells for $1750 and has a rating of 85%; motor Z sell

for $1000 and is rated to be 80% efficient. The cost of electricity is $0.065/ kilowatt-

hour. An8- year planning horizon is used, and zero salvage values are assumed for all

three motors. AMARR of 12% is to be used. Assume that the motor selected will be

loaded to capacity. Determine the range of values for annual usage of the motor (in

hours) that will lead to the preference of each motor. (Note: 0.746 Kilowatts= 1

horsepower).

4. Company W is considering investing $12,500 in a machine. The machine will last N

years, at which time it will be sold for L. Maintenance cost for this machine are estimated

to increase by 10% year over its life. The maintenance cost for the first year is estimated

to be $1500. The company has 10% MARR. Based on the probability distributions given

below for N and L; what is the expected equivalent uniform annual cost for the machine?

N L p(N)

6 $5,000 0.2

8 3,000 0.4

10 1,000 0.4

5. The Ajax Manufacturing company wishes to choose one of the following machines:

Machine 1 Machine 2

First cost $10.000 $12.000

Planning horizon 6 years 6 years

Salvage value $ 1.000 $ 1.000

Operating and maintenance cost for year K 800 + 80K 200+ 100K

MARR is 12%

A. Clearly specify the net cash flow profiles for each mutually exclusive alternative.

B. Determine which machine should be selected. Use the ranking approach and the

present worth method.

C. Repeat part (B) using the annual worth method.

D. Repeat part (B) using the future worth method.

E. Based on incremental cash flows, what is the discounted payback period?

F. Determine which machine should be selected. Use an incremental cash flow

approach and the internal rate of return method.

G. Repeat part (F) using external rate of return method.

H. Repeat part (F) using the saving/investment ratio method.

6. The telephone Company of America purchased a numerically controlled production

machine 5 years ago for $300,000. The machine currently has a trade-in value of $

70,000. If the machine is continued in use, another machine, X, must be purchased to

supplement the old machine. Machine X costs$200,000, has annual operating and

maintenance costs of $ 40,000, and will have a salvage value of $ 30,000 in 10 years. If

the old machine is retained, it will have annual operating and maintenance costs of $

70,000, has anticipated annial operating and maintenance costs of $70,000 and will have

a salvage value of $ 15,000 in 10 years.

Using a MARR of 15% and a present worth comparison, determine the preferred

economic alternative.

7. A highway construction firm purchased a particular earth-moving machine 3 years ago

for $ 125,000. The salvage value at the end of 8 years was estimated to be 35% of first

cost. The firm earns average annual gross revenue of $ 105,000 with the machine and the

average annual operating costs have been and are expected to be $ 65,000.

The firm now has opportunity to sell the machine for $70,000 and subcontract the work

normally done by the machine over the next 5 years. If the subcontracting is done, the

average annual gross revenue will remain$105,000 but subcontractor charge

$85,000 /end-of-years for these services.

If a 15% rate of return before taxes is desired, determine by the annual worth method

whether or not the firm should subcontract.



Depreciation & Cost Concepts 1. A mold for manufacturing medical supplies is purchased at the beginning of the fiscal

year for $30,000. The estimated salvage value after 10 years is $3000. Calculate the

depreciation deduction and the resulting unrecovered investment during each year of the

asset's life.

(a) Use traditional pre-1981 straight-line depreciation.

(b) Use traditional pre-1981200% declining balance switching to straight-line

depreciation.

(c) Use traditional pre-1981 sum of the years' digits depreciation.

2. A new engineering building of State University is to contain 10,000,000 square feet.

The total cost of the building (TC) is given by:

TC = (200 + 90 X + 2X2) A

Where X = number of floors

A = floor area in ft2/ per floor

a) Create a table shows the total building cost, average cost per floor, and

marginal cost per floor (using the difference equation approach)

b) Based on your table, what is optimal number of floors for the building? Justify

your answer based on the "total cost" column.

c) Justify your answer in part (b) based on the "marginal cost per floor" column.

d) Demonstrate, using differential calculus, that your answer in parts (b) and (c)

is correct. Note: For this part assume that X is continuous variable.

3. An oil refinery produces one base type of crude oil for southeastern U.S. market. The

two equations below give the relationships that approximate the total cost and the total

profit per week in dollars ( Note: This problem is for illustration purposes only; the total

cost function and the cost coefficients are not necessary realistic.)

Total cost, TC(x) = 50,000 + 20.2x + 0.0001x2, for x 0 = 0 otherwise

Total profit, TP (x) = S x TC(x)

Where x = amount of crude oil produced, barrels / week

S = sales price of crude oil, dollars / barrel = $ 35/ barrel

At what level of production in barrels/week is the cost/ barrel minimum? What is the

minimum cost/ barrel?

4. Production of particular type of annual crop is a function of fertilizer used and is given

by the following relationship:

P (t) = crop production, barrels/ acre

= 0.417 t ) - 0.00125 t2

Where t = amount of fertilizer used, pounds / acre

The crop can be sold at a price $ 15 / barrel. Given that one barrel pf crop weights

about 120 pounds, the total cost of the production is

TC (t) = $ (220 + 2t) per acre

a) How much fertilizer should the farmer use for this crop per acre of land to

maximize his annual profit?

b) What is maximum annual profit per acre of land for this crop?

c) Between what range of fertilizer application is a profit possible?

5. Assume the total annual inventory cost for a particular item carried un inventory is

TC (Q) = annual cost of ordering + annual cost

of carrying inventory, dollars / years

= Pc ) + (0.60 Q + 150)

Where Pc = cost of preparing a purchase order (a constant value, regardless of the

quantity ordered)

= $ 15 per purchase order

Q = the number of items ordered each time a purchase order is placed.

A = total annual demand for this item = 2000 units

A/Q = the number of orders placed each year.

Note that the total annual inventory cost TC (Q) is a function of the order size q

a) Determine the value of Q that will minimize the total annual inventory cost(i>e>

determine the economic order quantity Q*)

b) What will be corresponding total annual inventory cost, TC (Q*) ?

c) For the economic order Q* , determine the number of orders that will be placed

each year.

d) If the cost of placing a purchase order is decreased by 50% what is the effect on

the economic order quantity?

principles of engineering economic analysis

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