Engineering EconomyReferences: Engineering EconomyLeland Blank and Anthony Tarquin, McGraw Hill

(2) Fundamentals of Engineering EconomicsChan S. Park, Prentice Hall

Engineering EconomyOutlinesRole of Engineering Economy in Decision makingTime value of moneySimple and Compound InterestTerminology and SymbolsCash flows - formation and diagrammingFactors-how time and interest affect moneyPresent and annual worth analyses

Engineering EconomyOutlines (continued)Rate of return analysis (single and multiple alternatives)Benefit/Cost analysisBreakeven analysisDepreciation methodsIncome statement and Management ratios

Role of Engineering Economy in Decision makingEngineers often deal with different kinds of projects.They need to analyze, synthesize, and come to decisions. These decisions involve the fundamental elements of cash flows of moneytime of occurrence and interest rates

Role of Engineering Economy in Decision makingTypical questions that can be addressed by Engineering EconomyShould a new bonding technique be incorporated into the manufacture of automobile brake pads?Will the operating costs decrease if computer-vision system replaces the human inspector in performing quality tests on an auto welding line?

Role of Engineering Economy in Decision makingTypical questions that can be addressed by Engineering Economy (continued)Shall we make the required ROR if we install the new technology onto our medical laser manufacturing line?What are graduate studies worth financially over my professional career?

Role of Engineering Economy in Decision makingTime frame of economy is primarily the future.Engineering economy offers estimates of what is expected to occur in future.Stochastic nature of estimates is likely to make the observed value in future differ from estimates made now. Commonly sensitivity analysis is performed considering probable changes.

Time value of moneyWhen determining a measure of worth, the fact that money today is worth a different amount than in the future.The change in the amount of money over a given time period is called the time value of money.It is the most important concept in engineering economy.

Simple and compound InterestInterest is the manifestation of the time value of money.Interest = amount owed now original amountInterest rate(%) = [interest accrued per unit time/original amount]x[100%] Time unit of the rate is called the interest period.

Simple and compound InterestSimple interest =(principal) (number of periods) (interest rate)

Example: Loan $1000 for 3 years at 5% per year simple interest. How much to repay?Ans: Total interest for 3 years = ($1000)(3)(0.05) = $150Amount to repay = $1000 + $150 = $1150

Simple and compound InterestCompound interest = =(principal + all accrued interest)(interest rate)The compound interest for the previous case can be calculated asYear 1 interest: $1000(0.05) = $50.00Total amount due after year 1 = $1000 + 50 = 1050Year 2 interest: $1050(0.05) = $52.50Total amount due after year 2 = $1050 + 52.50 = $1102.50Year 3 interest: $1102.50(0.05) = $55.13Total amount due after year 3 = $1102.50 + 55.13 = $1157.63

Simple and compound InterestAssignment #1Graph and compare the results.Hints: Draw bar chartShow end of year in the x-axis and interest per year ($) on the y-axisIn another graph show end of year in the x-axis and total owed ($)

Terminology and SymbolsFollowing terms and symbols will be usedP = value or amount of money at a time designated at the present (t=0)P is also referred to as present worth (PW),present value (PV), net present value (NPV)Discounted cash flow (DCF)Capitalized cost (CC)

Terminology and SymbolsF = value or amount of money at some future time. F is also called thefuture worth (FW), and future value (FV), dollar, ringgit or pound etc. A = series of consecutive, equal, end-of-period amounts of money. A is also called the annual worth (AW), and equivalent uniform annual worth (EUAW), dollars per year or per month, ringgit per year or per month.

Terminology and Symbolsn = number of interest periods; years, months, daysi = interest rate or rate of return per time period; percent per year, percent per montht = time, stated in periods; years, months, days

Terminology and SymbolsThe symbols P and F represent one-time occurrences.Symbol A represents a uniform amount (i.e. the same amount each period)Interest rate i is assumed to be a compound rate, unless specifically stated as simple interest. Unless otherwise stated, the rate i applies throughout the entire n years or interest periods.

Terminology and SymbolsAll engineering economy problems involve the element of time, t. Of the other five, every problem will involve at least four of the symbols, P, F, A, n, and i.

Terminology and SymbolsExample 1.10: A new college graduate has a job with Boeing Aerospace. She plans to borrow $10,000 now to help in buying a car. She has arranged to repay the entire principal plus 8% per year interest after five years.Identify the engineering economy symbols involved and their values for the total owed after 5 years.

Terminology and SymbolsSolution In this case only P and F are involved, since all amounts single payments. Time is expressed in years.P = $10,000, i = 8% per year, n = 5 years, F = ?Future amount F is unknown.

Terminology and SymbolsExample 1.11: Assume you borrow RM 2000 now at 7% per year interest for 10 years and must repay the loan in equal yearly payments (annuity). Determine the symbols involved and their values.

SolutionTime is in years.P = RM 2,000, A = ? Per year for 10 yearsi = 7% per year, n = 10 years.

Terminology and SymbolsExample 1.14: Last year Janes grandmother offered to put enough money into a savings account to generate $1000 this year to help pay Janes expenses at college. (a) Identify the symbols(b) Calculate the amount that had to be deposited exactly 1 year before to earn $1000 in interest now, if the rate of return is 6% per year.

Solution(a) Time is in years, P = ?, i = 6% per year, n = 1 year, F = P + interest = ? + $1000(b) For this case, F - P = $1000 is the accrued amount. Now, we can write F = P + P (interest rate) Or, Interest = F-P = [P + P (interest rate)] P = P (interest rate) Or$1000 = P(0.06) => P = (1000/0.06)= $16,666.67

Terminology and SymbolsMinimum Attractive rate of Return (MARR)For any investment to be profitable, the investor expects to receive more money than the amount invested.A fair rate of return or return on investment must be realizable.The fair or reasonable rate is called MARR.

Terminology and SymbolsThe MARR is higher than the rate expected from a bank or some safe investment that involves minimal investment risk.Fig 1-6 indicates the relations between different ROR values.MARR is also referred to as the hurdle rate for projectsFor a viable project, the expected ROR must meet or exceed the MARR or hurdle rate.

Fig. 1-6 Size of MARR relative to other ROR valuesROR (%)Expected ROR on a new proposalMARRROR on safe investmentAll proposals must offer at least MARR to be consideredRange for the ROR on accepted proposal, if other proposals were rejected for some reason

Terminology and SymbolsNote that the MARR is not a rate that is calculated like ROR.MARR is established by management as a criterion for making the accept/reject decision.So the inequality ROR MARR > Cost of capital must be correct for an accepted project

Cash flows are described as the inflows and outflows of moneyEvery person or company has Cash receipts revenue and income (inflows) andCash disbursements expenses, and costs (outflows)Cash flows: Their estimation and diagramming

These receipts and disbursements are the cash flows.Plus sign represents cash inflows andMinus sign represents cash outflows.Cash flow estimates are usually made for an uncertain future. Cash flows: Their estimation and diagramming

Some examples of Cash inflow estimatesRevenues Asset salvage valueReceipt of loan principalReceipts from stock and bond salesOperating cost reductionsCash flows: Their estimation and diagramming

Some examples of Cash outflow estimatesFirst cost of assetsOperating costsEngineering design costsLoan interest and principal paymentsIncome taxesPeriodic repair and maintenance costs Cash flows: Their estimation and diagramming

Background information may be available in departments such asAccountingFinanceMarketingSalesEngineeringDesignManufacturingField servicesComputer services etc.Cash flows: Their estimation and diagramming

Usually point (or a single value) estimates are made.For statistical approach, a range estimate may be developed:To analyze an uncertain situation or riskTo make a sensitivity analysis In this course we shall deal with only point estimates.Cash flows: Their estimation and diagramming

Once the cash inflow and outflow estimates are developed, the net cash flow can be determined.Net cash flow = receipts disbursements = cash inflows cash outflowsSuch cash flows normally take place at varying time points within an interest period.Cash flows: Their estimation and diagramming

However, a simplifying assumption is made to adopt the end-of-period convention.The end-of-period convention means that all cash flows are assumed to occur at the end of an interest period. When several receipts and disbursements occur within a given interest period, the net cash flow is assumed to occur at the end of the interest period.Cash flows: Their estimation and diagramming

Cash flow diagram is a very important tool in an economic analysis.It is a graphical representation of cash flows drawn on a time scale.Cash flow diagram time, t = 0 is the present, t = 1 is the end of time period 1.Cash flows: Their estimation and diagramming

A typical cash flow time scale for 5 years (Fig 1-7)

On the cash flow diagram it is not necessary to use an exact scale.

Cash flows: Their estimation and diagramming

An example of positive and negative cash flow (Fig 1-8)

A vertical arrow pointing up indicates a positive cash flow. Cash flows: Their estimation and diagramming

Conversely an arrow pointing down indicates a negative cash flow.Example 1.15: P=$10,000 is borrowed at 8% per year and F is sought after 5 years. Construct the cash flow diagram.Fig 1-9 presents the cash flow diagram from the vantage point of the borrower.Cash flows: Their estimation and diagramming

Fig 1-9: Cash flow diagramVantage point: position that gives one an overall viewCash flows: Their estimation and diagramming

Cash flows: Their estimation and diagrammingThe present sum P is the cash inflow of the loan principal at year 0. The future sum F is the cash outflow of the repayment at the end of year 5.The interest rate (in this case, i=8%)should be indicated on the diagram.

Example 1.16Each year Exxon-Mobil expends large amounts of funds for mechanical safety features throughout its worldwide operations. Carla Ramos, a lead engineer for Mexico and Central American operations, plans expenditures of $1 million now and each of the next 4 years just for the improvement of field-based pressure release valves. Construct the cash flow diagram to find the equivalent value of these experiments at the end of year 4, using a cost of capital estimate for safety-related funds at 12% per year.

Example 1.16 (continued)

Example 1.19A rental company spent $2500 on a new air compressor 7 years ago. The annual rental income from the compressor has been $750. Additionally, the $100 spent on maintenance during the first year has increased each year by $25. The company plans to sell compressor at the end of next year for $150. Construct the cash flow diagram from the companys perspective.Solution: Use now as time t = 0, The incomes and costs for years -7 through 1 (next year) are tabulated with net cash flow.

Example 1.19(Contd)

End of yearIncomeCostNet cash flow-7-6-5-4-3-2-101$ 0750750750750750750750750+150$2500100125150175200225250275$-2500650625600575550525500625

Example 1.19(Cash flow diagram)

Assignment #1#1: A start-up chemical company has established a goal of making at least a 25% per year rate of return on its investment. If the company acquired $40 million in venture capital, how much did it have to earn in the first year.#2: An investment of $40,000 one year ago and $50,000 one year from now are equivalent at what interest rate?#3: How long will it take for an investment of $100,000 to accumulate to $200,000 at an interest rate of 10% per simple interest?

Assignment #1#4: A company that manufactures in-line mixers for bulk manufacturing is considering borrowing $1.75 million to update a production line. If it borrows the money now, it can do so at an interest rate of 10% per simple interest for 5 years. If it borrows next year, the interest rate will be only 8% per year, but the interest rate will be compound interest for 4 years. (a) How much interest (total) will be paid under each scenario? (b) Should the company borrow now or 1 year from now? Assume the total amount due will be paid when the loan is due in either case.

Assignment #1#5: Rank the following from the lowest to the highest interest rate:Cost of capital, acceptable rate of return on an investment, minimum attractive rate of return on a safe investment.#6: Construct a cash flow diagram for the following cash flows: $10,000 outflow at time zero, $3000 per year inflow in years 1 through 5 at an interest of 10% per year, and an unknown future amount in year 5.

Assignment #1#7: Construct a cash flow diagram to find the present worth for the following situation at an interest rate of 20% per year:

YearCash flows 0$-50,000 1-7 -8,000#8: Construct a cash flow diagram that represents the amount of money that would be accumulated in 15 years from investment of $20,000 now at an interest rate of 8% per year.

Assignment For Practice#9: Estimate the time it would take for money to quadruple in value at a compound interest rate of 8%. (Use the rule of 72).#10: Use the rule of 72 to estimate the interest rate that would be required for $5000 to accumulate to $10,000 in 5 years.

Rule of 72: Estimating doubling time and interest rate

Sometimes it is helpful to estimate the number of years, n or the rate of return, i required for a single cash flow amount to double in size. The rule of 72 for compound interest rates can be used to estimate i or n, given the other value. The estimation is simple as given below:

Estimated

Rule of 72: Estimating doubling time and interest rateFor example, at a rate of 5% per year, it would take approximately 72/5 = 14.4 years for a current amount to double. Alternatively, the compound rate i in percent required for money to double in a specified period of time n can be estimated as

Estimated

Rule of 72: Estimating doubling time and interest rateIn order for money to double in a time period of 12 years, a compound rate of return of approximately 72/12 = 6% per would be required.If the interest rate is simple, a rule 100 may be used in the same way. In this case the answers obtained will always be exactly correct.For example, money doubles in exactly 12 years at 100/12 = 8.33% simple interest. Or at 5% simple interest it takes exactly 100/5 = 20 years to double.

An Engineer and a Manager (a joke)A woman in a hot air balloon realized she was lost.She reduced altitude and spotted a man below.She descended a bit more and shouted. Excuse me Sir, can you help me? I don't know where I am, I had promised someone, I should be there.The man below replied, "You're in a hot air balloon hovering approximately 30 feet above the ground.You're between 40 and 41 degrees north latitude and between 59 and 60 degrees west longitude."

An Engineer and a Manager (a joke)"You must be an Engineer", said the lady balloonist."I am", replied the man. "How did you know that?""Well", answered the lady in the balloon "Everything you told me is technically correct, but I have no idea what to make of your information. And the fact is I'm still lost. Frankly, you've not been much help to me at all. If anything, you've delayed my trip even more."

An Engineer and a Manager (a joke)The engineer below responded, "You must be in Top Management.""I am", replied the lady balloonist, "but, how did you know that?""Well", said the Engineer, "You don't know where you are, or where you're going and seem to be in your place due to lot of hot air. You made a promise, which you've no idea how to keep and you expect people beneath you to solve your problems. And finally, you hold others responsible for the plight you are in."