Engineering Economy Terms and Calculations
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Questions and Answers

From the borrower's perspective, what financial term is most closely associated with the cost of borrowing money?

  • Net Cash Flow
  • Present Value
  • Interest Rate (correct)
  • Rate of Return

What does 'P' commonly represent in financial calculations?

  • Number of Periods
  • Annual Cash Flow
  • Future Value
  • Present Value (correct)

If revenues for a project are $200,000 and disbursements are $150,000, what is the Net Cash Flow (NCF)?

  • \$150,000
  • \$350,000
  • \$50,000 (correct)
  • \$200,000

What is the primary difference between a point estimate and a range estimate in cash flow estimation?

<p>A point estimate provides a single value, while a range estimate provides a minimum and maximum value. (C)</p> Signup and view all the answers

An investor earned $50 in interest on an investment of $1000 over one year. What is the rate of return on the investment?

<p>5% (D)</p> Signup and view all the answers

What does the variable 'A' represent in the context of financial calculations?

<p>A series of consecutive, equal, end-of-period amounts of money. (A)</p> Signup and view all the answers

What is the 'end-of-period assumption' in financial analysis?

<p>Funds flow, or are assumed to flow, at the end of a given interest period. (B)</p> Signup and view all the answers

Which of the following provides a better understanding of the variability of economic parameters when making financial decisions?

<p>Using range estimates with probabilities attached. (A)</p> Signup and view all the answers

Which of the following best describes the primary reason engineering economy is crucial for engineers?

<p>It provides a basis for selecting the most cost-effective solution from various design alternatives. (C)</p> Signup and view all the answers

What is the MOST important concept in engineering economy?

<p>Time value of money (B)</p> Signup and view all the answers

In the context of engineering economy, what does 'economic equivalence' primarily address?

<p>The idea that different sums of money at different times can have the same economic worth. (C)</p> Signup and view all the answers

Which of the listed steps is NOT a part of the general decision-making process in engineering economy?

<p>Ignoring sunk costs in the analysis (B)</p> Signup and view all the answers

Which activity is NOT directly included in the scope of Engineering Economy?

<p>Designing detailed technical specifications for a project. (A)</p> Signup and view all the answers

An engineer is considering two mutually exclusive projects. Project A has a higher initial cost but promises greater long-term savings. Project B has a lower initial cost but offers less savings. Which of the following steps should the engineer take to make a sound economic decision?

<p>Evaluate both projects using appropriate economic analysis techniques considering the time value of money. (B)</p> Signup and view all the answers

When evaluating different engineering project alternatives, why is sensitivity analysis performed?

<p>To assess how changes in input parameters affect the chosen alternative. (A)</p> Signup and view all the answers

A company is deciding whether to invest in new equipment that reduces labor costs. Which of the following factors should be considered in an engineering economic analysis?

<p>The resale value of old equipment and fluctuations in labor costs. (B)</p> Signup and view all the answers

Which factor is most critical in establishing economic equivalence between two sums of money at different points in time?

<p>The combination of the interest rate and the time value of money. (B)</p> Signup and view all the answers

Consider an investment where the future value is economically equivalent to the present value. As the interest rate increases, what happens to the present value required to maintain equivalence?

<p>The present value must decrease. (A)</p> Signup and view all the answers

What distinguishes compound interest from simple interest?

<p>Compound interest calculates interest on the principal and accumulated interest, while simple interest only calculates interest on the principal. (A)</p> Signup and view all the answers

Suppose you have two investment options: one with simple interest and one with compound interest, both at the same annual interest rate. Under what condition would the compound interest investment yield a higher return?

<p>When the investment period is longer than one year. (A)</p> Signup and view all the answers

If $5,000 is invested for 5 years at a simple interest rate of 8% per year, what is the total interest earned at the end of the 5 years?

<p>$2,000 (A)</p> Signup and view all the answers

You borrow $10,000 at an annual interest rate of 6% compounded annually. What is the amount of interest accrued after 2 years?

<p>$1,236 (C)</p> Signup and view all the answers

What is the primary purpose of creating a cash flow diagram in economic analysis?

<p>To visually represent the timing and amount of cash inflows and outflows for an investment. (D)</p> Signup and view all the answers

An investor is considering two projects. Project A returns $10,000 in simple interest over 5 years and Project B returns $9,000 in compound interest over the same period. Which project has the higher annual interest rate, assuming the same principal investment?

<p>Project B has a slightly higher annual interest rate. (C)</p> Signup and view all the answers

What is the primary purpose of the Minimum Attractive Rate of Return (MARR) in project evaluation?

<p>To establish a baseline return threshold for economically justifying investments. (A)</p> Signup and view all the answers

Which of the following is NOT a key characteristic of the Minimum Attractive Rate of Return (MARR)?

<p>It is solely determined by the risk-free rate of return. (B)</p> Signup and view all the answers

A company is evaluating a project with a Weighted Average Cost of Capital (WACC) of 8% and a risk premium of 3%. What is the Minimum Attractive Rate of Return (MARR) for this project?

<p>11% (C)</p> Signup and view all the answers

A project has an expected Rate of Return (ROR) of 10%, and the Minimum Attractive Rate of Return (MARR) has been set at 12%. Based on this information, what is the best course of action?

<p>Reject the project, as the ROR is less than the MARR. (D)</p> Signup and view all the answers

Which type of financing involves using funds from retained earnings or new stock issues?

<p>Equity Financing (C)</p> Signup and view all the answers

What is the best definition of 'Opportunity Cost' in the context of investment decisions?

<p>The highest rate of return forgone from rejected projects due to limited capital. (C)</p> Signup and view all the answers

Which of the following actions primarily reflects the application of professional engineering ethics?

<p>Choosing a design solution that prioritizes safety and environmental considerations despite higher initial costs. (B)</p> Signup and view all the answers

An engineer discovers a potential safety flaw in a completed project that, while unlikely to cause harm, does not meet current safety regulations. Applying universal morals, what is the MOST ETHICAL course of action?

<p>Disclose the flaw to the relevant authorities and stakeholders, and recommend corrective actions regardless of cost or potential liability. (D)</p> Signup and view all the answers

A company is funded by 60% equity and 40% debt. The cost of equity is 12%, and the cost of debt is 6%. Calculate the Weighted Average Cost of Capital (WACC).

<p>9.6% (A)</p> Signup and view all the answers

Which of the following conditions must be met for an economically justified project?

<p>ROR ≥ MARR &gt; WACC (D)</p> Signup and view all the answers

LaserKinetics.com borrows $20,000 with a repayment of $21,400 one year later. Calculate the interest rate paid on the loan.

<p>7% (B)</p> Signup and view all the answers

Stereophonics, Inc., borrows $40,000 at a simple annual interest rate of 8%. If they repay $46,400 at the end of the year, how much MORE than the agreed interest did they pay?

<p>$3,200 (D)</p> Signup and view all the answers

Alpha Technologies invested $500,000 in a new project. After one year, they received a total of $545,000 (principal + interest). What is the rate of return on their investment?

<p>9% (D)</p> Signup and view all the answers

An engineer is offered a substantial gift from a vendor in exchange for specifying the vendor's product in a project. Which aspect of ethics would MOST DIRECTLY address the acceptance of this gift?

<p>Professional or engineering ethics, adhering to formal codes that prohibit conflicts of interest. (C)</p> Signup and view all the answers

A company invests $1,000,000 in a project. After one year, the project yields $1,150,000. Determine the rate of return on this investment.

<p>15% (D)</p> Signup and view all the answers

If $5,000 is borrowed and $5,400 is repaid after one year, calculate the interest rate for the loan.

<p>8% (A)</p> Signup and view all the answers

A company with $200,000 of available capital is evaluating four independent projects. Project W requires $210,000 and has ROR of 16%. Project X requires $180,000 and has a ROR of 14%. Project Y requires $190,000 and a ROR of 15%. Project Z requires $170,000 and a ROR of 13%. Assuming no MARR is set, what is the opportunity cost?

<p>15% (B)</p> Signup and view all the answers

A firm has $500,000 to invest and is considering five projects. Which project's ROR should be used to substitute the firms' MARR, if no MARR is specified?

<p>The highest ROR from the projects after rejecting those the firm cannot afford. (B)</p> Signup and view all the answers

Which Excel function is used to calculate the number of periods required for an investment to reach a specific future value, given the interest rate, periodic payment, and present value?

<p>=NPER(i%,A,P,F) (B)</p> Signup and view all the answers

An investment of $10,000 is expected to generate the following cash flows over the next three years: $3,000 in Year 1, $4,000 in Year 2, and $5,000 in Year 3. Using an interest rate of 6%, which Excel formula calculates the present value of this series of cash flows?

<p>=NPV(6%,B1:D1)+A1 (C)</p> Signup and view all the answers

An engineer is evaluating a project with an initial investment of $25,000. The project is expected to generate uniform annual revenues of $8,000 for 5 years. Using an interest rate of 8%, which Excel function can be used to verify the economic viability, by determining the project's internal rate of return (IRR)?

<p>=IRR(A1:A6) (D)</p> Signup and view all the answers

Flashcards

Why is Engineering Economy Important?

Incorporates economic analysis into creative efforts, selects from multiple alternatives, and applies time value of money.

Time Value of Money (TVM)

The concept that money changes in amount/value over time due to earning potential.

Engineering Economy Involves:

Formulating, Estimating, and Evaluating the economic outcomes of alternatives.

Steps for Decision Making:

Understand, Collect, Define, Identify, Evaluate, Select, Implement.

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Economics

Desire to improve the well-being of individuals through goods and services.

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Interest Rate

A percentage reflecting the earning power of money over time.

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Cash Flows

Money moving in and out of an organization or project.

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Economic Equivalence

The condition when different sums of money at different times have equivalent economic worth.

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Interest Rate / Rate of Return

From the borrower's view: the percentage paid for borrowing money. From the lender's view: the percentage earned on an investment.

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Principal

The original sum of money deposited.

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t

Time, generally measured in years or months.

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P

The value or amount of money at the present time (time 0).

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F

The value or amount of money at a future point in time.

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A

A series of consecutive, equal, end-of-period payments or receipts.

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n

The number of interest periods (years, months, etc.).

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i

The interest rate or rate of return per time period (e.g., percent per year or month).

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Engineering Economy Study

A systematic process used to analyze and evaluate the economic aspects of proposed engineering projects or solutions.

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Universal Morals/Ethics

Fundamental beliefs about right and wrong that are universally accepted (e.g., do not steal).

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Personal Morals/Ethics

Individual beliefs that guide personal conduct, derived from universal morals.

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Professional/Engineering Ethics

A formal set of guidelines specific to a profession, influencing work-related conduct and decisions.

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Interest

The fee paid for the use of someone else's money or the difference between the final and initial amounts.

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Rate of Return

Interest earned over a period of time expressed as a percentage of the original amount (principal).

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Total amount due after 1 year

Calculates an amount due after n years considering the effects of compounding.

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Cash Flow Diagram

A visual representation of cash inflows and outflows over a period.

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Simple Interest

Interest calculated only on the principal amount.

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Compound Interest

Interest calculated on the principal plus accumulated interest from previous periods.

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Simple Interest Formula

I = Pni, where I = Interest, P = Principal, n = Number of periods, i = interest rate.

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Compound Interest Formula

The interest for compounding at time period t is: I_t = B_(t-1) * i, where B is the balance at the start of the time period t.

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Time Value Adjustment

To move money between time periods to find equivalent values.

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Minimum Attractive Rate of Return (MARR)

A rate of return used to decide if an investment is economically justifiable.

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MARR Characteristics

Established by financial managers, connected to the cost of capital, considers risk.

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Equity Financing

Funds from retained earnings, stock issues, or owner's money.

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Debt Financing

Borrowed funds from loans, bonds, etc., where interest is paid.

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Economically Justified Project

Rate of Return must be greater than or equal to MARR, which is greater than WACC.

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Opportunity Cost (in Investment)

Largest return of projects not accepted due to lack of funds.

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Weighted Average Cost of Capital (WACC)

The average cost of all capital sources, weighted by their proportion.

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Minimum Attractive Rate of Return (MARR) formula

MARR is the sum of the WACC and the project's risk premium.

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Opportunity Cost

The return rate of the best project not undertaken due to limited resources; used as a substitute for MARR when MARR isn't explicitly defined.

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Project Rejection (Capital)

Projects are rejected if their investment requirement exceeds available capital.

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PV Function in Excel

Excel function to calculate present value. Inputs include interest rate, number of periods, periodic payment, and future value.

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FV Function in Excel

Excel function to calculate the future value of an investment, given interest rate, number of periods, periodic payment, and present value.

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PMT Function in Excel

Excel function to calculate the periodic payment amount for a loan or investment. Inputs include interest rate, number of periods, present value, and future value.

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Study Notes

Introduction to Engineering Economy

  • Engineering involves designing and creating.
  • Engineers use economic analysis to integrate creative efforts.
  • Engineers often select and implement from multiple options.
  • Essential for engineers: understanding time value of money, economic equivalence, and cost estimation.
  • Economic analysis for selection and execution is fundamental to engineering.

Time Value of Money (TVM)

  • TVM explains how money changes over time for corporations or individuals.
  • Corporate investments should yield a return.
  • Investment always involves money.
  • Money possesses a "time value."
  • TVM is a core concept in engineering economy.

Engineering Economy

  • Engineering Economy Includes formulating, estimating, and evaluating expected economic outcomes of alternatives for a defined purpose.
  • Easy math techniques simplify evaluation.
  • Economic outcome estimates can be deterministic or stochastic.

Decision Making

  • Steps for general decision-making:
  • Problem understanding and objective definition.
  • Gather relevant data.
  • Designate viable alternatives.
  • Define decision-making criteria.
  • Evaluate options using sensitivity analysis.
  • Choose the optimal alternative.
  • Implement and monitor.

Ethics in Engineering

  • Universal morals or ethics involve fundamental beliefs like not stealing, lying, harming, or murdering.
  • Personal morals or ethics: individual beliefs that evolve; interpretation of universal morals.
  • Professional or engineering ethics: standards to guide work and decisions.
  • Engineers disciplines possess a formal ethics code.
  • National Society of Professional Engineers (NSPE) have specific codes, and many societies have their own codes.
  • Engineers must hold the public safety and welfare to very high standards.
  • Serve only in areas where they are competent.
  • Issue honest and unbiased public statements.
  • Act as faithful agents for employers/clients.
  • Avoid misleading or fraudulent actions.
  • Conduct ethically and lawfully.

Interest and Interest Rate

  • Interest reflects the time value of money.
  • Interest is the fee for using someone else's money or the difference between the ending and beginning amounts.
  • Formula: Interest = amount owed – principal.
  • Interest rate: Interest per time period, expressed as percentage.
  • Interest rate (%) = (Interest accrued per time unit / Principal) * 100%.

Rate of Return

  • Rate of Return: Interest earned over time, as percentage of the original principal.
  • Formula: Rate of return (%) = (Interest accrued per time unit / Original amount) * 100%.
  • Borrower: this is the interest rate paid.
  • Lender/investor: rate of return earned.

Commonly Used Symbols

  • t = time (years, months).
  • P = present value or amount at time t (present or time 0).
  • F = future value at time t = n.
  • A = series of equal, consecutive, end-of-period money amounts.
  • n = number of interest periods (years, months).
  • i = interest rate/rate of return per period (percent per year/month).

Cash Flow Terms

  • Cash Inflows: Revenues (R), and incomes generated (plus sign).
  • Cash Outflows: Disbursements (D), costs, expenses, taxes (minus sign).
  • Net Cash Flow (NCF): Cash inflows – Cash outflows = R - D.
  • End-of-period assumption: Funds flow at period's end.

Cash Flows Types of Estimations

  • Point Estimate: One value for cash flow, like Income = $150,000 per month.
  • Range Estimate: Min and max bounds like Cost is between $2.5 M and $3.2 M
  • Range estimates with probabilities give better understanding.

Economic Equivalence

  • Economic Equivalence: Combines interest rate and time value to find equivalent money amounts at different times.
  • Rate i and time t are used to equate money (P, F, A) across time points.

Simple and Compound Interest

  • Simple Interest: Interest calculated on principal only.
  • Formula: Interest = (principal) * (number of periods) * (interest rate) or I = Pni.
  • Compound Interest: Interest on principal plus all past interest.
  • Formula: Interest = (principal + all accrued interest) * (interest rate).

Minimum Attractive Rate of Return

  • MARR (percent) gauges and chooses alternatives, and is established.
  • An investment is feasible if its return meets or exceeds the MARR.
  • Terms for MARR include the hurdle/benchmark/cutoff rate.
  • Financial managers set the MARR.
  • MARR links to the capital cost.
  • Capital financing determines WACC and MARR.
  • MARR factors in project risk.

Types of Financing

  • Equity Financing: Uses Earnings, owner's money, or stock.
  • Debt Financing: Borrows from loans, bonds, etc.
  • Interest should be paid to the lender on these funds.
  • Economically sound ROR, MARR, WACC projects should be like this: ROR > MARR > WACC.

Opportunity Cost

  • Opportunity cost: The rate of return of projects not funded due to lack of capital, and is the largest Rate of Return (ROR) that is not accepted.
  • Unset MARR: the highest non-funded project ROR becomes the opportunity cost.
  • With a limited budget: if a project costs too much, it is rejected.

Spreadsheet Functions for:

  • Present Value (P) = PV(i%,n,A,F)
  • Future Value (F) = FV(i%,n,A,P)
  • Equal, periodic value (A) = PMT(i%,n,P,F)
  • Number of periods, n = NPER(i%,A,P,F)
  • Compound interest rate, i = RATE(n,A,P,F)
  • Compound interest rate, i = IRR(first_cell:last_cell)
  • Present value, any series,P = NPV(i%,second_cell:last_cell)+first_cell

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Explore key concepts in engineering economy, including borrowing costs and cash flow. Understand rate of return, point vs. range estimates, and the importance of variability in financial decisions. Learn why engineering economy is crucial for engineers.

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