Time Value of Money – Part I

1. Time Value of Money – Part I Economic basis to evaluate engineering projects

2. Time Management • The expected time to deliver this module is 50 minutes. 20 minutes are reserved for team practices and exercises and 30 minutes for lecture.

3. Learning Objective After this class the students should be able to: • Define the interest rate for calculating the time value of money. • Contrast simple and compound interest. • Draw a cash flow diagram.

4. Warm-up (Question 1) • If you had the possibility to receive $ 10,00.00 now or another amount one year from now, how much would you like to receive one year from now? Each team is invited to answer this question and list the reasons that justify their respective answers.(5 minutes)

5. Warm-up (Question 2) • The engineering group of Baker Designs must decide whether to spend $90K (K for thousands) on a new project. This project will cost $5K per year for operations, and it will increase revenues by $20K annually. Both the costs and the revenues will continue for 10 years. Should the project be done? Each team is invited to answer this question and list the reasons that justify their respective answers.(5 minutes)

6. Interest rate • Each person has a different answer for these questions, but the interaction among people in the financial market, under the same condition, offer us only one answer, which can be determined through the interest rate.

7. Warm-up • A dollar today, a dollar a year from now, and a dollar 10 years from now differ in value. These dollars that occur at different times must be combined to evaluate engineering projects. How is the difference in value due to the time value of money accounted for?

8. Key Words and Concepts • Interest: The return on capital. Capital Invested money and resources • Cash How diagram: The pictorial description of when dollars are received and spent. • Equivalence Occurs when different cash flows at different times are equal in economic value at a given interest rate. • Present worth A time 0 cash flow that is equivalent to one or more later cash flows. • Nominal interest rate The rate per year without adjusting for the number of compounding periods. • Effective interest rate The rate per year after adjusting for the number of compounding periods

9. What is Interest? • Interest is a rental fee for money; that is, a fee paid or a fee earned for the use of money. • Engineering economy generalizes this definition. Interest is the return on capital - Interest is the return on Capital. Capital, in turn, is invested money and resources. .

10. Interest rate • Interest rate equals the ratio of the interest amount and the capital amount. • If the interest rate is 5 %, $5 of interest is paid when $ 100 is borrowed for a year or a month (a given period of time).

11. Interest and the time value of money • Interest is used to calculate the time value of money, and it is crucial to the practice of engineering.

12. Table 1 Interest Rates Vary Homework: complete this table

13. Interest rate and Risk. • Drilling an oil well, developing a new computer chip, and building a new municipal transit system are relatively risky. • Opening a new gas station, redesigning a production line, and building a new municipal water reservoir are less risky. • Riskier projects are required to generate a higher rate of return.

14. Figure 2 Cash Flow diagram • The pictorial description of when and how much money is spent or received is a cash flow diagram. • Cash flow diagrams depict the timing and amount of expenses and revenues for engineering projects. • Positive cash flows are receipts (those arrows point up), and negative cash flows are expenses (those arrows point down). • This course follows the normal practice of engineering economy by assuming end‑of‑period cash flows for most cash flows.

15. Figure 3 Cash flow diagrams: Depositor and Bank

16. Reference • “Engineering Economic: Appling Theory to Practice” Ted G. Eschenbach Oxford University Press 2002 Part I, chapter 1