Engineering economy introduction Lec#02.ppt
- 1. Introduction HM-202 NFC Institute of Engineering & Technological Training, Multan Engineering Economics
- 2. Recap. Definitions I. Engineering II. Engineering Economy III. Alternatives IV. First cost, useful life, salvage value. V. Tangible & Intangible Factors. VI. Inflation, Depreciation.
- 3. Topics of the Day. • Cash flows • Time value of money. • Interest rate & ROR. • Equivalence. • Types of interest
- 5. Cash Flows • Inflows (Revenues) • Outflows (Costs) • Without cash flow estimates over a stated time period, no engineering economy study can be conducted.
- 6. Time Value of Money • 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. • Money makes money…. “If Invested”
- 7. TVM • The idea that money available at the present time is worth more than the same amount in the future, due to its potential earning capacity. • Any amount of money is worth more the sooner it is received. Also referred to as "present discounted value
- 8. TVM • For example, assuming a 5% interest rate, $100 invested today will be worth $105 in one year ($100 multiplied by 1.05). Conversely, $100 received one year from now is only worth $95.24 today ($100 divided by 1.05), assuming a 5% interest rate
- 9. Interest rate & Rate of return
- 10. Interest Rate and Rate of Return • Interest is the difference between an ending amount of money and the beginning amount • If the difference is zero or negative, there is no interest. • There are always two perspectives to an amount of interest – Interest paid – Interest earned • Interest is paid when a person or organization borrows money (obtained a loan) and repays a larger amount.
- 11. • Interest is earned when a person or organization saves, invests, or lent money and obtains a return of larger amount. • The computations and numerical values are essentially the same for both perspectives.
- 12. Interest Paid • Interest = amount owed now – original amount • When interest paid over a specific time unit is expressed as a %age of the original amount (principal), the result is called interest rate. • The time unit of the rate is called Interest period. • The most common interest period used to state an interest rate is 1 year. (but can be 6 months, 1 month and so on) • Normally stated 8.5% means over an interest period of 1-year. 100 amount original unit time per interest (%) rate Interest X
- 13. Notations • Notation – I = the interest amount is $ – i = the interest rate (% / interest period) – N = No. of interest periods (1 Normally)
- 14. Example 1.3 Given You borrow $10,000 for one full year Must pay back $10,700 at the end of one year Determine Interest amount = ? Interest rate paid = ?
- 15. Examples • Items which are not easily expressed in terms of dollars are called: A) Indirect costs B) Variable costs C) Intangible costs D) Legal issues • Interest that is calculated using only the principal is called: • A) Simple interest B) Effective interest C) Add-on interest D) Compound interest
- 16. Examples • If $1000 is borrowed at 10% per year simple interest, the total amount due at the end of five years is nearest to: A) $1,100 B) $1,250 C) $1,500 D) $1,611 • The amount of money five years ago that is equivalent to $1000 now at 10% per year compound interest is nearest to: A) $621 B) $667 C) $1,500 D) $1,611
- 17. Example 1.4 • FME plans to borrow Rs. 200,000 from a bank for 1 year at 9% interest for new equipment – Compute the interest and the total amount due after 1 year.
- 18. • When the interest rate is 10% per year, all of the following are equivalent to $5,000 now except: A) $4,545 one year ago. B) $5,500 one year hence. C) $4,021 two years ago. D) $6,050 two years hence.
- 19. Interest Earned • Interest = total amount now – original amount • Interest paid over a specific period of time is expressed as a %age of the original amount and is called Rate of Return (ROR). • ROR is also called the Return on Investment (ROI). 100 amount original unit time per interest (%) Return of Rate X
- 20. Example 1.5 • Calculate the amount deposited 1 year ago to have $1000 now at an interest rate of 5% per year. • Calculate the amount of interest earned during the time period.
- 21. Example • A person borrows Rs. 1000 from bank and must pay a total of 1100 after one year. • Calculate the amount of interest and interest rate. Interest = amount owed now – original amount 100 amount original unit time per interest (%) rate Interest X Formulae for use in problem:
- 23. Equivalence
- 24. Economic Equivalence • The time value of money and the interest rate help develop the concept of economic equivalence. • $100 today = $106 after one year, if the interest rate is 6% • $100 today = $94.34 before one year, of the interest rate is 6%
- 25. Simple and Compound Interest • The terms interest period, and interest rate are useful in calculating equivalent sums of money for one interest period in the past and one period in the future. • But for more than one interest period, the terms simple and compound interest become important.
- 26. Simple Interest • Simple interest is calculated using the principal only. • Interest = (Principal) (number of periods) (interest rate) where the interest rate in this case is in decimals
- 27. Example 1.7
- 28. Compound Interest • The interest accrued for each interest period is calculated on the principal plus the total amount of interest accumulated in all previous periods. • Compound interest mean interest on top of interest. • Interest=(Principal + all accrued interest) (interest rate) • Total due after a number of years = P(1+i) n Interest rate in this case is in decimals
- 29. Example 1.8 • If an engineer borrows $1000 from the company credit union at 5% per year compound interest, compute the total amount due after 3 years.