Lo 2 a key terminologies
- 1. EGN 3203 Engineering Economics LO 2 – a Financial Appraisal Tools Key Terminologies
- 2. Financial Appraisal Tools – Key Terminology:
- 3. Financial Appraisal Tools – Key Terminology: Fundamental terminology: Alternative -- stand-alone solution Cash flows -- estimated inflows (revenues, savings) and outflows (costs, expenses) for an alternative Evaluation criteria -- basis used to select ‘best’ alternative; usually money (currency of the country) Time value of money -- change in amount of money over time (Most important concept in Engineering Economy) Interest Rate, ROR, MARR: Interest is a manifestation of time value of money Calculated as difference between an ending amount and a beginning amount of money Interest = end amount – original amount …… (1.1)
- 4. Financial Appraisal Tools – Key Terminology: Equivalence:Different sums of money at different times may be equal in economic value Interpretation: $94.34 last year, $100 now, and $106 one year from now are equivalent only at an interest rate of 6% per year
- 5. Financial Appraisal Tools – Key Terminology: Interest Rate, ROR, MARR: Interest rate is interest over specified time period based on original amount Interest rate (%) = Interest rate and rate of return (ROR) have same numeric value, but different interpretations
- 6. Financial Appraisal Tools – Key Terminology: Interest Rate and ROR Interpretations: Borrower’s perspective (money paid to lender) Take loan of $5,000 for one year; repay $5,350 Interest paid = $350 Interest rate = 350/5,000 = 7% INTEREST RATE Investor’s perspective (money earned by lender) Invest (or lend) $5,000 for one year; receive $5,350 Interest earned = $350 Rate of return = 350/5,000 = 7% RATE OF RETURN (ROI has same numeric
- 7. Financial Appraisal Tools – Key Terminology: Example 1: An employee at LaserKinetics.com borrows $10,000 on May 1 and must repay a total of $10,700 exactly 1 year later. Determine the interest amount and the interest rate paid.
- 8. Financial Appraisal Tools – Key Terminology:
- 9. Financial Appraisal Tools – Key Terminology:
- 10. Financial Appraisal Tools – Key Terminology:
- 11. Financial Appraisal Tools – Key Terminology: Simple and Compound Interest: Simple interest is always based on the original amount, which is also called the principal Interest per period = (principal)(interest rate) Total interest = (principal)(number of periods)(interest rate) Example: Invest $250,000 in a 3-year bond at 5% per year simple Interest each year = 250,000(0.05) = $12,500 Interest over 3 years = 250,000(3)(0.05) = $37,500
- 12. Financial Appraisal Tools – Key Terminology:
- 13. Financial Appraisal Tools – Key Terminology:
- 14. Financial Appraisal Tools – Key Terminology: Simple and Compound Interest: Compound interest is based on the principal plus all accrued interest Interest per period = (principal + accrued interest)(interest rate) Total interest = (principal)(1+interest rate)n periods – principal Total due = principal(1+interet rate)n periods Example: Invest $250,000 for 3 years at 5% per year compounded Interest, year 1 = 250,000(0.05) = $12,500 Interest, year 2 = 262,500(0.05) = $13,125 Interest, year 3 = 275,625(0.05) = $13,781 Interest over 3 years = 250,000(1.05)3 – 250,000 = $39,406 Total due after 3 years = 250,000(1.05)3 = $289,406
- 15. Financial Appraisal Tools – Key Terminology:
- 16. Financial Appraisal Tools – Key Terminology:
- 17. Financial Appraisal Tools – Key Terminology: Terminology and Symbols: t = time index in periods; years, months, etc. P = present sum of money at time t = 0; $ F = sum of money at a future time; $ A = series of equal, end-of-period cash flows; currency per period, $ per year n = total number of periods; years, months i = compound interest rate or rate of return; % per year
- 18. Financial Appraisal Tools – Key Terminology: Terminology and Symbols: Example: Borrow $5,000 today and repay annually for 10 years starting next year at 5% per year compounded. Identify all symbols. Given: P = $5,000 Find: A = ? per year i = 5% per year n = 10 years t = year 1, 2, …, 10 (F not used here)
- 19. Financial Appraisal Tools – Key Terminology: Cash Flow Estimates: Cash inflows – receipts, revenue, income, savings Cash outflows – cost, expenses, disbursements, losses Net cash flow (NCF) = inflows – outflows End-of-period convention: all cash flows and NCF occur at the end of an interest period
- 20. Financial Appraisal Tools – Key Terminology: Cash Flow Diagrams:
- 21. Financial Appraisal Tools – Key Terminology: ROR and MARR: Example: Find an amount to deposit 2 years from now so that $4,000 per year can be available for 5 years starting 3 years from now. Assume i = 15.5% per year
- 22. Financial Appraisal Tools – Key Terminology: ROR and MARR: Cost of capital (COC) – interest rate paid for funds to finance projects Minimum Attractive Rate of Return MARR (hurdle rate) – Minimum ROR needed for an alternative to be justified and economically acceptable. MARR ≥ COC. If COC = 5% and 6% must be realized, MARR = 11% Always, for acceptable projects ROR ≥ MARR > COC
- 23. Financial Appraisal Tools – Key Terminology: Introduction to Spreadsheet and Financial Calculator FunctionsTo display Spreadsheet Function Calculator Function Present value, P = PV(i%,n,A,F) PV(i,n,A,F) Future value, F = FV(i%,n,A,P) FV(i,n,A,P) Annual amount, A = PMT(i%,n,P,F) PMT(i,n,P,F) # of periods, n = NPER(i%,A,P,F) n(i,A,P,F) Compound rate, i = RATE(n,A,P,F) i(n,A,P,F) i for input series = IRR(first_cell:last_cell) P for input series = NPV(i%,second_cell:last_cell) + first_cell Items to remember Spreadsheets: Omitted parameters are assumed to be zero Interior parameters omitted require entry of comma Calculators: Procedures and notation varying between manufacturers
- 24. Notes