1. Engineering Economics

2. Excel Financial Functions

3. Excel Example: P = $10,000, i = 8% per year, n = 5 years, F = ? P = $10,000 Hint, when entering numbers, don’t use commas or percent symbols, dollar signs, etc. 5 F = ???

4. Excel Use the FV function to find F, the future value. i = Rate =.08 (not 8) n = Nper = 5 years P = Pv = 10000 (no dollar sign or commas) F = Note: PMT and Type are blank

5. Excel Example: P = $2,000, A = $? Per year for 10 years, i = 7% per year, n = 10 years. P = $2,000 A = $?i = 7% n = 10 years 1 2 3 4 5 6 7 8 9 10

6. Excel Use the PMT function to find A, the equal annual payment. i = Rate =.07 (not 7) n = Nper = 10 years P = Pv = 2000 (no dollar sign or commas) A =

7. Excel Useful financial functions in Excel: Present value P: PV (Rate, Nper, Pmt, Fv) Future value F: FV (Rate, Nper, Pmt, Pv) Equal sum series A: PMT (Rate, Nper, Pv, Fv) Number of periods n: NPER (Rate, Pmt, Pv, Fv) Compound interest rate i: RATE (Nper, Pmt, Pv, Fv) Where: Rate = i, Nper = N, Pmt = A, Pv = P, Fv = F

8. Present Worth of Annuity Series Example: Lottery The lottery company agreed to pay annually an amount of $3.4 M for 15 years with interest i = 8% find the present worth of those payments using Excel functions. Contemporary Engineering Economics, 5th edition, © 2010 1 2 3 N P = ? A 0

9. Excel Solution Given:  A = $3.4M  i = 8%  N = 15 Find: P P =PV(8%,15,3.4,0) = ??

10. 0 1 2 3 4 5 6 7 8 9 10 11 12 44 Option 2: Deferred Savings Plan $2,000 Example: Early Savings Plan – 8% interest 0 1 2 3 4 5 6 7 8 9 10 44 Option 1: Early Savings Plan $2,000 ? ?

11. Option 1 – Early Savings Plan 0 1 2 3 4 5 6 7 8 9 10 44 Option 1: Early Savings Plan $2,000 ? 6531Age

12. Option 2: Deferred Savings Plan 0 11 12 44 Option 2: Deferred Savings Plan $2,000 ?

13. At What Interest Rate These Two Options Would be Equivalent?

14. Using Excel’s Goal Seek Function

15. Result

17. 0 1 2 3 4 5 6 7 8 9 10 44 0 1 2 3 4 5 6 7 8 9 10 11 12 44 Option 1: Early Savings Plan Option 2: Deferred Savings Plan $2,000 $396,644 $317,253

18. Unconventional Equivalence Calculations Situation 2: What value of A would make the two cash flow transactions equivalent if i = 10%?