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Econ. Lecture 3

Econ. Lecture 3. Economic Equivalence and Interest Formula’s Read 45-70 Problems 2.6, 2.8, 2.11, 2.14, 2.15. First an example from last lecture. Single Payment To Find Given Functional Notation Compound Amount Factor F P (F/P, i, n)

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Econ. Lecture 3

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  1. Econ. Lecture 3 Economic Equivalence and Interest Formula’s Read 45-70 Problems 2.6, 2.8, 2.11, 2.14, 2.15

  2. First an example from last lecture Single Payment To Find Given Functional Notation Compound Amount Factor F P (F/P, i, n) Present Worth Factor P F (P/F, i, n) This notation refers to interest tables in the back of your text, Appendix C. The table works out multiplication factors for a given interest rate over a given number of years.

  3. Example: • To raise money for a business, a person asks for a loan from you. They offer to pay you $3000 at the end of four years. How much should you give him if you want 12%/year on your money? • P = unknown • n = 4 years • i = 12% • F = $3000 • P = F/(1+i)n = 3000/ (1+0.12)4 = $1906.55

  4. With the Interest Tables • P = F(P/F,i,n) = 3000(P/F,12%,4) = 3000 (0.6355) = $1906.50 • Slight difference in the answer that you get is minimal.

  5. Back to Equivalence • Economic equivalence – exists between cash flows that have to same economic effect • Economic indifference – if two cash flows are equal to each other, we don’t care which is chosen

  6. There are four simple principles of Equivalence: • 1)Alternatives require a common time basis – A point in time will be used that best fits the analysis of our alternatives, given P,F • 2)Dependent on interest rate • 3)May require conversion of multiple payments to a single payment • 4)Equivalence is maintained regardless frame of reference

  7. Example of Principle One: Deposit $4000 today and 10%. In 15 years you have $16,708.80. How much do you have after 10 years?

  8. From both time directions find V10? • F = $4000(F/P,10%,10)= $4000 (2.5937) = $10374.80 • P = $16,708.80(P/F, 10%,5) = $16,708.80 (0.6209) = 10,374.49 • Equal in time!

  9. Five types of cash flows 1)Single Cash Flow – one P or F 2)Uniform Series – equal payment series, equal series of payments for n years 3) Linear Gradient – changing payment by a constant amount G, in each cash flow

  10. 4)Geometric Gradient – changing payment by a constant percentage, g, in each cash flow 5)Irregular Series – no overall regular pattern in payment scheme

  11. Uneven Cash Flow • When presented with an uneven payment series, the F or P can be calculated by summing the individual payments.

  12. Example: For the given cash flow, determine F at 30 years, 4%. Example: For the given cash flow, determine F at 30 years, 4%. F? 0 7 10 13 25 30 800 400 3000 3800

  13. F = 3000(F/P,4%,23) + 800(F/P,4%,20) + 3800(F/P,4%,17) + 400(F/P,4%,5) • = 3000*(2.4647) + 800*(2.1911) + 3800*(1.9479) + 400*(1.1699) • = 7394.10 + 1752.88 + 7402.02 + 467.96 = $17,016.96

  14. Uniform Payment Series

  15. Consider the following situation:

  16. F = A + A(1+i) + A(1+i)2 (1) • In this case, n = 3, equation (1) can be written as: • F = A + A(1+i) + A(1+i)n-1 (2)

  17. Multiplied by (1+i): • (1+i)F = A(1+i) +A(1+i)n-1 +A(1+i)n (3) • Subtract (2) F = A + A(1+i) + A(1+i)n-1 • Equals iF = -A + A(1+i)n

  18. Equal Payment Series compound amount Factor or • Uniform Series Compound Amount (F/A,i,n)

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