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.
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 = $
With the Interest Tables P = F(P/F,i,n) = 3000(P/F,12%,4) = 3000 (0.6355) = $ Slight difference in the answer that you get is minimal.
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
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
Example of Principle One: Deposit $4000 today and 10%. In 15 years you have $16, How much do you have after 10 years?
From both time directions find V 10 ? F = $4000(F/P,10%,10)= $4000 (2.5937) = $ P = $16,708.80(P/F, 10%,5) = $16, (0.6209) = 10, Equal in time!
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
4) Geometric Gradient – changing payment by a constant percentage, g, in each cash flow 5) Irregular Series – no overall regular pattern in payment scheme
Uneven Cash Flow When presented with an uneven payment series, the F or P can be calculated by summing the individual payments.
Example: For the given cash flow, determine F at 30 years, 4%. F? Example: For the given cash flow, determine F at 30 years, 4%.