2First an example from last lecture Single Payment To Find Given Functional NotationCompound 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.
3Example: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 = unknownn = 4 yearsi = 12%F = $3000P = F/(1+i)n = 3000/ (1+0.12)4 = $
4With 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.
5Back to EquivalenceEconomic equivalence – exists between cash flows that have to same economic effectEconomic indifference – if two cash flows are equal to each other, we don’t care which is chosen
6There 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,F2) Dependent on interest rate3) May require conversion of multiple payments to a single payment4) Equivalence is maintained regardless frame of reference
7Example of Principle One: Deposit $4000 today and 10%. In 15 years you have $16, How much do you have after 10 years?
8From both time directions find V10? F = $4000(F/P,10%,10)= $4000 (2.5937) = $P = $16,708.80(P/F, 10%,5) = $16, (0.6209) = 10,374.49Equal in time!
9Five types of cash flows 1) Single Cash Flow – one P or F2) Uniform Series – equal payment series, equal series of payments for n years3) Linear Gradient – changing payment by a constant amount G, in each cash flow
104) Geometric Gradient – changing. payment by a constant 4) Geometric Gradient – changing payment by a constant percentage, g, in each cash flow5) Irregular Series – no overall regular pattern in payment scheme