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**preview**shows half of the first page. to view the full**3 pages of the document.**Financial Management Time Value of Money Chapter 5

• Time Lines

o Time line – helps you visualize what’s happening in a particular problem

▪ FV = PV(1+I)N

• Future Values

o The process of going to Future Value from Present Value is called compounding

• Different Methods to find FV

o Step by Step Approach

▪ Find each periods value manually

o Formula Approach

▪ Listed above

o Financial Calculators

o Spreadsheets

• Graphic View of the Compounding Process

o Time Value concept can be applied to anything that grows

▪ Sales, population, earnings per share, etc

• Present Value

o Discounting is finding present values

o PV = FVN/(1+I)N

o Opportunity costs – the rate of return you could earn on an alternative investment of a

similar risk

• Graphic View of the Discounting Process

o The present value of a sum to be received in the future decreases and approaches zero

as the payment date is extended further into the future

o The present value falls faster at higher interest rates

• Finding the interest Rate, I

o You can’t factor out I algebraically

o Inputs N, PV, PMT (0), and FV

o Outputs I/YR

• Finding the Number of Years, N

o Inputs I/YR, PV (Negative), PMT (0), and FV

• Annuities

o Annuity – a series of equal payments at fixed intervals for a specified number of periods

▪ Ex. Student loans, auto loans, mortgage loans

o Ordinary Annuity (Deferred annuity) - payments occur at the end of each year or pay

period

▪ Most common in finance

o Annuity Due – payments are made at the beginning of the year

• Future Value of an Ordinary Annuity

o FVAN = PMT ([(1+I)N-1]/I)

o Inputs N, I/YR, PV (0), PMT (Negative)

o Output FV

• Future Value of an Annuity Due

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