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Present ValuePresent Value

Future ValueFuture Value# of Periods# of Periods Rate of InterestRate of Interest

Time Value of MoneyTime Value of Money

Computing Simple InterestComputing Simple Interest

I = P I = P xx R R xx T TInterest Principal Annual RateInterest Principal Annual Rate Period of Time the Note Period of Time the Note

of Noteof Note of Interest of Interest is Outstanding in is Outstanding in YearsYears

Compound InterestCompound Interest Interest is earned on both the initial Interest is earned on both the initial principal plus any interest previously principal plus any interest previously earnedearned

The Future Value of a Single The Future Value of a Single Lump Sum Amount...Lump Sum Amount...

… … is described as the amount that is described as the amount that money invested today will be worth money invested today will be worth

at a future point in timeat a future point in time

F = P x (1 + r)F = P x (1 + r)nn

nn

or or F = P x FVF F = P x FVFnn n,rn,r

Future Value Calculations are used for Future Value Calculations are used for planning purposesplanning purposes

Present Value Calculations are used to Present Value Calculations are used to measure the value of business measure the value of business transactions in U.S. Dollars transactions in U.S. Dollars

• Notes ReceivableNotes Receivable• Notes PayableNotes Payable• LeasesLeases• Amortization of Premiums Amortization of Premiums • Amortization of DiscountsAmortization of Discounts• PensionsPensions

• Long-term AssetsLong-term Assets• Sinking FundsSinking Funds• Business CombinationsBusiness Combinations• DisclosuresDisclosures• Installment ContractsInstallment Contracts

Major Time Value Concepts:Major Time Value Concepts:

• Future Value of a Single, Lump Sum AmountFuture Value of a Single, Lump Sum Amount• Future Value of an Ordinary AnnuityFuture Value of an Ordinary Annuity• Future Value of an Annuity DueFuture Value of an Annuity Due

• Present Value of a Single, Lump Sum AmountPresent Value of a Single, Lump Sum Amount• Present Value of an Ordinary AnnuityPresent Value of an Ordinary Annuity• Present Value of an Annuity DuePresent Value of an Annuity Due

• Deferred AnnuitiesDeferred Annuities

Calculating the Present Value of Calculating the Present Value of an Annuity Duean Annuity Due

1) Find the present value of an ordinary annuity 1) Find the present value of an ordinary annuity factor (PVF-OA factor (PVF-OA @@ n=N-1, r=%) for n-1 n=N-1, r=%) for n-1 periodsperiods

2) Add “1” to that factor to get the “PVF-AD” 2) Add “1” to that factor to get the “PVF-AD” factorfactor

3) Multiply the periodic “amount” times this 3) Multiply the periodic “amount” times this PVF-AD to get the present value of paymentsPVF-AD to get the present value of payments

Calculating the Present Value Calculating the Present Value of a Deferred Annuityof a Deferred Annuity

• Calculate the deferred annuity factorCalculate the deferred annuity factor– (a) Find the “factor” assuming payment (a) Find the “factor” assuming payment

started the first year (assuming no deferral)started the first year (assuming no deferral)– (b) Find the “factor” relating the period of (b) Find the “factor” relating the period of

time when payment is not madetime when payment is not made– (c) Subtract (b) from (a)(c) Subtract (b) from (a)

• Use this new calculation as the factor in Use this new calculation as the factor in your calculationyour calculation