Time Value of Money
Time Value of Money – dollar today is worth more than a dollar in the future (interest)
 Financial Manager – decisions about proposals with CF over long time periods
Variables:
 Present Value (PV) – $ today (principal)
 Interest rate (i)
Need 3 to find unknown
 Period of time (n)
 Future Value (FV) – $ in future
 PMT – periodic payment
Interest
Simple Interest
Simple Interest (Flat rate) – calculated only on original principal


Doesn’t account for changes in principal
Use – valuation in ST financial instruments (term <12 months, bills of exchange)
Future Value
FV = PV (1 + i x n)
Present Value
PV =
FV
(1 + i x n)
Compound Interest
Compound Interest – interest added to principal each period (interest on interest)
Future Value
FV = PV (1 + i)n
Present Value
PV = FV (1 + i)-n
Frequency of Compounding
Compounding Periods (m) – semi-annually, quarterly, monthly
 Nominal rate – compounded more frequently
i÷m
nxm
Effective Annual Rates (EAR)
Effective Rate – Interest rate with annual compounding
 Nominal rate  effective rate
EAR = (1 + i)m – 1
Discount FV to PV


If PV > given PV, invest
If PV < given PV, don’t invest
Annuity
Annuity – multiple CF, number of equal cash flows occurring at equal time intervals
 Ordinary Annuity – all cash flows occur at end of each period
Future Value
n
(1+i) -1
FV = PMT(
i
)
Future Value:
 1st Payment – interest for 2 periods
 2nd Payment – interest for 1 period
 3rd Payment – no interest