TIME VALUE OF MONEY

Time line

important tool used in time value of money analysis; it is a graphical representation used to show the timing of cash flows

Time :

0 1 2 3 4 5

Outflow cash deposit ,cost , or amount paid

has a minus sign

Inflow cash receipt

Time:

Cash flows: ?

5%0 1 2 3

100

Time:

10%

?100

1 25%

0

Compounding

arithmetic process of determining the final value of a cash flow or series of cash flow when compound interest is applied

PV = present value, beginning amounti = interest rateINT= interest earned during the year

(PVxi)= future value, ending

amountn = number of periods

= PV + INT = PV + PV(i) = PV (n+i) = $100 (1+0.05) = $100 (1.05) = $105

Future value (FV) amount to which a cash flow or a series of cash flows will grow over a given period of time when compounded at a given interest rate

Initial deposit:

Interest earned:

Amount at the end of each

period = 127.63

121.55115.76

110.25105.00

6.085.795.515.00

=?=?=?=?=?100

543210

:

5.25

i

N = the number of periodsI = interest rate of periodsPV = present valuePMT = paymentFV = future value

Relationship among Future Value, Growth, Interest Rates, and Time

0 2 4 6 8 100

1

2

3

4

5

i = 0%I =5%i = 10%i = 15%

Periods

Future Value of $1

Opportunity Cost Rate rate of return on the best available alternative investment of equal risks

Present Value (PV) value of today of a future cash flow or series of cash flow

Fair(Equilibrium)Value price at which investors are indifferent between buying or selling a security

Discounting

process of finding the present value of a cash flow or a series of cash flows; discounting is the reverse of compounding

PV =

0 1 2 3 4 55%

PV=? 127.63

0 1 2 3 4 55%

127.63

÷1.05

121.25115.76110.25105.00100

÷1.05 ÷1.05 ÷1.05 ÷1.05

Relationship among Present Value, Interest Rates, and Time

0 2 4 6 8 100

0.25

0.5

0.75

1

i = 0%i = 5%i = 10%i = 15%

i= i=

0 1 2 3 4 5?

78.35 100

n= n=

05%

78.35 100

n=?

Annuity

series of payment of an equal amount at fixed intervals for a specified number of periods

Ordinary (Deferred) Annuity annuity whose payment occur at the end of each period

Annuity Due

annuity whose payment occur at the beginning of each period

future value of an annuity over n periods

Perpetuity

stream of equal payments expected to continue forever

CONSOL

perpetual bond issued by the British government to consolidated past debts; in general, any perpetual bond

Uneven Cash Flow Stream series of cash flow in which the amount varies from one period to the next

Payment (PMT)

term designates equal cash flows coming at regular intervals

Cash Flows (CF)

term designates uneven cash flows

Terminal Value

future value of an uneven cash flows stream

Annual compounding arithmetic process of

determining the final value of a cash flow or series of cash flows when interest is added once a year

Semiannual Compounding arithmetic process of determining the final value of a cash flow or series of cash flows when interest is added twice a year

Nominal (Quoted, or Stated, or APR) Interest Rate contracted, or quoted, or

stated, interest rate

Effective (Equivalent)Annual Rate (EFF% or EAR) annual rate of interest

actually being earned, as opposed to the quoted rate

“equivalent annual rate”

Annual Percentage Rate (APR)

periodic rate X the number of periods per year

Amortized Loan

loan that is repaid in equal payments over its life

Amortization schedule

table showing precisely how a loan will be repaid

gives the required payment on each payment date and a breakdown of the payment, showing how much is interest and how much is repayment of principal