ECON*2560 Theory of Finance
CHAPTER 4 THE TIME VALUE OF MONEY

Companies invest in hopes to receive even more than they invested

Companies pay for their investments by raising money – and in the process assume
liabilities

All financial decisions ( of assuming liabilities) require comparisons of cash payments at
different dates

The time value of money describes the relationship between the value of the dollar today
and the value of the same dollar in the future
o
How much do you need to invest today to produce a specified sum of money in
the future ?
o
How does inflation affect these financial decisions ?
4.1 FUTURE VALUES AND COMPOUND INTEREST
Interest= interest rate x initial investment

In general, for any interest rate (r )
the value of the investment at the end of the period
will become (1+r) times the amount invested
at the end of an investing period
Future value (FV):
amount to which and investment will grow after earning interest
Compound interest:
interest earned on interest.
Simple interest:
interest earned only on the original investment; no interest is earned on interest.

The higher the rate of interest, the faster your savings will grow

The future value of any investment can be calculated with the future value formula
FV of $investment = I x ( 1 + r)
t
Future value interest factor:
future value of a current cash flow of $1
Future value factor , FVIF(r,t)= (1+r)
t

The future value of an investment can be calculated by multiplying in invested amount
( principle) by the future value factor of $1 investment for the same period and interest
rate
FV= Ix future value factor
= I x FVIF (r,t)
= I x (1+r)
t

Can also look up values in the FV table
Compound growth means that value increases each period by the factor (1+growth rate ) .
the value after t periods will equal the initial value times (1 + growth rate )
t
. when money is
invested at compound interest, the growth rate is the interest rate.
4.2 PRESENT VALUES
‘ a dollar today is worth more than a dollar tomorrow’
o
this statement is true such that money can be invested to earn interest
•
ex. If offered $100,000 now and $100,000 later, the clear choice
would be to accept the money now and earn a year’s interest

we have examined how to grow a future value, BUT how much do we need to invest now
in order to produce a certain amount?
This phenomenon is called, present value
Present value( PV):
value today of a future cash flow
Preset value = future value after t periods
(1+r)
t
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How much is this money worth today, on the basis that we will gain interest of a certain
amount over a specific time period
On the basis that we can invest this money at a specific rate; how much
more is this dollar worth today as to tomorrow?

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 Spring '11
 Bower
 Time Value Of Money, Future Value

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