*This preview shows
pages
1–2. Sign up
to
view the full content.*

QUANTITATIVE REVIEW
Time Value of Money:
Evaluating financial transactions requires valuing uncertain
future cash flows.
Determinants of future value:
Present value
Compounding periods
Interest rate
COMPOUND (FUTURE) VALUE:
FV = Pv(1+i)^n
Frequency of compounding:
When interest is compounded more frequently than on an annual basis, adjust the
interest rate
and the
compounding periods
, accordingly.
Continuous compounding
:
One can compound multiple periods per year (semiannually,
quarterly, monthly, daily, hourly, etc.).
The limiting case would be to compound every
infinitesimal instant, which is commonly called continuous compounding.
The
compound factor uses the exponential function, e, the inverse of the natural logarithm.
Continuous compounding =
PV[e^(i)(n)]
Example
: Suppose you invest $5,000 in an account that earns 10% interest.
How much
more would you have after 20 years if interest is compounded continuously instead of
compounded semi-annually?
Semiannually:
$35199.94
Continuously:
$36945.28
Difference:
$1745.34
PRESENT VALUE
:
Translating a value back in time (discounting) to determine what a future amount or
cash flow is worth today.
FV
FV[ 1/(1+i)^n]
PV =
(1+i)^n
or
From the formula for the present value we know that:
o
as the number of discount periods, n, becomes smaller, the discount factor
becomes smaller and the present value becomes larger, and
o
as the interest rate per period, i, becomes smaller, the discount factor becomes
smaller and the present value becomes larger.

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
This is the end of the preview. Sign up
to
access the rest of the document.