88
Business Finance
Lecture 16
Review of the Previous Lecture
z
Annuities cash Flows
{
Present Value
{
Future Value
z
Annuities Due
Topics under Discussion
z
Perpetuities
z
The Effect of Compounding Periods
{
Effective Annual Rate
{
Annual Percentage Rate
z
Loans
{
Pure discount Loans
{
Interest Only Loans
{
Amortized Loans
Perpetuities
z
A special case of annuity, where the stream of cash flows continue forever.
z
The present value of a perpetuity is
Perpetuity PV = C / r
Perpetuities
z
Suppose we expect to receive $1000 at the end of each of the next 5 years. Our opportunity
rate is 6%. What is the value
today
of this set of cash flows?
PV
=
$1000 x (1  [1/1.06
5
]) / 0.06
=
$1000 x 4.212364
=
$4212.364
z
Now suppose the cash flow will be $1000 per year
forever
, making it a
perpetuity
. In this case,
the PV is easy to calculate:
PV = C/r = $1000/.06 = $16,666.67
Summary of Annuity and Perpetuity
I.
Symbols
PV
=
Present value, what future cash flows bring today
FV
t
=
Future value, what cash flows are worth in the future
r
=
Interest rate, rate of return, or discount rate per period
t
=
Number of time periods
C
=
Cash amount
II.
FV of C per period for t periods at r percent per period:
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FV
t
= C °
[(1 + r)
t
 1] / r
III. PV of C per period for t periods at r percent per period:
PV = C °
(1  [1/(1 + r)
t
]) / r
IV. PV of a perpetuity of C per period:
PV = C / r
Effective Annual Rates
z
If a rate is quoted as 10% compounded semiannually, then what this means is that the
investment actually pays 5% every six months.
z
Is 5% every six months the same thing as 10% per year?
{
$1 x 1.10 = $1.10
{
$1 x 1.05
2
= $1.1025
z
10% compounded semiannually is equivalent to 10.25% compounded annually.
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 Spring '11
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 Interest Rates, Annual Percentage Rate, Mortgage loan, Annual Rates

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