time value of money
it is better to recieve money sooner than later, money that you have in hand today can be invested to earn a positive rate of return, producing more money tomorrow.
compounding/discounting (time value of money)
the future value technique uses compounding to find the future value of each cash flow at the end of the investments life and then sums thses values to find the investments future value.
the present value technique uses discounting to find the present val
basic patterns of cash flow
single amount: a lump sum amount either currently held or expected at some future date. examples include $1000 today and $650 to be recieved at the end of 10 years.
annuity: a level periodic stream of cash flow. for our purposes, well work primarily with
future value
the value at a given future date of an amount placed on deposit todsy and earning interest at a specified rate. the future value depends on the rste of interest earned and the length of time the money is left on deposit.
compound interest
indicate that the amount of interest earned on a given deposit has become part of the principal at the end of a specified period.
principal
the amount of money in which interest is paid.
present value
the current dollar value of a future amount- the amount of money that would have to be invested today at a given interest rate over a specified period to equal the future amount.
discounting cash flows
the process of finding present values; the inverse of compounding interest.
commonly referred to as the discount rate, required return, cost of capital and opportunity cost.
1: the higher the discount rate, the lower the present value.
2: the longer the p
annuity
a stream of equal periodic cash flows over a specified time period. these cash flows can be inflows of returns earned on investments or outflows of funds invested to earn future returns.
ordinary annuity
the cash flow that occurs at the end of each period.
ordinary annuities are more frequently used in finance.
future value:
1000 PMT
5 N
7 i
Fv
present value:
700 PMT
5 N
8 I
PV
annuity due
the cash flow occurs at the beginning of each period.
the annuity due would earn a higher future value thsn the ordinary annuity becuase each of its five annual cash flows can earn interest for 1 year more than each of the ordinary annuitys cash flows.
BE
perpetuity
is an annuity with an infinite life- in other words, an annuity that never stops providing its holder with a cash flow at the end of each year (for example, the right to recieve $500 at the end of each year forever)
PV = CF / r
mixed stream
a stream of unequal periodic cash flows that reflect no particular pattern
nominal (stated) annual rate
contractual annual rate of interest charged by the lender or promised by a borrower
effective (true) annual rate (EAR)
the annual rate of interest actually paid or earned
annual percentage rate (APR)
the nominal annual rate of interest found by multiplying the periodic rate by the number of periods in one year, that must be disclosed to consumers on credit cards and loans as a result of "truth-in-lending laws.
annual percentage yield (APY)
the effective annual rate of interest that must be disclosed to consumers by banks on their savings products as a result of "truth-in-savings laws
loan amortization
the determination of the equal periodic loan payments necessary to provide a lender with s specified interest return and to repay the loan principal over a specified period.
6000 PV
4 N
10I
PMT
loan amortization schedule
a schedule of equal payments to repay a loan. it shows the allocation of each loan payment to interest and payment
interest rate
usually applied to debt instruments such as bank loans or bonds; the compensation paid by the borrower of funds to the lender; from the borrowers point of view, the cost of borrowing funds.
required return
usually applied to equity instruments such as common stock; the cost of funds obtained by selling an ownership interest.
inflation
a rising trend in the prices of most goods and services
liquidity preference
a general tendency for investors to prefer short-term (that is, more liquid) securities.
real rate of interest
the rate that creates equilibrium between the supply of savings and the demand for investment funds in a perfect world, without inflation, where suppliers and demanders of funds have no liquidity preferences and there is no risk.
factors that influence equilibrium interest rate
one factor is inflation, a rising trend in the prices of most goods and services. typically, savers demand higher returns (higher interest rates) when inflation is high becuase they want their investments to more than keep pace with rising prices. a secon
nominal rate of interest
the actual rate of interest charged by the supplier of funds and paid by the demander. the nominal rate of interest differs from the real rate of interest, r* , as a result of two factors, inflation and risk.
investors will demand a higher nominal rate of
3-month u.s. treasury bills (t-bills)
are short term IOU's issued by the u.s. treasury and they are widely regarded as the safest investments in the world. they are as close as we can get in the real world to a risk free investment. to estimate the real rate of interest, analyst typically try