Chapter 5: Time value of money Flashcards
what does time value mean for money
it can be invested today and be worth more tomorrow
what is the opportunity cost of money
the interest rate that would be earned by investing it
what is the discount rate also called
required rate of return (k)
what do you need to make time value decisions
identify the relevant discount rate you should use
what is simple interest
interest paid or received only on the initial investment (principal)
- the same amount of interest is earned each year
what is compound interest
interest that is earned on the principal amount and on the future interest payments
how do you calculate FV on financial calculator
PV = - , I/y, n, cpt FV
what is discounting also called
computing for PV
what does PV or discounting mean
asking how much will a person need to invest today at that interest rate to have $xxx in so many years``
what is of exchange
something that can be used to facilitate transactions
money in a sense represents out ability to buy goods and services, that is it operates s a medium of exchange and has no value in and of itself.
what is the compound value interest factor (CVIF)
a term that represents the future value of an investment at a given rate of interest and for a stated number for periods (1 + K)to the power of n
- basic compounding equation
what is basis point
1/100 of 1 percent is a basis point
what happens when earning just a few basis points more on one investment
causes the future value of the portfolio to compound that much faster
- just be careful not underestimate the associated risks, it can cause you to loose big
what is discounting
finding the present value of a future value by accounting for the time value of money
what is present value interest factor (PVIF)
a formula that determines the present value of $1 to be received at some point in the future n based on a given interest rate k
if people don’t want to pay in the full price for something, they ask for a discount
so $1 million in 40 years is
in the same way, $1 million dollars in 40 years is not worth $1 million today, so you discount or take something off to get it to its true value
the discount factors (PVIF) are always less than one as long as
discount rates are positive k is greater than 0
this means that future dollars are usually worth less than the same dollars today
- this is not always the case (pay german gov. to lend them money)
the greater the discount rate, the
greater the CVIF and future value
and
the smaller the PVIF and present value
and vice versa
consider low interest rates on pension funds, what happens when interest rates are low
based on discounting these future pension payments using current interest rates
- as a result of very low interest rates, the PV of these pension liabilities has increased dramatically
volatile (and largely negative ) capital market returns hit pension funds how
on both sides of their funding equation
- resulted in major funding issues
- the effect of these low interest rates, combined with poor investment returns has meant that many defined-benefit pension plans have significant deficits as their assets have not increased as fast as the PV of their lia bilities
Time or “holding” Periods
how long do we need to invest 20, 00 at 10% to get 31,000
how do you calculate the holding period or time when you invest 20,000 at 10% to get 31,000?
0 PMT 31,000 FV -20,000 PV 10 I/Y CPT N = 4.5982 or 4.6 years
what is the rate of return
Price is 20,000 invesetment that has a payoff of 31,000 in 5 years
0 PMT 31,000 FV -20,000 PV 5 N CPT I/y 9.16 rate of return
what is interest rate also called
rate of return
what does discounting ask
how much will aperson need to inveset today at that interest rate to have a certain amount in 40 years
what is an ordinary annuity
series of equal payments over a fixed amount of time
- payments are mde at the END of each period
assuming a player earning an average of 2.4 million decides to invest 10% which is $141,600 at the END of each year for the next 6 years and expects to earn 8% per year. how much will the have at the end of 6 years
141,600 PMT 6 N 0 PV (no deposit today) 9 I/y CPT FV = 1,038,768
what are Annuities due
payments are made at the beginning rather than the end of each year (set calculator to BGN mode)
assuming a player earning an average of 2.4 million decides to invest 10% which is $141,600 at the Beginning of each year for the next 6 years and expects to earn 8% per year. how much will the have at the end of 6 years
2nd BGN 2nd set 141,600 PMT 6 n 0 pv 8 I/y CPT FV = 1,121,869
what are perpetuities
special annuities in that they go on forever
- so n gets to infinity in the annuity equation
use 1000 as your place holder for time?
definition of an annuity
regular payments on an investment that are for the same amount and are paid at the same interval
definition of cash flows
the actual cash generated from an investment
definition ordinary annuity
equal payments that are made at the end of each period
definition of lessee
a person who leases an item
definition of annuity due
an annuity (such as a lease) for which the payments are made at the beginning of each period
what is the nominal rate
quoted rate
what is effective interest rate
the rate at which a dollar invested grows over a given period, usually stated in % terms based on an annual period
- looking at the rate alone is not enough it is important to look at the compounding frequency
as the frequency of the compounding increases,
the effective annual rate also increases
how do you calculate the effective interest rate with a quoted rate of 12% compounded annually
2nd Iconv, 2nd clrwork NOM - enter 12 (quoted rate) enter down arrow down arrow C/Y = 1 compounded annually enter down arrow down arrow EFF = CPT = 12.747%
how do you calculate the effective interest rate with a quoted rate of 12% semi annually
2nd iconv, 2nd clrwork
NOM = 12 enter down arrow down arrow
C/Y = 2 enter down arrow down arrow
EFF = CPT = 12.36%
how do you calculate the effective interest rate with a quoted rate of 12% compounded continuously
0.12
2nd ex
-1
= 12.75%
definition of mortgage
a loan, usually secured by real property, that involves “blended” equal payments (both interest and a principal repayment) over a specified payment period
definition amortize
to retire a loan over a given period by making regular payments
the balance at the end of the term will be zero
what can a mortgage be viewed as and why
an annuity
because these loans involve equal payments at regular intervals, based on one fixed interest rate specified when the loan is taken out, the payments can be viewed as annuities
what does an amortization schedule do
it divides the blended payments into the interest portion and the principal repayment portion
important for business because
- interest portion is a deductible expense for tax purpsoes.
for mortgages how is the interest portion determined
by applying the effective period interest rate to the principal outstanding at the beginning of each period
- the remaining portion of the payment is used to reduce the amount of principal outstanding
how are mortgages in Canada compounded
semi-annually , similar to bonds
payments on mortgages can be made
at least monthly
what is the term of a mortgage payment
the period for which investors can “lock in” at a fixed rate (usually shorter than the actual period to repay the amount in full)
