chapter 5 book: Time Value of Money Flashcards
time value of money
the idea that a dollar today is worth more than a dollar in the future
medium of exchange
something that can be used to facilitate transactions
The opportunity cost of money
the interest rate that would be earned by investing it
what we would get instead of just holding it like wankers
basically, the price of money
required rate of return or discount rate
the market interest rate
Simple interest
interest paid or received on only the initial investment (the principal)
the formula to calculate simple interest
Value (time n) =
P + (n × P × k)
P: principal
n: number of periods
k: interest rate
compound interest
interest that is earned on the principal amount invested and on any accrued interest
amount of interest earned increases every year or period
we reinvest the amount we have year after year
reinvesting
continuing to invest principal as well as interest each year
formula for future value using compound interest
FV = PV · (1 + k)^n
FV: future value
PV: present value
k: interest rate
n: number of periods
future value interest factor (FVIF)
a term that represents the future value of an investment at a given rate of interest and for a stated number of periods
(1 + k)^n
always less than one if k is positive
basis point
1/100 of 1 percent
why do finance experts focus so much on basis points?
because of compound interest
small and even minimal differences in interest rates can makes huge differences in many many years
discounting
determining present values
finding the present value of a future value by accounting for the time value of money
formula for finding present value using the time value of money
PV = FV / (1 + k)^n
FV: future value
PV: present value
k: interest rate
n: number of periods
discount factor or present value interest factor (PVIF)
1 / (1 + k)^n
a formula that determines the present value of $1 to be received at some time in the future, n, based on a given interest rate, k
what do we mean when we say that PVIF and FVIF are reciprocals?
the greater the discount rate, the greater the FVIF (and future value) and the smaller the PVIF (and present value), and vice versa
annuity
a series of payments or receipts (cash flows)
regular payments on an investment that are for the same amount and are paid at the same interval of time
cash flows
the actual cash generated from an investment
Ordinary annuities
involve end-of-period payments
equal payments that are made at the end of each period of time
lessee
a person who leases an item
annuity due
cash flows are paid at the beginning of a period
ex: a lease
perpetuity
a special annuity that provides payments forever
formula of present value of normal perpetuity
PV = PMT / k
formula of present value of growing perpetuity and needed conditions for it to work
PV = PMT / (k - g)
g: constant rate per period
1. only works when k > g
2. Only future estimated cash flows and estimated growth in these cash flows are relevant
3. The relationship holds only when growth in payments is expected to occur at the same rate indefinitely
formula of present value of growing annuity
its the same as the growing perpetuity but the last payment occurs at time n, that is, the payments do not go on to infinity
PV =
(PMT / (k - g)) ·
[1 - ((1 + g)/(1 + k))^n]
The effective rate for a period
the rate at which a dollar invested grows over that period
It is usually stated in percentage terms based on an annual period
formula to find the effective rate
k = (1 + (QR / m))^m - 1
k: effective rate
QR: quoted rate
m: number of compounding periods per year
formula to find the effective rate when compounding is conducted on a continuous basis
k = e^QR − 1
mortgage loan
involves “blended” equal payments (both interest and a principal repayment) over a specified payment period
involves usually an amortized loan
for real assets such as properties
compounded semi annually (In Canada)
amortization
killing a loan over a given period by making regular payments
payments can be viewed as annuities
does the principal payment increase or decrease each period?
what about interest payment?
why tho?
principal payment increases each period because the total payment stays the same but the interest payments decrease
interest payments decrease because the total amount outstanding decreases after each payment
interest are higher at the beginning because the cost of borrowing money is higher at the beginning
the term of a loan
refers to the period for which investors can “lock in” at a fixed rate
interest rates on the mortgage can change after the term ends
usually shorter than the period over which the loan is to be repaid, or amortized
amortization period
he period over which the loan is to be repaid, or amortized
formula to find the mount you pay of interest (excluding principal payment) on mortgage payments
k monthly =
(1 + (k / 2))^(2 / 12) - 1
