Quantitative Methods Flashcards
interest rate (r)
r = real risk-free interest rate + inflation premium + default risk premium + liquidity premium + maturity premium
a rate of return that reflects the relationship between diffrently dated cash flows; can be thought of as 1. required rate of return; 2. discount rate; 3. opportunity cost
nominal risk-free interest rate
rnominal risk-free = real risk-free interest rate + inflation premium
1 + r**nominal risk-free = (1 + rreal risk-free) * (1 + rinflation premium)
often represented by governmental short-term debt interest rate (e.g. 90-day US Treasury bill)
real risk-free interest rate
single-period interest rate for a completely risk-free security if no inflation were expected
reflects time preferences of individuals for current versus future real consumption
inflation premium
compensates investors for expected inflation
reflects average inflation rate expected over the maturity of the debt
default risk premium
compensates investors for possibility that the borrower will fail to make a promised payment at the contracted time and in the contracted amount
liquidity premium
compensates investors for the risk of loss relative to an investment’s fair value if the investment needs to be converted to cash quickly
maturity premium
compensates investors for increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended, in general (ceteris paribus)
simple interest
interest rate times the principal
future value (FV)
FV<em>N</em> = PV(1 + r)N
NB: r and N must be defined in the same time units
FV<em>N</em> = PV(1 + (rs /m))<em>m</em>N
future value factor = (1 + r)N
stated annual interest rate = rs
number of compounding periods per year = m
future value (FV) with continuous compounding
FV<em>N</em> = PVer(s)N
where e = 2.7182818
effective annual rate (EAR)
EAR = (1 + periodic interest rate)<em>m</em> - 1
EAR = er(s) - 1
where m is the number of compounding periods per year
annuity
finite set of level sequential cash flows
ordinary annuity
annuity with first cash flow that occurs one period from now (indexed at t=1)
annuity due
annuity that has first cash flow that occurs immediately (indexed at t=0)
perpetuity
a perpetual annuity, or a set of level never-ending sequential cash flows, with the first cash flow occuring one period from now (indexed at t=1)
examples: dividends from stocks, some government bonds and preferred stocks
general annuity formula
future value factor
(1 + r)N
present value factor
1 / (1 + r)<em>N</em>
present value formula
PV = FVN / (1 + r)N
PV = FVN / (1 + (rs/m)<em>mN</em>
- m* = number of compounding periods per year
- rs =* quoted annual interest rate
- N* = number of years
present value of an ordinary annuity
present value of a perpetuity
PV = A/r
only for perpetuities with level payments
growth rate formula
g = (FV<em>N </em>/ PV)1/<em>N</em> - 1
rule of 72
72 divided by the stated interest rate is the approximate number of years it would take to double an investment at the stated interest rate
converse: it takes 12 years to double an investment at 6% interest rate (6 x 12 = 72)
cash flow additivity principle
dollar amounts indexed at the same point in time can be added