1 - Time Value of Money Flashcards
Notes
Interest rate - definition
An interest rate, denoted r, is a rate of return that reflects the relationship between differently dated cash flows.
Interest rate - Equation
r = Real risk-free interest rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium
Opportunity cost - definition
An opportunity cost is the value that investors forgo by choosing a particular course
What can interest rates be thought off - 3 ways (3)
First, they can be considered required rates of return—that is, the minimum rate of return an investor must receive in order to accept the investment.
Second, interest rates can be considered discount rates. In the example above, 5.26 percent is that rate at which we discounted the $10,000 future amount to find its value today. Thus, we use the terms “interest rate” and “discount rate” almost interchangeably.
Third, interest rates can be considered opportunity costs.
Real risk-free interest rate - definition
The real risk-free interest rate
is the single-period interest rate for a completely risk-free security if no inflation were expected. In economic theory, the real risk-free rate reflects the time preferences of individuals for current versus future real consumption.
Inflation premium - definition
The inflation premium
compensates investors for expected inflation and reflects the average inflation rate expected over the maturity of the debt.
Inflation - definition
Inflation
The percentage increase in the general price level from one period to the next; a sustained rise in the overall level of prices in an economy.
Default risk premium - definition
Default risk premium
compensates investors for the possibility that the borrower will fail to make a promised payment at the contracted time and in the contracted amount.
Default risk - definition
Default risk
The probability that a borrower defaults or fails to meet its obligation to make full and timely payments of principal and interest, according to the terms of the debt security. Also called default probability.
The liquidity premium - definition
The 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
Liquidity - definition
Liquidity
The extent to which a company is able to meet its short-term obligations using cash flows and those assets that can be readily transformed into cash.
Liquidity risk - definition
Liquidity risk
The risk that a financial instrument cannot be purchased or sold without a significant concession (you do not want to but you have to for example pay the price for something without haggling) in price due to the size of the market.
Maturity premium - definition
The maturity premium
compensates investors for the increased sensitivity
of the market value of debt to a change in market interest rates as maturity is extended, in general (holding all else equal).
Simple interest - definition
Simple interest
The interest earned each period on the original investment; interest calculated on the principal only. = Interest rate x the principal
Principal - definition
Principal
The amount of funds originally invested in a project or instrument; the face value to be paid at maturity.
Compounding - definition
Compounding
The process of accumulating interest on interest.
Future value - Equation
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Non-Annual Compounding (Future Value)
Stated annual interest rate or Quoted interest rate - definition
Stated annual interest rate or Quoted interest rate
A quoted interest rate that does not account for compounding within the year. Also called stated annual interest rate. = rs.
Effective annual rate (EAR) - defintion
Effective annual rate (EAR)
The amount by which a unit of currency will grow in a year with interest on interest included.
Future value of a sum in N years with continuous compounding - Equation
Effective annual rate (EAR) - definition
Effective annual rate (EAR)
The amount by which a unit of currency will grow in a year with interest on interest included.
EAR with continuous/discrete compounding - Equation
EAR with continuous compounding - Equation
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Periodic interest rate - definition
The periodic interest rate
is the stated annual interest rate divided by m, where m is the number of compounding periods in one year.
Annual percentage rate (APR) - definition
Annual percentage rate (APR)
Measures the cost of borrowing expressed as a yearly rate.
Present Value - Equation
Non-annual compounding (Present Value) - Equation
m = number of compounding periods per year rs = quoted annual interest rate N = number of years
What happens to the PV when the discount rate is larger?
Holding time constant, the larger the discount rate, the smaller the present value of a future amount.
What happens to the PV when the discount rate the farther in the future the amount to be received?
For a given discount rate, the farther in the future the amount to be received, the smaller that amount’s present value.
An annuity - definition
An annuity
is a finite set of level sequential cash flows. Two types:
1) ordinary annuity
2) annuity due
Annuities may be handled in a similar approach as single payments if we use annuity factors rather than single-payment factors.
An ordinary annuity - definition
An ordinary annuity
has a first cash flow that occurs one period from now (indexed at t = 1).
An annuity due - definition
An annuity due
has a first cash flow that occurs/is paid immediately (indexed at t = 0).
A perpetuity - definition
A perpetuity
is a perpetual annuity, or a set of level never-ending sequential cash flows, with the first cash flow occurring one period from now. A bond that does not mature.
Present Value of a Series of Equal Cash Flows - Equation
A = the annuity amount r = the interest rate per period corresponding to the frequency of annuity
payments (for example, annual, quarterly, or monthly) N = the number of annuity payments
General annuity formula (future value) - Equation
General annuity formula if we define the annuity amount as A, the number of time periods as N, and the interest rate per period as r.
Ordinary annuity is called a perpetuity (a perpetual annuity) - Equation
The present value of a perpetuity - Equation
where A is the periodic payment to be received forever.
When present values, future values, and a series of cash flow are indexed at the same point in time what does this mean?
A lump sum can be seen as equivalent to an annuity, and an annuity can be seen as equivalent to its future value. Thus, present values, future values, and a series of cash flows can all be considered equivalent as long as they are indexed at the same point in time.
The cash flow additivity principle - definition
The cash flow additivity principle
the idea that amounts of money indexed at the same point in time are additive—is one of the most important concepts in time value of money mathematics.
Growth rate - Equation
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