Time Value Of Money Flashcards
In investment management applications the IRR is commonly referred to as
Dollar-Weighted rate of return
Market Risk in a revenue producing project can be adjusted for by :-
Adjusting the discount rate upward for increasing risk
Time Value of Money Purpose
-Time value of money concerns equivalence relationships between cash flows occurring on different dates
Three Ways to Consider Interest Rates
- Rates of return:* the minimum amount an investor must receive in order to accept an investment
- Discount rate:* the rate at which an amount of money is discounted to the present
- Opportunity cost:* the cost one is forgoing by spending money today
The Composition of the Interest Rate (r)
- Real risk-free interest rate
- Inflation premium
- Default risk premium
- Liquidity premium
- Maturity premium
-Real Risk-free Interest Rate
- 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
- Compensates investors for expected inflation and reflects the average inflation rate expected over the maturity of the debt
- Inflation reduces the purchasing power of a unit of currency
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
-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 the increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended, in general
-The difference between the interest rate on longer-maturity, liquid Treasury debt and that on short-term Treasury debt reflects a positive maturity premium for the longer-term debt
Nominal Risk-free Interest Rate
The sum of the real risk-free interest rate and the inflation premium
Simple Interest
-Interest rate times the principal
Principal
The amount of funds originally invested
Compounding
The interest earned on interest
Single Cash Flow Investment Equation for Multiple Periods (FV)
FV = PV(1 + r)^N
Important Note about N and r
Both variables must be defined in the same time units
-For example, if N is stated in months, then r should be the one-month interest rate, unannualized
PEMDAS Order of Operations
Parentheses first
- Exponents second
- Multiply and divide (left-to-right)
- Add and subtract (left-to-right)
Single Cash Flow Investment Equation for Multiple Compounding Periods per Year (FV)
FV = PV(1 + r/m)^(m*N)
- r = stated annual interest rate
- m = number of compounding periods per year
- N = number of years
Single Cash Flow Investment Equation with Continuous Compounding (FV)
FV = PVe^(r*N)
-N = number of years
Effective Annual Rate (EAR) Equation with Multiple Compounding Periods
EAR = (1 + Periodic interest rate)^m - 1
-m = number of compounding periods per year
Effective Annual Rate (EAR) Equation with Continuous Compounding
EAR = e^r - 1
Annuity
-A finite set of level sequential cash flows
Ordinary Annuity
-Has a first cash flow that occurs one period from now (t = 1)
Annuity Due
Has a first cash flow that occurs immediately (t = 0)
Ordinary Annuity
Has a first cash flow that occurs one period from now (t = 1)
Perpetuity
A set of level never-ending sequential cash flows, with the first cash flow occurring one period from now (t = 1)
Simple Annuity Equation (FV)
FV = A*[((1 + r)^N -1)/r]
- A = annuity amount
- r = interest rate per period
- N = number of periods
- The term in brackets is the future value annuity factor
Solve for Unequal Cash Flows
-Solve for each cash flow at a time using the simple FV/PV equation
Single Cash Flow Investment Equation for Multiple Periods (PV)
PV = FV[1/(1 + r)^N]
How Present Value Relates to the Discount Rate
For a given discount rate, the farther in the future the amount to be received, the smaller that amount’s present value
-Holding time constant, the larger the discount rate, the smaller the present value of future amount
Single Cash Flow Investment Equation for Multiple Compounding Periods per Year (PV)
PV = FV/[(1 + (r/m))^(m*N)]
m = number of compounding periods per year r = quoted annual interest rate N = number of years
Present Value of a Series of Equal Cash Flows Equation (PV)
PV = A[(1 - (1/((1 + r)^N))/r]
The Present Value of an Infinite Series of Equal Cash Flows - Perpetuity
PV = A/r
Growth Rate Equation
g = (FV/PV)^(1/N) - 1
- The single growth rate that, when added to 1 and compounded, with yield the FV
- Averages out the individual interest rates
Solving for N when Compounding Annually
N ln(1 + r) = ln(FV/PV)
Cash Flow Additivity Principle
When dealing with uneven cash flows, we take maximum advantage of the principle that dollar amounts indexed at the same point in time are additive
Time Value of Money
A relationship between time and money-that a dollar received today is worth more than a dollar promised at some time in the future.
Interest
Payment for the use of money, the excess cash received over and above the amount lent or borrowed.
Measurement options in financial reporting
1-Historical cost for equipment
2-Net realizable value for inventories
3-Fair value for investments
Three variables that determine the amount of interest that will be involved in a financial transaction?
1-Principal
2-Interest Rate
3-Time
Principal
The amount of money borrowed or invested
Interest Rate
A percentage of the outstanding principal
Time
The number of years or fractional portion of a year that the principal is outstanding.
Simple interest
The return on the principal for one time period.
Formula for simple interest
Interest = p * i * n
Compound interest
Interest computed on principal and on any interest earned that has not been paid or withdrawn.Return on principal for two or more periods.
How is compound interest calculated?
Compound interest uses the accumulated balance at the end of each year to compute interest in the succeeding year.
Stated Rate
Also known as nominal or face rate
What is the effective yield?
The effective yield is the interest that is actually earned based on how often the interest is compounded.
Rate of interest
An annual rate, unless otherwise stated, that must be adjusted to reflect the length of the compounding period if less than one year.
Number of time periods
The number of compounding periods
Future Value
The value at a future date of a given sum or sums invested assuming compound interest
Present Value
The amount needed to invest now to produce a known future value.
What are the two types of single sum problems?
1-Computing the unknown future value of a known single sum of money that is invested now
2-Computing the unknown present value of a known single sum of money in the future.
Future Value of a Single Sum Formula
FV=PV (FVF)
Present Value of a Single Sum Formula
PV= FV (PVF)
Annuity
A process of periodic payments that represents a sum of money
What is required to be defined as an annuity?
1-Periodic payments or rents
2-The same length intervals in between such rents
3-Compounding of interest once each interval
Future value of an annuity
The sum of all the rents plus the accumulated compound interest on them.
Ordinary Annuity
Annuity in which the rents occur at the end of each period.
Annuity Due
Annuity in which the rents occur at the beginning of each period.
What is the present value of an annuity?
The present value of an annuity is the single sum that if invested at compound interest now would provide for an annuity for a certain number of future periods.
How is the present value of an annuity due found?
Multiply the present value of an ordinary annuity factor times by 1 plus the interest rate.
Deferred Annuity
An annuity in which the rents begin after a specified number of periods, does not produce rents until two or more periods have expired.
How does the future value of a deferred annuity differ from the future value of an annuity?
They are treated the same, interest computation is not done for the deferral period.
How must the interest in the deferral period be handled when determining the present value of a deferred annuity?
The interest must be recognized from the deferral period when computing the present value of a deferred annuity.
Expected cash flows approach
Uses a range of cash flows and incorporates the probabilities of those cash flows to provide a more relevant measurement of present value.
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