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Time Value Of Money Flashcards

0
Q

In investment management applications the IRR is commonly referred to as

A

Dollar-Weighted rate of return

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1
Q

Market Risk in a revenue producing project can be adjusted for by :-

A

Adjusting the discount rate upward for increasing risk

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3
Q

Time Value of Money Purpose

A

-Time value of money concerns equivalence relationships between cash flows occurring on different dates

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4
Q

Three Ways to Consider Interest Rates

A
  • 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
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5
Q

The Composition of the Interest Rate (r)

A
  • Real risk-free interest rate
  • Inflation premium
  • Default risk premium
  • Liquidity premium
  • Maturity premium
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6
Q

-Real Risk-free Interest Rate

A
  • 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
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7
Q

-Inflation Premium

A
  • 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
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8
Q

Default Risk Premium

A

-Compensates investors for the possibility that the borrower will fail to make a promised payment at the contracted time and in the contracted amount

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9
Q

-Liquidity Premium

A

Compensates investors for the risk of loss relative to an investment’s fair value if the investment needs to be converted to cash quickly

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10
Q

Maturity Premium

A

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

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11
Q

Nominal Risk-free Interest Rate

A

The sum of the real risk-free interest rate and the inflation premium

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12
Q

Simple Interest

A

-Interest rate times the principal

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13
Q

Principal

A

The amount of funds originally invested

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14
Q

Compounding

A

The interest earned on interest

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15
Q

Single Cash Flow Investment Equation for Multiple Periods (FV)

A

FV = PV(1 + r)^N

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16
Q

Important Note about N and r

A

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

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17
Q

PEMDAS Order of Operations

A

Parentheses first

  • Exponents second
  • Multiply and divide (left-to-right)
  • Add and subtract (left-to-right)
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18
Q

Single Cash Flow Investment Equation for Multiple Compounding Periods per Year (FV)

A

FV = PV(1 + r/m)^(m*N)

  • r = stated annual interest rate
  • m = number of compounding periods per year
  • N = number of years
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19
Q

Single Cash Flow Investment Equation with Continuous Compounding (FV)

A

FV = PVe^(r*N)

-N = number of years

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20
Q

Effective Annual Rate (EAR) Equation with Multiple Compounding Periods

A

EAR = (1 + Periodic interest rate)^m - 1

-m = number of compounding periods per year

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21
Q

Effective Annual Rate (EAR) Equation with Continuous Compounding

A

EAR = e^r - 1

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22
Q

Annuity

A

-A finite set of level sequential cash flows

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23
Q

Ordinary Annuity

A

-Has a first cash flow that occurs one period from now (t = 1)

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24
Q

Annuity Due

A

Has a first cash flow that occurs immediately (t = 0)

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25
Q

Ordinary Annuity

A

Has a first cash flow that occurs one period from now (t = 1)

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26
Q

Perpetuity

A

A set of level never-ending sequential cash flows, with the first cash flow occurring one period from now (t = 1)

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27
Q

Simple Annuity Equation (FV)

A

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
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28
Q

Solve for Unequal Cash Flows

A

-Solve for each cash flow at a time using the simple FV/PV equation

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29
Q

Single Cash Flow Investment Equation for Multiple Periods (PV)

A

PV = FV[1/(1 + r)^N]

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30
Q

How Present Value Relates to the Discount Rate

A

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

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31
Q

Single Cash Flow Investment Equation for Multiple Compounding Periods per Year (PV)

A

PV = FV/[(1 + (r/m))^(m*N)]

m = number of compounding periods per year
r = quoted annual interest rate
N = number of years
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32
Q

Present Value of a Series of Equal Cash Flows Equation (PV)

A

PV = A[(1 - (1/((1 + r)^N))/r]

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33
Q

The Present Value of an Infinite Series of Equal Cash Flows - Perpetuity

A

PV = A/r

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34
Q

Growth Rate Equation

A

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
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35
Q

Solving for N when Compounding Annually

A

N ln(1 + r) = ln(FV/PV)

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36
Q

Cash Flow Additivity Principle

A

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

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37
Q

Time Value of Money

A

A relationship between time and money-that a dollar received today is worth more than a dollar promised at some time in the future.

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38
Q

Interest

A

Payment for the use of money, the excess cash received over and above the amount lent or borrowed.

39
Q

Measurement options in financial reporting

A

1-Historical cost for equipment
2-Net realizable value for inventories
3-Fair value for investments

40
Q

Three variables that determine the amount of interest that will be involved in a financial transaction?

A

1-Principal
2-Interest Rate
3-Time

41
Q

Principal

A

The amount of money borrowed or invested

42
Q

Interest Rate

A

A percentage of the outstanding principal

43
Q

Time

A

The number of years or fractional portion of a year that the principal is outstanding.

44
Q

Simple interest

A

The return on the principal for one time period.

45
Q

Formula for simple interest

A

Interest = p * i * n

46
Q

Compound interest

A

Interest computed on principal and on any interest earned that has not been paid or withdrawn.Return on principal for two or more periods.

47
Q

How is compound interest calculated?

A

Compound interest uses the accumulated balance at the end of each year to compute interest in the succeeding year.

48
Q

Stated Rate

A

Also known as nominal or face rate

49
Q

What is the effective yield?

A

The effective yield is the interest that is actually earned based on how often the interest is compounded.

50
Q

Rate of interest

A

An annual rate, unless otherwise stated, that must be adjusted to reflect the length of the compounding period if less than one year.

51
Q

Number of time periods

A

The number of compounding periods

52
Q

Future Value

A

The value at a future date of a given sum or sums invested assuming compound interest

53
Q

Present Value

A

The amount needed to invest now to produce a known future value.

54
Q

What are the two types of single sum problems?

A

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.

55
Q

Future Value of a Single Sum Formula

A

FV=PV (FVF)

56
Q

Present Value of a Single Sum Formula

A

PV= FV (PVF)

57
Q

Annuity

A

A process of periodic payments that represents a sum of money

58
Q

What is required to be defined as an annuity?

A

1-Periodic payments or rents
2-The same length intervals in between such rents
3-Compounding of interest once each interval

59
Q

Future value of an annuity

A

The sum of all the rents plus the accumulated compound interest on them.

60
Q

Ordinary Annuity

A

Annuity in which the rents occur at the end of each period.

61
Q

Annuity Due

A

Annuity in which the rents occur at the beginning of each period.

62
Q

What is the present value of an annuity?

A

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.

63
Q

How is the present value of an annuity due found?

A

Multiply the present value of an ordinary annuity factor times by 1 plus the interest rate.

64
Q

Deferred Annuity

A

An annuity in which the rents begin after a specified number of periods, does not produce rents until two or more periods have expired.

65
Q

How does the future value of a deferred annuity differ from the future value of an annuity?

A

They are treated the same, interest computation is not done for the deferral period.

66
Q

How must the interest in the deferral period be handled when determining the present value of a deferred annuity?

A

The interest must be recognized from the deferral period when computing the present value of a deferred annuity.

67
Q

Expected cash flows approach

A

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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EAR

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EAR

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EAR

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