Chapter 6 Flashcards
Time value of money
Indicates a relationship between time and money.
The dollar received today is worth more than a dollar promises at some time in the future. Why?
Bc the opportunity to invest today’s dollar and receive interest on the investment
Historical cost used for
Net realizeable value used for
Fair value used for
Equipment
Inventories
Investments
FASB requires the use of what to measure assets and liabilities?
Fair value
The most useful fair value measures are based on what?
Market prices in active markets
How can fair value be estimated
Based on expected future cash flows related to asset or liability
Notes
valuing incurrent receivables and payables that carry no stated interest rate or a lower than market interest rate
Leases
Valuing assets and obligations to be capitalized under long term leases and measuring the amount of the lease payments and annual leasehold amortization
Pensions and other post retirement benefits
Measuring service cost components of employers post retirement benefits expense and post retirement benefits obligations
Long term assets
Evaluating alt long term investments by discounting future cash flows.
Determining the value of assets acquired under deferred payment contracts. Measuring impairments of assets
Stock based compensation
Determining fair value of employee services in compensatory stock option plans
Business combinations
Determining the value of receivables payables liabilities accruals and commitments acquired or assumed in a purchase
Disclosures
Measuring the value of future cash flows from oil and gas reserves for disclosure in supplementary information
Environmental liabilities
Determine fair value of future obligations for asset retirements
Interest
Payment for use of money
Principal
Excess cash received or repaid over and above the amount lent or borrowed (principal).
How do business managers make investing and borrowing decisions ?
On th basis of rate interest involved rather than on the actual dollar amount of interest to be received or paid
How is interest rate determined?
One important factor is the level of credit risk involved.
The higher the credit risk, the higher
The interest rate
What are the variables in interest computation?
Principal – the amount borrowed or invested
Interest rate – a % of outstanding principal
Time – the # of years or fractional portion of a year that principle is outstanding
Three relationships apply:
Larger principal amount the larger the dollar amount of interest
The higher the interest rate, the larger the dollar amount of interest
The longer the time period, the larger the dollar amount of interest
Simple interest
On the amount of principal only.
It is the return on (or growth of) principle for one time period.
Simple interest formula
Interest = p x i x n
P = principal R = rate of interest for a single period N = # of periods
Compound interest
Compute c.i. On principal and any interest earned that has not been paid or withdrawn
Compound interest uses what at the year end to compute interest in succeeding year?
Uses the accumulated balance
Principal plus interest to date
Any rational investor would choose _____ over ______ if available
Choose compound interest if available over simple interest
Which is the typical interest computation applied in business situations?
Compound interest
Simple interest usually applies to only what?
Short term investments and debts that involve a time span of one year or less
Future value of 1 table
Contains amounts to which 1 will accumulate if deposited now at a specified rate and left for a specified number of periods
Present value of 1 table
Contains the amounts that must be deposited now at a specified rate of interest to equal 1 at the end of a specified number of periods
Future value of an ordinary annuity of 1 table
Contains the amounts to which periodic rents of 1 will accumulate of the payments (rents) are invested at the end of each period at a specified rate of interest for a specified # of periods
Present value of an ordinary annuity of 1 table
Contains the amounts that must be deposited now at a specified rate of interest to permit withdrawals of 1 at the end of regular periodic intervals for the specified # of periods
Present value of an annuity due of 1 table
Contains the amounts that must be deposited now at a specified rate of interest to permit withdrawals of 1 at the beginning of regular periodic intervals for the specified number of periods
Interest is generally expressed as?
In terms of annual rate
But when businesses circumstances dictate a compounding period of less than one year….. a company must what?
Concert the annual interest rate to correspond to the length of the period
How to convert annual interest rate into compounding period interest rate ?
Divides the annual rate by the # of compounding periods per year
How to determine # of periods
Multiplying # of years involved by the # of compounding periods per year
Fundamental variables are
Rate of interest – unless otherwise stated, an annual rate that must be adjusted to reflect the length of compounding period if less than a year
of time periods – # of compounding periods ( a period maybe equal to or less than a year)
FV – the value at a future date of a given sum or sums invested assuming compound interest
PV– the value now (present) of a future sum or sums discounted assuming compound interest
Single sum problems are classified into one of the following
- Computing the unknown FV, of a known single sum of money that is invested now for a certain # of periods at a certain interest rate
- Computing unknown PV of a known single sum of money in the future that is discounted for a certain # of periods at a certain interest rate
Rule for solving a FV
Accumulate all cash flows to a future point
In this instance, interest increases the amounts or values over time so that the FV exceeds PV
Rule for solving for a PV
Discount all cash flows from future to present
In this case discounting reduces amounts of values, PV is less than FUture amount
Present value is the amount needed to invest now,
To produce a known fv
Present value of a single sum
The present value is always smaller than
Known FV due to earned and accumulated interest
Present value of a single sum
In determining FV ,
The company moves forward in time using the process of accumulation
Present value of a single sum
In determining PV,
It moves backward in time using a process of discounting
In many business situations both the FV and PV are known but what could be unknown?
Interest rate or the number of periods
Annuity by definition requires the following
- Periodic payments or receipts (called rents) of same amount
- Same length interval between such rents
- Compounding of interest once each interval
Future value of annuity
Is the sum of all rents plus the accumulated compound interest on them
If the rent occurs at the end of each period
It is classified as ordinary annuity
If rent occurs at beginning of each period,
Annuity is classified as an annuity due
What is one way in determine future value of annuity?
Compute value to which each of the rents in the series will accumulate and then totals their individual FV
Because of ordinary annuity consists of rents deposited at the end of each period, the rents earn no what?
No interest during the period in which they are deposited
When computing FV of an ordinary annuity , the # of compounding periods will always be
One less than the # of rents
Preceding analysis of an ordinary annuity assumes that periodic rents occur when?
At end of each period
Annuity due assumes periodic rents occur
At the beginning of each period
This means annuity due will accumulate interest during first period and ordinary annuity rent will NOT
How to find future value of annuity due factor?
Multiply the FV of an ordinary annuity factor by 1 plus interest rate
In determining FV of an annuity there will be one less interest period than if the rents occur
At the beginning of the period (annuity due)
Present value of an ordinary annuity
Present value of series of equal rents to be withdrawn at equal intervals at the end of th period
One approach to finding PV of annuity determines
PV of each of the rents in series and then totals their individual present values
Present value of ordinary annuity,
Discounted final rent based on # of rents periods
Determining PV of an annuity due
There is always one fewer discount period
To find PV of an annuity due factor
Multiplying PV of an ordinary annuity factor by 1 plus interest rate
(1 + i)
What are the other time value of money issues
- Deferred annuities
- Bond problems
- PV measurement
Deferred annuity
Is the annuity in which the rent begin after a specified # of periods
A deferred annuity does not begin to produce rents until
Two or more periods have expired
Why is computing FV of a deferred annuity relatively straightforward?
There is no accumulation or investment on which interest may accrue, FV of a deferred annuity is the same as FV of annuity not deferred
That is, COMPUTING FV SIMPLY IGNORES DEFERRED PERIOD
Computing PV of deferred annuity must recognize what?
The interest that accrues on the original investment during the deferral period
To compute PV of deferred annuity
We compute PV of an ordinary annuity of 1 as if the rents had occurred for entire period
We then subtract PV of rents that were not received during deferral period
We are left with PV of rents actually received subsequent to the deferral period
Long term bond produces 2 cash flows
- periodic interest payment during the life of bond
2. Principle (FV) paid at maturity
Valuation of long term bonds
Period interest payments represent what?
Principal represents
Annuity
Single sum problem
Effective interest method
The preferred procedure for amortization of a discount or premium
Under the effective interest method
- Company issues bond first computes bond interest expense by multiplying the carrying value of bonds at beginning of period by effective interest rate
- The company then determines bond discount or premium amortization by comparing bond interest expense with interest to be paid
The effect interest method produces what?
A periodic interest expense equal to a constant % of carrying value of the bonds
Expected cash flow approach
It uses range of cash flows and incorporates the probabilities of those cash flows to provide a more relevant measurement of PV
3 components of interest
- Pure rate of interest (2-4%)
- Expected inflation rate of interest (0%-?)
- Credit risk rate of interest (0-5%)
A company should discount those cash flows by
Risk free rate of return
The rate is defined as
Pure rate of return plus the expected inflation rate
