Chapter 6: Accounting and the Time Value of Money Flashcards
Present Value Factor
PVF of n, i = 1 / (1+i)^n
i= interest rate per period n= number of compounding periods
Effective Rate
= (1+i)^n - 1
i = interest rate PER PERIOD n= number of periods
Future value of an ordinary annuity
where:
n= number of compounding periods
i = interest rate for compounding period
= ((1+i)^n-1)/i
Future value of an ordinary annuity also = R (periodic rent)
Compounding periods, ordinary annuity
Number of compounding periods = number of rents minus one
Ordinary annuity vs annuity due
Ordinary = rents due at the END of each period
Rents earn no interest in the period in which they are deposited
Annuity Due = rents occur at the beginning of each period
Future value of 1 table
Amounts to which $1 will accumulate if deposited now at a specified rate, left for a specified number of periods
Annuity
Periodic payments (rents) of the same amount made at equal intervals compounding interest once each interval
Future value factor
where:
i = rate of interest for a single period
n = number of periods
FvFn,i = (1+i)^n
periods = years x compounding periods per year
Computing present value
When future value is known
Discount all cash flows from future to present PV < Future Value
Present Value = Future value x PVFn,i
PVFn,i = present value factor for n periods at i interest
Computing Future Value
When present value is known
Must accumulate all cash flows to a future point (FV > PV)
Future value = present value x FVFn,i
FVFn,i = Future value factor for n periods at i rate
Discounting
Opposite of accumulation: removing accumulated interest
Future Value
Value at a future date of a given sum or sums invested assuming compound interest
Number of Periods
Total number of compounding interest
Rate of interest
Annual interest rate adjusted to reflect the length of a compounding period (if period is less than a year)
Time Value of Money
A dollar receiving today is worth more than a dollar promised in the future due to the potential investment returns on that dollar
Present Value
Per moneychimp: the amount of money one would need to invest today in order to have a specified balance in the future
per book: the value now of a future sum or sums discounted assuming compounding interest
Present Value techniques
Use to convert expected cash flows into present value as an estimate of fair value
Present value based accounting measurements
Notes - noncurrent with no stated interest or lower than market Leases Pensions/ retirement benefits long term assets stock-based compensation business combinations disclosures environmental liabilities
Present value of an annuity due of $1 table
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
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 intervals for the specified number of periods
Future Value of an ordinary annuity of $1 table
Rents = payments
Contains the amounts to which periodic rents (will accumulate?) if the rents are invested at the END of each period at a specified rate of interest 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
Effective Yield
Total yield received when the interest payments are reinvested at the same rate as the principal
Simple Interest
= principal x rate x number of periods
rate must be the rate for a single period, whatever it is - need to adjust annual interest rate
Converting annual interest rate to compounding interest rate
Annual rate / number of compounding periods in a year
Future Value
Value at a later date of a single sum that is invested at compound interest
Preset value
Value at an earlier date (usually now) of a given future some discounted at compound interest
Pure rate of interest
Amount a lender would charge if there were no possibilities of default and no expectations of inflation
