Flashcards in Time Value of Money Module Deck (67):
It is important to understand the role that __________ plays in making financial decisions in the short and long term so that future revenues and cash flow can be analyzed in today's dollars.
We operate in the present time, therefore it is crucial to be able to translate the impact of current and future financial decisions in terms of the dollar's current value.
Time value calculations can be made using the future value or _______ value techniques.
The amount of cash at a particular date in the future that is equivalent in value to a specified sum today.
The present value technique refers to the current value of one or more future cash payments, discounted at a specific ________ rate.
Present value relates to a sequence of future cash flows expressed in today's dollars and therefore _________ has to take place in order to account for the present value.
Financial ________ tend to prefer the present value technique because they make decisions at the start of the project.
Since the present value technique measure values at the start of the project time zero, these tend to be preferred.
A ________ is a horizontal line that has the present time and value on the far left hand corner and future periods and value are displayed as you move towards the right.
Money has a time value and therefore a dollar is worth more now than later, even after adjustment for _________, because the dollar received now can appreciate in value until the time the dollar in the future would be received.
A dollar received now can be _______ and appreciate in value whereas a dollar received at a future time will not be given this opportunity.
What are three computational aids that can be used in order to calculate present and future values?
1) Financial tables
2) Handheld business and financial calculators
3) Personal Computers
These calculations are complex and require these aids.
The general structure of a financial table consist of two rows displaying the ___________ and interest rate.
In order to ascertain the future or present value of money, time and the _______ rate are the two key factors required.
To calculate the future value of a single amount, interest is __________ on the principal sum over a particular period.
The effect that interest has on an amount of money when the interest rate is applied to both the initial sum invested as well as the interest that has already been received on that sum is called ___________.
A invests $100 at 10% interest per year. Assume the interest stays fixed over a 2 year period. After Year 1, interest earned is $10 ($100 x 10%). That is added on to the _______ sum of money invested to make a total of $110 ($100 + $10). In year 2 interest earned is $11 ($110 x 10%). The total is now $121($110+$11).
The principal is the amount of money on which ________ is calculated and paid.
Interest is owed on a loan and the principal is the amount borrowed.
Where FV=______ value, k=Annual interest rate, PV=present value and n=number of periods eg years, the formula for calculating the future value is FVn=PV x(1+K)n
___________ is the general formula for calculating future value.
Future value calculations can be simplified by using a _____ factor.
What does FVIF stand for?
Future Value Interest Factor
FVIF, Future Value Interest Factor, is a multiplier used to calculate the future value of an amount of money as of a particular time by applying a specifed interest rate. This formula is expressed as FVIFk,n= (1+k)n These factors can be easily looked up in ________ tables.
The future value at the end of a specified period will be higher where the interest rate is higher and the time period is ______.
Future value is impacted directly by these 2 factors. A higher interest rate over a longer time period will yield a higher ______ value.
The present value is equal to the future value when the ________ rate is zero.
Where the interest rate is zero, there is ________ of the present value.
Semi-annual and quarterly compounding of interest means that interest is compounded two and ____ times respectively over a period of one year.
A saves $100 at an interest rate of 10% for 1 year. Bank Y offers semi-annual compounding and Bank Z offers quarterly compounding. At bank Y, A would accumulate $110.25 after 1 year. ($100 x 5%) after 6 months and the (105 x 5%) =$110.25 and at Bank Z it would total $110.38. ($100 x 2.5%) 1st quarter ($102.5 x 2.5%) 2nd quarter ($105.06 x 2.5%) 3rd quarter (107.69 x 2.5%) 4th quarter.
The amount of money accumulated will be higher when the compounding is more _______.
This is because as interest is compounded, the total money accumulated is greater and repeated compounding increases this even further.
An _______ is a series of regular equal annual payments.
This is the definition of an annuity, payments must be at regular intervals and the cash flows are level.
Where FVAn = future value of an n year annuity, FVIFAk,n = future value interest factor for a $1 annuity compounded at k% for n years and PMT=amount deposited annually at the end of each year, the future value of an annuity can be calculated using this formula FVAn = _______________.
PMT x (FVIFAk,n).
FVAn = PMT x (FVIFAk,n) is the formula for calculating the future value of an ______.
The present value of a single amount is the _______ dollar value of a future amount.
Future because the present value must be calculated according to the amount of present dollars having to be _______ at a given interest rate in order to be equal to the future amount.
In order to calculate the present value, a technique known as ___________ cash flows must be used.
It is called discounting because it is actually the ________ process for compounding interest.
Discounting determines the _______ value of future amount, assuming that there is an opportunity to earn a particular rate of return on the money.
Discounting takes into account the ____ of capital of an investment, which examines the rate of return that could have been earned had that investment been selected.
Cost of capital OR _____________ cost OR discount rate OR required return are terms that are used interchangeably to describe the discounting process where the future amount is given a present value, which can be calculated using the opportunity cost at a given rate.
_______ value calculations assume that the future values are measured at the end of the stated time period.
A constant needs to be applied for these calculations and this assumption is therefore made.
The present value ________ factor (PVIF) is a multiplier used to calculate the present value of an amount to be received in the future based on a given discount rate.
What does (PVIF) stand for?
Present value interest factor
The discount rate is used to calculate the present value based on a given amount in the future. It is the reverse process of _____________.
Where PV=present value, FV=future value, PVIF=present value interest factor, k=interest rate and n=number of years or given period, the formula for calculating present value is PV = FVn x (_____,n).
PV = ____x (PVIFk,n) is the formula for calculating present value.
Generally speaking, the ______ the discount rate, the lower the present value and the longer the time period, the lower the present value.
If the discount rate is higher, this in effect means that present value must have been lower in order for the discount rate to have inflated the future value. As for the length of time being indicative of a lower present value, that is because a smaller amount of money needs to be invested to reach the designated future value over a _______ period of time.
If John Davis wishes to find out the present value of $10,000 that he would obtain in 10 years, assuming an opportunity cost of 10%, then he would need to multiply $10,000 by the ____ at 10% for 10 years.
By taking $10,000 and multiplying it by the PVIF at 10% for 10 years, he would get the present value of the $10,000 assuming an opportunity cost of 10%.
Where the discount rate is zero the present value is always _____ to the future value.
If the discount rate is zero, then there is no opportunity for _______ to occur to the future value.
A mixed stream of cash flows is one where there is no particular _______.
The cash flows can be mixed, of unequal amounts and at irregular time periods.
The present value of a _____ stream is calculated by determining the present value of each future amount and then adding up all individual streams to obtain the total present value.
In order to calculate the present values, the current value of the future dollar amount must be determined.
The present value interest factor for an annuity (PVIFAk,n) is the multiplier for calculating the present value of an annuity at a particular discount rate for a particular _______.
The discount rate must be used to calculate present values from a ______ amount.
Where PVAn=present value of an n-year annuity, PMT=equal cash flow received annually at the end of the year, PVIFAk,n=present value interest factor for a $1 annuity discounted at k% over n years, then the formula for calculating the present value of an annuity is PVAn=PMT x (______,n).
PVAn = PMT x (PVIFAk,n)is the formula for calculating the present value of an ________.
A _________ is an annuity that makes continual annual payments for an infinite period of time.
The present value of a perpetuity can be calculated by multiplying the amount to be received annually (___) by the present-value interest factor for a perpetuity.
(PMT) amount to be received annually
The present value interest factor (PVIAk a)of a perpetuity is found by using 1 divided by the _______ rate.
Future and present value techniques have important applications in calculating the ________ needed to accumulate a future amount.
Deposits are needed to accumulate a future sum and individuals and companies need to know how much they need to deposit over a period of time to pool a certain amount of money. For example, if Mr A wishes to save up $5000 for a holiday in 3 years time, then he needs to work out how much money he needs to deposit annually into an account paying 5% interest, to have this sum of money in 3 years.
The formula for calculating the annual deposit required to accumulate a future sum is equal to FVAn /________.
In other words, the future value amount you wish to attain divided by the future value interest factor at k% for n years.
The gradual elimination of a liability, such as a mortgage, in regular payments over a given period of time to cover both principal and interest is better known by the term loan __________.
Lenders use a loan ____________ schedule to determine the amounts of interest and principal necessary to pay off the loan.
This schedule is available in tables at banks and are calculated by creating an annuity out of the present amount.
In order to amortize a $6000 loan at 10% interest over 4 years where the borrower repays equal amounts at the year end; the lender has to work out the amount of a 4 year annuity _________ at 10%, that has a present value of $6000.
The process of amortization involves creating an annuity out of the present amount and so it is the inverse of finding the present value of an annuity and hence the process of discounting.
The formula for calculating the annual payment required to pay of a loan is to take the loan amount and divide it by the _______ value interest factor for an annuity at the given interest rate and loan duration.
This is the formula for finding the annual payment required to pay off a loan. The actual equation is PVAn/PVIFAk,n
In the loan amortization schedule, each annual loan payment made is offset against both the ________ and principal.
The loan repayments are meant to cover both the cost of the interest for the loan as well as the paying off the _______ amount owed.
When amortizing a loan, the borrower will notice that the allocations of the loan payments representing the interest will ________, whereas the portion for the principal will increase.
At the beginning of the loan, the majority portion of the loan payments will cover the interest and a smaller proportion to paying off the principal. As the principal is reduced with each payment, hence the interest portion will consequently reduce and more of the payment will be allocated to paying off the __________.