CHAP 5 Fin 335 Cengage
Future value
A future value represents the amount to which a current (present) value will grow over a given period of time when compounded at a given rate of interest. Mathematically, a future value is calculated as FV = PV x (1 + r)nn.
mortgage
A mortgage is a home loan in which a home buyer borrows a lump-sum amount at either a fixed or variable interest rate and repays it in monthly installments over a certain period of time. Variable-rate mortgages, called adjustable-rate mortgages, typically offer relatively lower rates than fixed-rate mortgages but are riskier because they fluctuate based on macroeconomic factors. When a home buyer makes a mortgage payment, part of the payment pays the interest on the loan, and the rest goes toward repaying the principal amount. The part that actually goes toward the principal amount is calculated as payment made minus interest due. At the end of the contract term, the home buyer should have paid the entire principal amount and the interest charged on it; thus, the ending balance of an amortized loan contract will be zero.
Perpetuity
A perpetuity is a series of equal cash flows that are expected to continue forever. A perpetuity can be considered to be a special type of annuity. While both a perpetuity and an annuity exhibit constant periodic cash flows, the annuity has a definite end date, and the perpetuity does not. Instead, a perpetuity's cash flows are expected to continue indefinitely.
Uneven Cash Flows
A series of cash flows that are not equal. example: *SOE Corp. hires an average of 10 people every year and matches the contribution of each employee toward his or her retirement fund. **Franklinia Venture Capital (FVC) invested in a budding entrepreneur's restaurant. The restaurant owner promises to pay FVC 10% of the profit each month for the next 10 years. ***SOE Corp. matches every employee's contribution toward his or her retirement fund. Because employees' contributions toward their retirement may change and the number of employees changes every year due to new hires, the contribution that SOE Corp. makes every year will keep changing. Thus, these contribution payments are an example of uneven cash flows. ****A restaurant will generate revenues and profits that will vary based on such factors as economic conditions, competition, and so on. FVC receives 10% of the restaurant's profit each month. Because the profit will vary, FVC's earnings from the investment will also vary every month. Thus, the payments that FVC receives are an example of uneven cash flows.
Ordinary annuity
A series of equal cash flows that are paid or received at regular intervals, such as a day or a month, is called an annuity. When the cash flows occur at the end of each of the regular intervals, the series is called an ordinary annuity. An example of an ordinary annuity is the 60 monthly payments of $676.65 made at the end of each month to repay a $35,000 loan that charges 6% interest and is to be repaid over five years. If the cash flow were to occur at the beginning of each of the regular intervals, then the annuity would be called an annuity due.
amortization schedule
An amortization schedule or table reports the amount of principal and the amount of interest that make up each payment made to repay a loan by the end of its regular term. Remember, the term amortization has two meanings. One meaning refers to the process of decreasing the principal outstanding on a loan via payments containing both interest and principal. The second meaning refers to the depreciation of the intangible assets owned by a firm.
Amortized loan
An amortized loan is one that is repaid with payments that are composed of both the interest owed on the loan and a portion of the loan's principal. In contrast, a zero-interest loan is one on which interest is not charged and the payments made to repay the loan will consist only of principal.
Annuity due
An annuity due is the name given to a series of equal cash flows that occur at the beginning of each of the equally spaced intervals (such as daily, monthly, annually, and so on).
There are two categories of cash flows: single cash flows, referred to as "lump sums," and annuities. Based on your understanding of annuities, answer the following questions. Which of the following statements about annuities are true? Check all that apply.
An ordinary annuity of equal time earns less interest than an annuity due. When equal payments are made at the beginning of each period for a certain time period, they are treated as an annuity due. Annuities are structured to provide fixed payments for a fixed period of time.
Discounting
One of the four major time value of money terms; the amount to which an individual cash flow or series of cash payments or receipts will grow over a period of time when earning interest at a given rate of interest.
Time value of money calculations can be solved using a mathematical equation, a financial calculator, or a spreadsheet. Which of the following equations can be used to solve for the future value of a lump sum?
PV x (1 + r)n
Annual percentage rate
The annual percentage rate (APR) is the cost of borrowed funds as quoted by lenders and paid by borrowers, in which the interest required is expressed as a percentage of the principal borrowed. This rate does not reflect the effects of compounding if interest is earned more than once per year.
Time value of money
The financial concept that maintains that the timing of a receipt or payment of a cash flow will affect its value is called the time value of money (TVM). The time value of money illustrates that, due to its capacity to earn interest, a cash flow received today is worth more than an identical cash flow to be received on a future date. The exact current value of a future cash flow is a function of the magnitude of the future cash flow, the return required by the owner (recipient) of the cash flow, and when in the future the cash flow will occur.
Opportunity cost of funds
The interest rate that represents the return on an investor's best available alternative investment of comparable (equal) risk is the investor's opportunity cost of funds.
Compounding Frequency
The number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the present and future values of cash flows.. A nominal rate is also called the annual percentage rate. Therefore, the nominal interest rate (IIII) is the same as the APR
annuity due
When a payment is made at the end of each period, it is treated as an ordinary annuity; when a payment is made at the beginning of each period, it is treated as an annuity due **Annuity due payments are made one period earlier than ordinary annuity payments, so they will earn interest for an additional period. Therefore, the value of an annuity due will be greater than the value of a similar ordinary annuity. To take this additional period of interest into account, multiply the value of the ordinary annuity by 1 plus the interest rate (1 + I) to find the value of the annuity due.
Annuities are defined as
a series of equal payments at regular intervals either made, received, or both, for a certain number of periods.
perpetuity
is a series of payments made at fixed intervals that continue infinitely and can be thought of as an infinite annuity. The present value of a perpetuity is calculated by dividing the amount of the payment by the investor's opportunity interest rate.
Compounding
is the term used to describe the process of computing a future value. It requires knowledge of three of the four time-value-of-money variables: •The present value (PV) of the amount deposited •The interest rate (I) that could be earned by deposited funds •The duration of the deposit (N) The trend between the present and future values of an investment is not directly relevant to the calculation of a future value.
types of cash flow streams
lump sum annuity streams uneven cash flow streams
Effective Annual Rate (EAR)
the interest actually being earned by the investment. If interest is compounded more than once per year, the effective annual rate is greater than the nominal interest rate, because the investment earns interest on the principal as well as on the interest previously earned. The effective annual rate of this investment is solved using the following equation:
cash flow
the total amount of money being transferred into and out of a business, especially as affecting liquidity. - what you can use
