Intro to Finance: Chapter 5

Entering positive numbers designates...

cash inflows.

Negative numbers designates....

cash outflows.

How fast a firm can grow its sales, earnings, or cash flows is an important signal about its:

competitive position.

moving cash flow forward

compounding

moving cash flow backward

discounting

more than annual compounding

= more than the nominal rate, increases as compounding becomes more frequent

annual compounding

= nominal rate

finding an unknown number of period equation

log (FVn/PV0 ____________________ log(1 + r)

annual percentage yield (APY)

"Truth-in-savings laws," in contrast, require banks to quote the annual percentage yield (APY) on their savings products. The APY is the effective annual rate a savings product pays. For example, a savings account that pays 0.75% per month would have an APY of 9.38% .

Future-value and present-value techniques have a number of important applications in finance. Name four of them.

(1) determining deposits needed to accumulate a future sum, (2) loan amortization, (3) finding interest or growth rates, and (4) finding an unknown number of periods.

What are the two general types of annuities?

1) ordinary annuity 2) annuity due

What are the three types of basic cash flow patterns?

1) single amount 2) annuity 3) mixed stream

What is annuity?

A level periodic stream of cash flows. Many financial arrangements involve making or receiving a fixed payment each month or year, such as a loan. The classic example from consumer finance is the home mortgage.

What is a loan amortization schedule?

A loan amortization schedule is a record of the payments that a borrower makes, including the interest and principal components of each payment, and the schedule shows the remaining loan balance after each payment. Many consumer loans such as home mortgages and car loans are typically structured as amortizing loans.

What is a single amount?

A lump sum amount either currently held or expected at some future date. For example, we might want to know how much a $1,000 investment made today might be worth in five years. Or we might wish to know how much money we have to set aside today to cover some specific one-time payment we'll have to make in the future.

perpetuity equation

A number of business and personal investment decisions involve payouts that occur indefinitely into the future and are therefore excellent applications of the idea of a perpetuity. Fortunately, the calculation for the present value of a perpetuity is one of the easiest in finance :)

What is a timeline?

A timeline depicts the cash flows associated with an investment. It is a horizontal line on which time zero appears at the leftmost end and future periods are marked from left to right.

annual percentage rate (APR)

APR is the nominal annual rate, which is found by multiplying the periodic rate by the number of periods in one year. At the consumer level, "truth-in-lending laws" require disclosure on credit card and loan agreements of the (APR).

Explain continuous compounding.

As the number of compounding periods per year gets very large, we approach a situation in which we continuously compound interest. This means interest compounds every second (or even every nanosecond)—literally, interest compounds all the time

Explain the present value of an annuity due.

Because the cash flows of an annuity due occur at the beginning rather than end of the period, we discount each annuity due cash flow one fewer period than an ordinary annuity. each payment of the annuity due is discounted less (by one period), so it's worth r% more than each ordinary annuity payment. (page 214)

When is it necessary to compare loan costs? How do we do that (what do we need to distinguish)?

Both businesses and investors need to compare loan costs or investment returns when compounding intervals differ. To make such comparisons, we distinguish between nominal and effective annual rates.

How often can compounding occur?

Compounding may occur daily, monthly, annually, or at almost any time interval. Annual compounding is the simplest type.

How do you get the future value of a mixed stream?

Determining the future value of a mixed stream of cash flows is straightforward. We compute the future value of each cash flow at the specified future date and then add all the individual future values to find the total future value.

How do you get the present value of a mixed stream?

Finding the present value of a mixed stream is similar to finding the future value. We determine the present value of each cash flow and then add all the individual present values together to find the total present value.

Quoting loan interest rates at their lower nominal annual rate (the APR) and savings interest rates at the higher effective annual rate (the APY) offers what advantages? (There's two)

First, it tends to standardize disclosure to consumers. Second, it enables financial institutions to quote the most attractive interest rates: low loan rates and high savings rates.

What is future value?

Future value is the value on some future date of money that you invest today. The future value depends on how much money you invest now, how long it remains invested, and the interest rate earned by the investment.

When does the growing perpetuity method concept/equation apply?

It applies only when the discount rate is greater than the growth rate in cash flows (i.e., r > g). If the discount rate is less than or equal to the growth rate, cash flows grow so fast that the present value of the stream is infinite. Don't want the denominator to be 0.

What does the time value of money refer to?

It refers to the observation that it is better to receive money sooner than later. You can invest money you have in hand today to earn a positive rate of return, producing more money tomorrow.

How do you find the percentage difference between the value of the ordinary annuity and the value of the annuity due?

It's the interest rate! Because of the extra year of interest on each of the annuity due's payment. This makes the annuity due x% more valuable than the ordinary annuity.

What is growing perpetuity?

Many financial applications require analysts to calculate the present value of a perpetuity that grows at a steady rate. Calculating the present value of a growing perpetuity is not much more complicated than finding the present value of a level perpetuity. For a perpetuity that begins next year, pays an initial cash flow of , and grows at a constant rate g, the present value is

Explain the future value of an ordinary annuity.

Remember that the cash flows of an annuity due occur at the start of the period. If we are dealing with annual payments, each payment in an annuity due comes one year earlier than it would in an ordinary annuity, which in turn means that each payment can earn an extra year of interest.

What is simple interest?

Simple interest is interest earned only on an investment's original principal and not on accumulated interest. Naturally, money accumulates faster when an investment earns compound interest rather than simple interest.

What is the annual rate of return variously referred to as?

The discount rate, required return, cost of capital, and opportunity cost.

Is future value of an annuity due or ordinary annuity larger?

The future value of an annuity due exceeds the future value of an otherwise identical ordinary annuity. This is because there is an extra period of compounding.

Explain the present value of an ordinary annuity.

The method for finding the present value of an ordinary annuity is similar to the method just discussed. One approach is to calculate the present value of each cash flow in the annuity and then add up those present values.

Compare the annuity due with the ordinary annuity present value.

The present value of an annuity due is always greater than the present value of an otherwise identical ordinary annuity. Because the cash flows of the annuity due occur at the beginning of each period rather than at the end, their present values are greater. The % difference between the two is the discount rate the person will be using.

What is loan amortization?

The term loan amortization refers to a situation in which the borrower makes fixed periodic payments and gradually pays down the loan principal over time.

What is principal?

The term principal may refer to the original amount of money placed into an investment or to the balance on which an investment pays interest.

How do lenders attract homebuyers?

To attract home buyers who could not afford fixed-rate 30-year mortgages requiring equal monthly payments, lenders offered mortgages low "teaser" interest rates that adjusted over time. Recall that subprime mortgages are mortgage loans made to borrowers with lower incomes and poorer credit histories as compared to "prime" borrowers.

For using the financial calculator, what important concept do you need to understand?

To provide a correct answer, financial calculators and electronic spreadsheets require that users designate whether a cash flow represents an inflow or an outflow

Sometimes individuals want to know how long it will take them to reach a particular savings goal if they set aside a lump sum today or if they make fixed deposits into an investment account each year. What relationship fo you rely on? What is different about this particular situation?

To solve this problem, we will once again rely on the basic future value relationship described in Equation 5.1, except that here we want to solve for n rather than FVn.

Explain compounding & future value.

Typically, the single point in time is either the end or the beginning of the investment's life. The future value technique uses compounding to find the future value of each cash flow at the end of the investment's life and then sums these values to find the investment's future value

What do time-value-of-money techniques help us determine?

What the monthly mortgage payment will be given the size of the loan required to buy a home.

What is a mixed stream?

Whereas an annuity is a pattern of equal periodic cash flows, a mixed stream consists of unequal periodic cash flows that reflect no particular pattern. Financial managers frequently need to evaluate opportunities that they expect to provide mixed streams of future cash flows. Here we consider both the future value and the present value of mixed streams.

What do you need to know future value?

You must know the present value, or the amount of money we have today; the interest rate; the number of periods the investment will earn interest; and the compounding interval, that is, the number of times per year that interest compounds.

What is an annuity?

a stream of equal periodic cash flows over a specified time. These cash flows may arrive at annual intervals, but they can also occur at other intervals, such as monthly rent or car payments. The cash flows in an annuity can be inflows or outflows.

What is perpetuity?

an annuity with an infinite life. In other words, it is an annuity that never stops providing a cash flow at the end of each period.

In other words, given the principal, the interest rate, and the term (i.e., the length of time that the borrower makes payments) of the loan, we can calculate the periodic loan payment by:

finding an annuity that has the same present value as the loan principal.

One of the performance measures that investors and corporate managers focus on most is _____.

growth

What is compound interest?

interest paid on an investment's original principal and on interest that has accumulated over previous periods.

Explain quarterly compounding.

involves four compounding periods within the year. One-fourth of the stated interest rate is paid four times a year.

n * m

number of periods that the money is compounded

Explain semiannual compounding.

occurs when an investment pays interest twice in a year with interest compounding after each payment. The investment pays half its annual stated interest rate every six months, rather than making one payment at the end of the year.

How does compound interest work?

ompound interest works by adding the interest earned from one period to the original principal, to create a new principal value for the next period. *Thus, an investor receives (or a borrower pays) interest not only on the original principal but also on interest that has been earned in previous periods and added to the original principal balance.*

r/m

periodic compound rate of interest

At higher interest rates and for longer investment horizons, the differences can be....

quite substantial.

g =

retention rate x roi

In terms of time-value-of-money concepts, the stream of fixed payments in an amortizing loan has the ____ present value as the original principal.

same

What is the general equation for compounding?

situations when compounding takes place more than once per year. If r is the interest rate per year, n is the number of years, and m equals the number of times per year interest compounds, the formula for the future value of a lump sum becomes PV x (1 + (r/m)) ^ (m*n)

What is the effective/true annual rate?

the annual rate of interest actually paid or earned once the effects of compounding have been taken into account. The effective annual rate reflects the effects of compounding frequency, whereas the nominal annual rate does not.

What is an annuity due?

the cash flow occurs at the beginning of each period. ex: rent, car payments

What is the nominal/stated annual rate?

the contractual annual interest rate charged by a lender or promised by a borrower.

When the interest rate is very low and the time that the money remains invested is vey short...

the difference between earning compound interest and simple interest is small.

The concept of present value is...

the inverse of compounding interest. Instead of finding the future value of present dollars invested at a given rate, discounting determines the present value of a future amount, assuming an opportunity to earn a certain return on the money

What is present value?

the value in today's dollars of some future cash flow An equivalent definition is that the present value is the amount that one would have to invest today such that the investment would grow to a particular value in the future.

What is an ordinary annuity?

where the cash flow occurs at the end of each period ex: mortgage payment