Acct 301A exam 2 Chapter 6

How much will $5,000 grow into by the end of 3 years with a compounding interest of 10%?

$5,000 * 1.33100 (table 6-1) = $6655

Name the 3 properties of an annuity?

(1) Same/Identical amount every period (2) Compound interest once every period (3) Each interval between amounts is equal

For the future value of an ordinary annuity, when you have only 1 period, what is the future value factor of $1?

1

Applications to Time Value Concepts for Present Value-Based Accounting Measurements examples

1. Notes 2. Leases 3. Pensions and other postretirement 4. Long term assets 5. Shared based compensation 6. Business combinations 7. Disclosures 8. Enviornmental liabilities

Name 2 types of annuities?

1. Ordinary annuity 2. Annuity due

Name two types of cash flows for the valuation of long term bonds?

1. Periodic interest payments (annuity) 2. Principle paid at maturity (single-sum)

Name 3 things that annuities require?

1. Periodic payments or receipts (called rents) of the same amount, 2. Same-length interval between such rents, and 3. Compounding of interest once each interval.

Name 3 variables in interest computation?

1. Principle 2. Interest rate 3. Time

Name 4 fundamental variables?

1. Rate of interest 2. Number of time periods 3. Future value 4. Present value

The future value of an ordinary annuity can be seen on which table?

6-3

The present value of an ordinary annuity can be seen on which table?

6-4

What does the time value of money mean?

A relationship between time and money.

Federal law requires the disclosure of interest rates on an ____ basis

Annual basis

Formula for finding compounding period interest rate

Annual rate divided by the number of compounding periods per year.

Name two types of annuities?

Annuity (OA) vs. Annuity Due (AD)

DEF: Rent occurs at the beginning of each period.

Annuity due

Timing of the periodic amount is at the start of each compounding period is known as what kind of annuity?

Annuity due

DEF: Computes interest on principle and interest earned that has not been paid or withdrawn.

Compound interest

When interest is earned on a PRINCIPLE and INTEREST amount, what kind of interest is this?

Compound interest

When you take out the embedded interest of a future value to arrive at the present value, what is this process called?

Discounting

_____ future value to the present value is the process of removing interest (i.e. time value of money) from the future value given certain time periods and compound interest rate

Discounting

Formula for computing FV of a single sum?

FV = PV * FVi,n

True/False. For an annuity at the START of the period, it is not considered an annuity due?

False

True/False. Most business situations do not use compound interest?

False. Most businesss situations use compound interest.

The future value of a series of $1 made at the end of each period given certain number of time periods at compound interest rate is interpreted as what kind of annuity factor?

Future value factor of an ordinary annuity

Example: Chris Spear invested $15,000 today in a fund that earns 8% compounded semiannually. To what amount will the investment grow in 3 years? First determine what table will be used?

Future value of 1 (table 6-1) Present value $15,000 x 1.26532 factor = $18,980 future value

The table shows how much principal plus interest a dollar accumulates to at the end of each of five periods, at three different rates of compound interest. Which table is this referring to?

Future value of 1 at compound interest (table 6-1)

DEF: Value at a future date of a given amount invested, assuming compound interest.

Future value of a single sum

The table shows how much you accumulate to by investing a dollar at the end of each compounding period (number of compounding periods range from one to five), at three different rates of compound interest. Which table is this referring to?

Future value of an ordinary annuity of 1 (table 6-3)

What is the future value of five $5,000 deposits made at the end of each of the next 5 years, earning interest of 12%? What table do we use?

Future value of an ordinary annuity of 1 (table 6-3) $5,000 deposits x 6.35285 factor = $31,764 FV

Example: Bayou Inc. will deposit $20,000 in a 12% fund at the beginning of each year for 8 years beginning January 1, Year 1. What amount will be in the fund at the end of Year 8? What table are we using?

Future value of an ordinary annuity of 1 (table 6-3) Factor = 12.29969 x 1.12 = 13.775652 $20,000 deposit x 13.775652 = $275,513 FV

How much a dollar can accumulate to given certain time periods and compound interest rate in the future is the interpretation of what formula?

Interepretation of FVF = (1+i)^n

DEF: A percentage of the outstanding principal.

Interest rate

Future $1 less the amount of interest embedded in a future one dollar given certain time periods and compound interest rate is known as which interpretation?

Interpretation of PVF

Do the number of periods need to be annual?

It depends on the compounding situation. Ex: If you compound interest at 5 periods annually, that future value amount will equal to 5 years. If you compound interest every 3 months for 4 periods, that is one year.

What two components do you need to know before you can locate the proper time value factor in the tables?

Number of periods and compound interest rate

DEF: Rent occurs at the end of each period

Ordinary annuity

Timing of the periodic amount is at the end of each compounding period is known as what kind of annuity?

Ordinary annuity

Formula for computing the PV of a single sum?

PV = FV * PVFi,n

Clancey Inc. issues $2,000,000 of 7% bonds due in 10 years with interest payable at year-end. Find the bond current market value.

PV interest $939,411 + PV of principle $926,380 = $1,865,791

The sum of periodic rents less the amount of interest embedded in the series of $1 made at the start of each period given certain number of time periods and compound interest rate is known as?

PV of an annuity due

The sum of periodic rents less the amount of interest embedded in the series of $1 made at the END o each period given certain number of time periods and compound interest rate is known as?

PV of an ordinary annuity

Formula for finding the present value of long term bonds

PV of principal + PV of periodic interest (Principal * PVF_i%,n) + (principal * stated interest rate) * PVF_OA_i%,n

Formula for PVF

PVF = 1/(1+i)^n

Example: Tony Bautista needs $25,000 in 4 years. What amount must he invest today if his investment earns 12% compounded quarterly? What table do we use for this problem?

Present value of 1 (table 6-2) $25,000 future value x 0.62317 factor = $15,579 PV

The table shows how much you need now to accumulate to a dollar at the end of each of five periods, at three different rates of compound interest. Which table is this referring to?

Present value of 1 at compound interest (table 6-2)

If you are trying to find the present value of a FUTURE value, which table do you use?

Present value of 1 at compound interest table 6-2

What does the present value of an annuity due mean?

Present value of a series of equal amounts to be withdrawn or received at equal intervals. Periodic rents occur at the beginning of the period.

What does the present value of an ordinary annuity mean?

Present value of a series of equal amounts to be withdrawn or received at equal intervals. Periodic rents occur at the end of the period.

DEF: Value now of a given amount to be paid or received in the future, assuming compound interest.

Present value of a single sum

Hugo Reyes wins $2,000,000 in the state lottery. He will be paid $100,000 at the beginning of each year for the next 20 years. How much has he actually won? Assume an appropriate interest rate of 8%. What table are we using?

Present value of an annuity due of 1 (Table 6-5) =$100,000 receipts x 10.60360 = $1,060,360 PV

The table shows how much an annuity of $1 is worth now if a dollar is invested at the beginning of each compounding period (number of compounding periods ranges from one to five), at three different rates of compound interest. Which table is this referring to?

Present value of an annuity due of 1 (table 6-5)

Example: If you want to withdraw $1000 rent today for every END of each month for n = 36 and i = 2%, what table are we using for this example?

Present value of an ordinary annuity

The table shows how much an annuity of $1 is worth now if a dollar is invested at the end of each compounding period (number of compounding periods ranges from one to five), at three different rates of compound interest. Which table is this referring to?

Present value of an ordinary annuity of 1 (table 6-4)

Example: Hugo Reyes wins $2,000,000 in the state lottery. He will be paid $100,000 at the end of each year for the next 20 years. How much has he actually won? Assume an appropriate interest rate of 8%. What table are we using?

Present value of an ordinary annuity of 1 (table 6-4) =$100,000 Receipts x 9.81815 Factor = $981,815 PV

Ex: Clancey Inc. issues $2,000,000 of 7% bonds due in 10 years with interest payable at year-end. The current market rate of interest for bonds of similar risk is 8%. What amount will Clancey raise when it issues the bonds? What table are we using?

Present value of an ordinary annuity of 1 (table 6-4) $140,000 interest payment x 6.71008 Factor = $939,411 present value of interest $2,000,000 x 0.46319 = $926,380 present value of principal

Rent formula if you do not know it

Principal * Stated interest rate

DEF: The amount borrowed or invested.

Principle

Interest formula

Principle amount*Interest rate*Time

The equal identity amount at every period received at the end or the start of the period is called?

Rent

What is the general formula for the FV of an ordinary annuity?

Rent * FV factor_OA i%,n

What is the formula to find the PV of an annuity due if you only have the PV of an ordinary annuity formula?

Rent * PVF_OA i,n * (1+i)

What does the future value of an annuity due mean?

Rent occurs at the beginning of each period Interest will accumulate during 1st period

What does the future value of an ordinary annuity mean?

Rent occurs at the end of each period No interest during 1st period

Formula for PV of an ordinary annuity

Rent x PVF_OA i%,n

When interest is earned on a PRINCIPLE amount, what kind of interest is this?

Simple interest

Which two tables compute single sum?

Table 6-1 FV and table 6-2 PV

Since the book does not give us the table for a FV of an annuity due, which formula can we use to find it?

The FV of an ordinary annuity * (1+i%) Rent x FV factor -OA i%,n * (1+i%)

Since the present value of long term bonds = price of long term bonds, what does this also equal?

The amount of cash raised by bond issuer

When trying to find the discounted factor for the present value of long term bonds, which value do we consider?

The market interest rate

DEF: The number of years or fractional portion of a year that the principal is outstanding.

Time

Name the elements you need when computing interest problems?

Time periods compound interest rate FV or PV

True/False. A dollar received today is worth more than a dollar promised at some time in the future.

True

True/False. Annuity Due has one more interest period than Ordinary Annuity.

True

True/False. Prsent value of long term bonds = price of long term bonds = The amount of cash raised by bond issuer.

True

True/False. When deciding among investment or borrowing alternatives, it is essential to be able to compare today's dollar and tomorrow's dollar on the same footing—to "compare apples to apples."

True

True/False. You look at an ordinary annuity table when you are looking for an amount at the END of a year?

True

For the future value of an annuity due, how do you find your factor value?

multiply future value of an ordinary annuity factor by 1 plus the interest rate.

Formula for finding the number of periods

number of years x the number of compounding periods per year.

DEF: Interest computed on the principal only.

Simple interest

What do you always need to know to compute the FV of an ordinary annuity

The rent amount, the compounding interest rate, and the number of compounding periods