341 Chapter 6

Bonds issued at more than face value are said to? While bonds issued at less than face value are said?

- To be issued at a premium. - To be issued at a discount.

The calculation of future value requires the what of interest? The calculation of present value requires what of interest?

- addition - removal

Present value measurements has long been ______ and is _________.

- integrated with accounting valuation - specifically addressed in serveral accounting standards.

SFAC No. 7 statement provides?

A framework for using future cash flows as the basis for accounting measurement and asserts that the objective in valuing an asset or liability using present values is to approximate the fair value of that asset or liability.

In the future value of an ordinary annunity, the last cash payment will earn how much interest?

none

N

number of periods

Assume that you borrow $700 from a friend and intend to repay the amount in equal installments of $100 per year over a period of years. The payments will be made at the end of each year beginning one year from now. Your friend wishes to be reimbursed for the time value of money at a 7% annual rate. How many years would it take before you repaid the loan?

- Determing n where other variables are known i=7%, PV=-700, FV=0, PMT=100 CPT n = about 10 years

Suppose that a friend asked to borrow $331 today and promised to repay you $100 at the end of each of the next four years. What is the annual interest rate implicit in this agreement?

- Determining i when other variables are known PV=-331, FV=0, PMT=100, n=4 CPT i = 8%

Suppose that you borrowed $400 from a friend and promised to repay the loan by making three annual payments of $100 at the end of each of the next three years plus a final payment of $200 at the end of year four. What is the interest rate implicit in this agreement?

- Determining i when other variables are known-unequal cash flows PV=-400, n=3, PMT=100, FV=0 CPT i =

Assume that you borrow $700 from a friend and intend to repay the amount in four equal annual installments beginning one year from today. Your friend wishes to be reimbursed for the time value of money at an 8% annual rate. What is the required annual payment that must be made (the annuity amount), to repay the loan in four years?

- Determining the annuity amount (PMT) when other variable are know n=4, i=8%, PV=-700, FV=0 CPT PMT = $211.34

Rita wants to accumulate a sum of money to pay for grad school. She wants to invest a single amount today in a savings account earning 10% interest compounded annually that is equivalent to investing $10,000 at the beginning of each of the next three years. The future value of this annunity is $36,410. Find the present value.

- Present value of an annunity due First payment: FV= -10,000, n=0, i=10%, pmt=0 PV= $10,000 Second payment: FV= -10,000, n=1, i=10%, pmt=0 PV= $9,091 Thrid payment: FV= -10,000, n=2, i=10%, pmt=0 PV= $8,264 Total: $27,355

Rita wants to accumulate a sum of money to pay for grad school. She wants to invest a single amount today in a savings account earning 10% interest compounded annually that is equivalent to investing $10,000 at the end of each of the next three years. Find the present value.

- Present value of an oridnary annuity due First payment: FV= -10,000, n=1, i=10%, pmt=0 PV= $9,091 Second payment: FV= -10,000, n=2, i=10%, pmt=0 PV= $8,264 Thrid payment: FV= -10,000, n=3, i=10%, pmt=0 PV= $7,513 Total: $9,091 + $8,264 + $7,513 =$24,868

We value most receivables and payables at the what? Reflecting what?

- Present value of future cash flows. - An appropriate time value of money.

What does FASB expect?

- The traditional approach to calculating present value will continue to be used in many situations, particulary those where future cash flows are contractual. - The board also believes that the expected cash flow approach is more appropriate in more complect situations.

Most banks compound interest:

- more frequently than once a year. - Daily compounding is common for savings accounts. - More rapid compounding has the effect of increasing the actual rate.

The FASB board has incorporated the concepts developed in SFAC No. 7 into?

- standards on asset retirement obligations - impairment losses - business combinations

The marketplace will determine the price of the bonds based on what?

The market rate of interest for investments with similar characterisitics.

Determining future values and present values electronically avoids?

The need for tables, however, we the tables in the book to make it easier to visualize how the amounts are actually determined.

Suppose a friend asks to borrow $500 today and promises to repay you $605 two years from now. What is the annual interest rate you would be agreeing to?

n=2 PV=$500 FV=$605 i=? Ways to solve: 1. present value = future value x i, to get, present value/future value = i or 2. n=2, pmt=0, PV=-500, FV=605, CPT i= 10%

PV

present value

Financial instruments frequently involve multiple what?

receipts or payments of cash.

Because of the increased importance of present value measurement, the FASB issued Statement of Financial Accounting Concepts No.7, which says?

"Using Cash Flow Information and Present Value in Accounting Measurements."

If Cindy invested $1,000 today, what is her present value (PV)?

$1,000

Deferred annuity

(Present value) Exsist when the first cash flow occurs more than the one period after the date the agreement begins.

The Stridewell Shoe Company manufactures tennis shoes for sale to retailers. The company sold a large order of shoes to Harmon Sporting Goods for $50,000. Stridewell agreed to accept a note in payment for the shoes requiring payment of $50,000 in one year plus interest at 10%. How should Stridewell value the note receivable and corresponding sales revenue earned? How should Harmon value the note payable and corresponding inventory purchased?

As long as the interest rate explicitly stated in the agreement properly reflects the time value of money, the answer is $50,00, the face value of the note. It's important to realize that this amount also equals the present value of future cash flows at 10%. Future cash flows equal $55,000, the $50,000 note itself plus $5,000 interest ($50,000 x 10%). By calculating the present value of $55,000 to be received in one year, the interest of $5,000 is removed from the future value, resulting in the appropriate note receivables/sales revenue value of $50,000 for Stridewell and a $50,000 note payable/inventory value for Harmon.

When will the market place determine the price of the bonds?

At the date the bonds are issued (sold).

In the present value of an annuity due, why does the first cash payment contain interest?

Because it is made on the first day of the annuity period.

Ordinary annunity

Cash flows occur at the end of each period.

In situation when the compounding period is less than a year, the interest rate per compounding period is determined by?

Dividing the annual rate by the number of periods.

The present value of a single amount is today's?

Equivalent to a particular amount in the future.

The Stridewell Shoe Company recently sold a large order of shoes to Harmon Sporting Goods. Terms of the sale require Harmon to sign a noninterest-bearing note of $60,500 with payment due in two years. How should Stridewell and Harmon value the note receivable/payable and corresponding sales revenue/inventory?

Even though the agreement states a noninterest-bearing note, the $60,500 does, in fact, include interest for the two year period of the loan. We need to remove the interest portion of the $60,500 to determine the portion that represents the sales price of the shoes. We do this by computing the present value. PV of $50,000: n=2, i=10%, pmt=0, and FV=60,500. Bothe the notes receivable for Stridewell and the note payable for Harmon initially will be values at $50,000. The difference $10,500 represents interest revenue/expense to be recognizing over the life of the note.

The company's risk-free rate of interest is used when applying the?

Expected cash flow approach to the calculation of present value.

effective interest rate

Is the rate at which money actually will grow during the year.

Monetary liabilities

Obligations to pay amounts of cash, the amount of which is fixed or determinable. Most liabilites are monetary.

Compound interest

Occurs when money remains invested for multiple periods.

Do accountant use PV or FV more frequently?

PV

The stated interest payments are equal to?

The contractual stated rate multplied by the face value of the bonds.

"n" in the future value formula refers to?

The number of compounding periods, not necessarily the number of years.

How do you calculate the future value of a present amount?

The persent amount X (1+i)^n

The key SFAC No. 7 objective, is determining what?

The present value of future cash flows associated with the assets or liability, taking into account any uncertanity concerning the amounts and timing of the cash flows.

Most monetary assets and monetary liabilities are valued at?

The present value of future cash flows.

What is the difference between the present value of the investment and it's future value?

Time value of money

In the future value of an annuity due, will the last cash payment earn interest?

Yes

You wants to invest $10,000 today to accumulate $16,000 for graduate school. If you can incest at an interest rate of 10% compounded annually, how many years will it take to accumulate the required amount?

about five years

PMT

annuity payments

All liabilities and receivables are reported in the financial statements at their present values, except for?

certain trade receivables and payables.

CPT

compute button

Ex. Cindy wants to know the future value two years from today of $1,000 invested at 12% with quarterly compounding.

n = 8 (2 years x 4 times a year) Compounding rate = 3% (12% annual rate / 4 times a year)

How do you calculate the present value of a future amount?

future amount / (1+i)^n

FV

future value

%I

interest rate

Dalton Corporation faces the likelihood of having to pay an uncertain amount in five years in connection with an environmental cleanup. The future cash flow estimate is in the range of $100 million to $300 million with the following estimated probabilities: Loss amount Probability $100 million 10% $200 million 60% $300 million 30% 1. What is the expect cash flow? 2. If the company's risk-free rate of interest is 5%, Dalton Corporation will report a liability of?

1. $100 million x 10% = $10 million $200million x 60% = $120 million $300million x 30% = $90 million $10 + 120 + 90 = $220 million. 2. The present value of expected cash outflow: FV= -200 million, n=5, i=5%, pmt=0 = $172,376,600

What are four variables in the process of adjusting single cash flow amounts for the time value of money?

1. PV 2. FV 3. n 4. i (interest rate)

What are the four variables in present value problems involving annuities?

1. present value of ordinary annuity (PVA) or present value of an annuity due (PVAD) 2. the amount of each annuity payment 3. the number of periods, n 4. the interest rate, i - if you know any of three of these, the fourth can be determined.

Future value

Amount of money that a dollar will grow to at some point in the future.

Compound interest results in?

An increasingly large interest amount for each period of investment.

Interest rates are typically stated as?

Annual rate regardless of the length of the compounding period involved.

If Cindy invested $1,000 for 3 years at 10% compound annually, the $1,331 would be referred to as?

Future value (FV)

If given a choice between $1,000 now or $1,000 three years from now, what would you do and why?

I would have the money now, because if I have it now, I can put it to use.

Expected cash flow approach

Incorporates specific probabilities of cash flows into the analysis.

The time value of money concepts is only concerned with the growth in the dollar amount of money, but ignoring what?

Inflation

Annunity due

Cash flows occuring at the beginning of each period, sometimes referred to as an annuity in advance.

Annuity

Cash flows received or paid in the same amount each period. Ex. loan on which periodic interest is paid in equal ammounts.

Simple interest

Computed by multiplying an initial investments times both the applicable interest rate and the period of time for which the money is used. Ex. the simple interest earned each year on a $1,000 investment paying 10% is $100. ($1,000 X 10%)

The way uncertainty has been considered in present value calculations has been by?

Finding the present value of the bad estimate of the future cash flows applying an interest rate that has been adjusted to reflect the uncertainty or risk of those cash flows.

Deferred annuity: At 1/1/18, you are considering acquiring an investment that will provide three equal payments of $10,000 each to be received at the end of three consecutive years. However, the first payment is not expected until 12/31/20. The time value of money is 10%. How much would you be willing to pay for this investment?

First payment: FV= -10,000, n=3, i=10%, pmt=0 PV= $7,513 Second payment: FV= -10,000, n=4, i=10%, pmt=0 PV= $6,830 Thrid payment: FV= -10,000, n=5, i=10%, pmt=0 PV= $6,209 Total: $20,552

Future value of an ordinary annuity: Rita wants to accumulate a sum of money to pay for grad school. Rather than investing in a single amount today that will grow to a future value, she decides to invest $10,000 a year over the next three years in a savings account paying 10% interest compounded annually. She decides to make the first payment to the bank one year from today. Calculate the future value of this annunity by calculating the future value of each of the individual payments.

First payment: PV= -10,000, n=2, i=10%, pmt=0 FV= $12,100 Second payment: PV= -10,000, n=1, i=10%, pmt=0 FV= $11,000 Thrid payment: PV= -10,000, n=0, i=10%, pmt=0 FV= $10,000 Total: $12,100 + $11,000 + $10,000 = $33,100

Future value of an annuity due: Rita wants to accumulate a sum of money to pay for grad school. Rather than investing a single amount today that will grow to a future value, she decides to invest $10,000 a year over the next three years in a savings account paying 10% interest compounded annually. She decides to make the first payment to the bank immediately. How much will Rita have available in her account at the end of three years?

First payment: PV= -10,000, n=3, i=10%, pmt=0 FV= $13,100 Second payment: PV= -10,000, n=2, i=10%, pmt=0 FV= $12,100 Thrid payment: PV= -10,000, n=1, i=10%, pmt=0 FV= $11,000 Total: $13,100 + $12,100 + $11,000 = $36,410

The most common accounting applications of the time value of money involve? Why?

Determining present value of annunity, because most financial instruments specify equal periodic interest payments or installment payments.

Compound interest: Cindy invested $1,000 in a savings account paying 10% interest compunded annually. How much interest will she earn each year, and what will her investment balance be after three years?

Interest = Interest rate X outstanding balance - Initial deposit: $1,000 - End of year 1: 10% x $1,000 = $100, balance would be $1,000 + $100 = $1,100 - End of year 2: 10% x $1,100 = $110, balance would be $1,100 + $110 = $1,210 - End of year 3: 10% x $1,210 = $121, balance would be $1,210 + $121 = $1,331

Ex. Cindy invested $1,000 in a savings account paying 10% interest compounded twice a year. There are two six-month periods paying interest at 5%. How much interest will she earn the first year, and what will be her investment balance at the end of the year?

Interest= interest rate x outstanding balance - Initial deposit: balance of $1,000 - After six months: 5% x $1,000 = 50.00, balance of $1,000 + $50 = $1,050 - End of year 1: 5% x $1,050 = $52.50, balance of $1,050 + $52.20 = $1,102.50

Interest

Is the amount of money paid or received in excess of the amount borrowed or lent. Know also as the "rent" paid for the use of money for some period of time.

If given the choice between $740 now or $1,000 in three years, what would you choose and why?

It would depend on the time value of money. If the time value of money is 10%, I would choose $1,000 in three years. This is because $740 invested at 10% for three years would grow to only $984.49 (PV=-740, i=10%, n=3, pmt=o, CPT FV= 984.49). However, if the time value of money is 11% or higher, you would perfer $740 now. Presumably, you would invest the $740 now and have it grow to $1,012.05 in three years.

If the inflation rate is higher than the interest rate, the future value would be less or higher than the present value?

Less

The further into the future a amount of money is to be received, it is more or less valuable now?

Less, because this is the essence of the concept of the time value of money.

Time value of money

Means that money can be invested today to earn interest and grow to a larger dollar amount in the future.

Monetary assets

Money and claims to receive money, the amount of which is fixed or determinable. Ex. cash and most receivables

Bonds typically pay interest semiannually in an amount determined by?

Multiplying a stated rate by fixed principal amount.

The first cash flow (receipt or payment) of an ordinary annunity is made? The final?

One compounding period after the date on which the agreement begins. The final cash flow takes place on the last day covered by the agreement. Ex. an installment note payable date 12/31/18, might require the debtor to make three equal annual payments, with the first payment due on 12/31/19, and the last one on 12/31/21.

The time value of money has many applications in accounting. Most of these applications involve the concept of present value. Because financial instruments typically equal periodic payments, theses applications?

Quite often involve annuity situations. Ex. let's consider one accounting situation using both an ordinary annuity and the present value of a single amount (long-term bonds), one using an annuity due (long-term leases), and a third using a deferred annuity (pension obligations).

Interest is expressed as the?

Rate at which money will grow.

Long-term bond usually requires the issuing (borrowing) company to what?

Repay a specified amount at maturity and make periodic stated interest payments over the life of the bond.

Assuming an annual rate of 12%, what is the interest rate per compound period if interest is compounded: semiannually, quarterly, and monthly?

Semiannually: 12%/2=6% Quaterly: 12%/4=3% Monthly: 12%/12=1%

The present value of the deferred annuity is calculated by?

Summing the present values of the three individual cash flows, as of today.

Compound interest includes interest not only on the initial investment but alsso?

The accumulated interest in pervious periods.

Effective rate

The actual rate at which money grows per year.

When is the first and last payment of an annuity due made on?

The first payment is made on the first day of the agreement, and the last payment is made one period before the end of the agreement. Ex. a three year lease of a building that begins on 12/31/18, and ends on 12/31/21, may require the first year's lease payment in advance on 12/31/18. The third and last payment would take place on 12/21/20, the beginning of the third year of the lease.

What happens if the market rate at date of issuance does not equal a bond's stated rate?

The price of bonds (the amount the issuing company actually is borrowing) will not equal the bond's face value.

Present value

Today's equivalent to a particular amount in the future, after backing out the time value of money.

True or false: Although future cash flows in may instances are contractual and certain, the amounts and timing of cash flows are less certain in other situations.

True

True or false: As long as you now any three of the four variables in process of adjusting single cash flow amount for the time value of money, the fourth can be determine.

True

True or false: Some loans and most leases are pain in equal installments during a specified period of time.

True

True or false: While most notes, loans, and mortgages explicitly state an interest rate that will properly reflect the time value of money, there can exceptions.

True

The time value of money concepts are useful in?

Valuing several assets and liabilities for financial reporting purposes.

In future value of an annuity due, what would happen if the amounts invested each year were unequal?

We could not solve the problem using annuity tables. The FV of each payment would have to be calculated separately.