Intermediate Accounting Chapter 5: Time Value of Money Concepts

True or false: A lease is an annuity when it requires equal payments at the same interval.

True

True or false: Present value calculations are used in calculating pension contributions for defined benefit plans.

True

Required Information #5

We value most notes receivable and notes payable at the present value of future cash flows they call for, reflecting an appropriate time value of money.

Alex would like to deposit $1,000 in the bank today and would like to know what that will grow to in 5 years. Alex needs to compute the ___ value of the money.

future

The amount of money that a dollar will grow to at some point in the future is the

future value of a single amount.

Most monetary liabilities are valued at the ___ value of ___ cash flows.

present, future

We value most receivables and payables at the ___ value of ___ cash flows, reflecting an appropriate time value of money.

present, future

True or false: At the date of issue, the stated rate of interest on the bond is always equal to the market rate of interest on the bond.

False

Hailey wants to cash in her winning lottery ticket. She can either receive eight $200,000 semiannual payments starting today, based on a 6% annual interest rate, or she can receive a single-amount payment today. What is the single-amount payment she can receive today that would be equivalent to the eight-payment option except that she would not have to wait for years to collect her prize money? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

$1,446,056. PVAD = $200,000 × 7.23028* = $1,446,056*PVAD of $1: n = 8; i = 3%

Which of the following is an example of a monetary asset?

Accounts receivable

How are most monetary assets and liabilities valued?

At the present value of future cash flows.

FV = PV(1+i)^n

FV = future value of the invested amount I = amount invested at the beginning of the period i = interest rate n = number of compounding periods

Which of the following formulas represent the present value?

FV divided by (1 + i)n

A(n) ___ is a series of equal payments received or paid at equal intervals.

annuity

PVA

annuity amount x present value of an ordinary annuity amount (found on table)

Jenson rents equipment by signing a contract to pay $1,000 per month at the beginning of each month. The first payment is due upon signing the contract. The lease is a(n)

annuity due.

On a financial calculator, the PMT key is used to input the

annuity payment.

A fixed payment at fixed intervals is called a(n)

annuity.

Interest on the initial investment plus interest calculated on the previously earned interest is called ___ interest.

compound

Valuing defined benefit pension obligation typically requires the calculation of the present value of a ___ ___.

deferred annuity

What is the future value of $10,000 invested for two years at 10% interest compounded annually? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round final answer to the nearest whole dollars.)

$12,100 $10,000 x 1.21000 = 12,100 *use FV of $1 table

Dern Company recently sold a large order of tables to Knoll Furniture Store. Terms of the sale require Knoll to sign a noninterest-bearing note of $21,000 with payment due in three years. A rate of 9% reflects the appropriate interest rate for a loan of this type of loan. At what amount should Dern and Knoll value the note receivable/payable and corresponding sales revenue/inventory? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round final answer to the nearest whole dollars.)

$16,216 Find PV on PV of $1 table, under 9% at 3 years = .77218 $21,000 x .77218 = 16,216

Jean expects to receive $5,000 at the end of each year for 4 years. The annuity has an interest rate of 7%. The present value of this annuity at Time Zero, the inception of the annuity (rounded to the nearest dollar) is

$16,936 (The present value ordinary annuity factor of 7% for 4 periods is 3.38721. $5,000 x 3.38721 = $16,936.)

George will deposit $2,000 in a savings account at the beginning of each year for 8 years. Assuming the interest rate is 5%, how much money will George have in the account at the end of year 8? Round your answer to the nearest dollar.

$20,053 ($2,000 x 10.0266 (i.e., FVAD, the future value of annuity due, factor at 5% for 8 periods) = $20,053)

Milo decides to invest $1,500 in a savings account every year at the beginning of the year for 10 years. Assuming an interest rate of 7%, how much will Milo have at the end of the 10th year? (Round your answer to the nearest dollar.)

$22,175 ($1,500 X 14.7836 (i.e., FVAD, the future value of annuity due, factor at 7% for 10 periods) = $22,175)

What is the present value of $6,000 to be received at the end of each of eight periods, assuming the first payment occurs at the end of the fourth year and an interest rate of 10%?

$24,049 Use Present Value of an Ordinary Annuity Table, under 10% at 8 periods = 5.33493 $6,000 x 5.33493 = 32,009.58 Use Present Value Table, under 10% at 3 periods = .75131 $32,009.58 x .75131 = 24,049.12

Norton loans a customer $500 on January 1. On July 1 of the same year, the customer must repay Norton $525. The amount of interest earned by Norton is $___.

$25

Jeannie plans to deposit $6,000 in a money market sinking fund at the end of each year for the next four years. What is the amount that will accumulate by the end of the fourth and final payment if the sinking fund earns 9% interest? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answer to the nearest whole dollar amount.)

$27,439 Use FVA of $1 table, under 9% and 4 years = 4.5731 $6,000 x 4.5731 = 27,438.60

What is the present value of $5,000 to be received five years from now, assuming an interest rate of 8%? (FV of $1, PV of $1, FVA of $1,PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

$3,402.90 $5,000 x .68058 = 3,402.90 *use PV of $1 table

Carol expects to receive $1,000 at the end of each year for 5 years. The annuity has an interest rate of 10%. The present value of this annuity at Time Zero, the inception of the annuity (rounded to the nearest dollar) is

$3,791 (The present value ordinary annuity factor of 10% for 5 periods is 3.79079. $1,000 x 3.79079 = $3,791)

Kyle Carlson invested $10,000 in a savings account paying 12% interest compounded quarterly. Assuming that he makes no withdrawals, how much interest will he earn during the second quarter of the first year?

$309 $10,000 x 3% (12%/4) = 300 $300 x 3% = 9 $300 + 9 = $309 *4 = quarterly

What is the present value of $6,000 to be paid at the end of each of the next eight periods assuming an interest rate of 10%?

$32,010 Use Present Value of an Ordinary Annuity at $1 table, under 10% for 8 years = 5.33493 5.33493 x 6,000 = 32,009.58

What is the present value of $6,000 to be paid at the beginning of each of the next eight periods assuming an interest rate of 10%?

$35,211 Use Present Value of an Annuity Due Table, under 10% for 8 periods = 5.86842 5.86842 x 6,000 = 35,210.52

On January 1, McLean Corp. borrowed $50,000 with 8% simple interest. What is the amount of interest that must be repaid at year-end?

$4000

Dave plans to deposit $3,300 in an IRA account on April 15, Year 1. The account will earn 3% annually. If he makes this $3,300 deposit on April 15 of each of the next 14 years (total of 15 deposits), how much will he have on April 14, Year 16? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answers to the nearest whole number.)

$63,218 Use FVAD of $1 table, under 3% with 15 deposits = 19.1569 19.1569 x 3,300 = 63,218

On January 1, Biggs Corp. borrowed $20,000 with 4% simple interest. What is the amount of interest that must be paid at year-end?

$800

Which of the following statements about annuities are true? (Select all that apply.)

-The first cash flow of an annuity due is made on the first day of the agreement. -The last cash flow of an ordinary annuity is made on the last day covered by the agreement.

Which of the following are the four variables in present value annuity problems?

-The payment amount -The number of periods -The present value of an ordinary annuity -The interest rate

Which of the following are required to compute the present value of a known future amount? (Select all that apply.)

-interest rate -future value -number of compounding periods

Which of the following items require time value of money concepts? (Select all that apply.)

-pensions -bonds payable -capital leases

Determine the present value of the following single amounts (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar amount.): Future Amount, i, n, Present Value 1.$32,000, 5%, 11 2.$26,000, 6%, 19 3.$37,000, 11%, 40 4.$52,000, 10%, 13

1. $18,710 2. $8,593 3. $569 4. $15,062 1. PV = $32,000 (0.58468*) = $18,710*Present value of $1: n = 11, i = 5% (from PV of $1) 2. PV = $26,000 (0.33051*) = $8,593*Present value of $1: n =19, i = 6% (from PV of $1) 3. PV = $37,000 (0.01538*) = $569*Present value of $1: n =40, i = 11% (from PV of $1) 4. PV = $52,000 (0.28966*) = $15,062*Present value of $1: n = 13, i = 10% (from PV of $1)

Determine the future value of the following single amounts (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) (Round your final answers to nearest whole dollar amount.): 1.$19,000, i=4%, n=12 2.$30,000, i=8%, n=10 3.$42,000, i=8%, n=15 4.$63,000, i=6%, n=12

1. $30,420 2. $64,768 3. $133,231 4. $126,769 1. FV = $19,000 (1.60103*) = $30,420*Future value of $1: n = 12, i = 4% (from FV of $1) 2. FV = $30,000 (2.15892*) = $64,768*Future value of $1: n = 10, i = 8% (from FV of $1) 3. FV = $42,000 (3.17217*) = $133,231*Future value of $1: n = 15, i = 8% (from FV of $1) 4. FV = $63,000 (2.01220*) = $126,768*Future value of $1: n = 12, i = 6% (from FV of $1)

John Rider wants to accumulate $40,000 to be used for his daughter's college education. He would like to have the amount available on December 31, 2026. Assume that the funds will accumulate in a certificate of deposit paying 8% interest compounded annually. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) Answer each of the following independent questions. Required: 1. If John were to deposit a single amount, how much would he have to invest on December 31, 2021? 2. If John were to make five equal deposits on each December 31, beginning a year later, on December 31, 2022, what is the required amount of each deposit? 3. If John were to make five equal deposits on each December 31, beginning now, on December 31, 2021, what is the required amount of each deposit? (For all requirements, Round your final answers to nearest whole dollar amount.)

1. Amount: $27,223 2. Annuity amount: $6,818 3. Annuity amount: $6,313 1.PV = $40,000 (0.68058*) = $27,223 *Present value of $1: n = 5, i = 8% (from PV of $1) 2.Annuity amount =$40,000 / 5.8666* *Future value of an ordinary annuity of $1:n= 5,i= 8% (from FVA of $1) Annuity amount = $6,818 3. Annuity amount =$40,000 / 6.3359* *Future value of an annuity due of $1: n = 5, i = 8% (from FVAD of $1) Annuity amount = $6,313

Determine the future value of $25,000 under each of the following sets of assumptions (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar amount.): Annual Rate, Period Invested, i, n, Present Value, Future Value 1. 10%, 6 years, semiannually, ?, ?, $25,000, ? 2. 12%, 2 years, quarterly, ?, ?, $25,000, ? 3. 24%, 20 months, monthly, ?, ?, $25,000

1. i=5%, n=12, FV=$44,897 2. i=3%, n=8, FV=$31,669 3. i=2%, n=20, FV=$37,149 1. FV = $25,000 (1.79586*) = $44,896*Future value of $1: n = 12, i = 5% (from FV of $1) 2. FV = $25,000 (1.26677*) = $31,669*Future value of $1: n = 8, i = 3% (from FV of $1) 3. FV = $25,000 (1.48595*) = $37,149*Future value of $1: n = 20, i = 2% (from FV of $1)

A friend asks to borrow $635.52 today and promises to repay you $1,000 with interest compounded annually at 12%. How many years (compounding periods) will pass before you receive the payment? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answer to the nearest whole year.)

4 years 635.52 / 1,000 = .63553 Find .63552 on the PV of $1 table, under 12%

A series of equal periodic payments in which the first payment is made on the date of the contract

An annuity due. In an ordinary annuity, cash flows occur at the end of each period. In an annuity due, cash flows occur at the beginning of each period.

Required Information #6

An annuity is a series of equal-sized cash flows occurring over equal intervals of time. An ordinary annuity exists when the cash flows occur at the end of each period. An annuity due exists when the cash flows occur at the beginning of each period.

Interest Rate Per Compounding Period

Annual Rate divided by number of periods

Which of the following results in increasingly larger amounts of interest for each period of the investment?

Compound interest

Lenny borrowed $10,000 on a 5-year interest bearing note with an interest rate of 10%. At the end of 5 years, Lenny must repay the bank $16,105. Based on the amount that must be repaid, interest was calculated with what type of interest rate?

Compound interest (Simple interest would have yielded total interest of $10,000 x 10% = $1,000 x 5 years = $5,000.)

Required Information #1

Compound interest includes interest not only on the initial investment but also on the accumulated interest in previous periods.

Which of the following situations would involve the calculation of the future value of an ordinary annuity?

Depositing an amount to a savings account each month that will grow to purchase a car in 5 years.

If you borrow $30,000 from the bank for 5 years (60 months) at 12% interest, you would calculate the payment required at the end of each month by:

Dividing $30,000 by the present value of an ordinary annuity of $1, where i = 1% and n = 60. Since you make the payments at the end of each month, you have an ordinary annuity. To calculate the payments, find the present value of an ordinary annuity factor for 60 months at 1% per period (12% annual rate ÷ 12 months) and divide the loan amount by that present value factor.

$1,000 invested today at 10% compounded annually will grow to $1,210 at the end of two years. What is the $1,210 value referred to as?

Future value

Required Information #9

In present value problems involving annuities, there are four variables: PVA or PVAD, the annuity amount, the number of compounding periods (n) and the interest rate (i). If you know any three of these, you can determine the fourth.

The amount of money paid or received in excess of the amount of money borrowed or lent is referred to as what?

Interest

Mufala, Inc., will issue $10,000,000 of 6% 10-year bonds. The market rate for bonds with similar risk and maturity is 8%. Interest will be paid by Mufala semiannually. What is the issue price of the bonds? (Round your answer to nearest whole dollar.)

Interest payment = $10,000,000 × 3% (6% ÷ two semiannual payments) = $300,000 n = 20 (10 years × two semiannual payments); i = 4% (8% market rate ÷ 2 semiannual payments) PVA = $300,000 × 13.59033 (n = 20, i = 4%) = $4,077,099 PV of the $10,000,000 face amount that will be received in 10 years: n = 20 (10 years × two semiannual payments); i = 4% (8% market rate ÷ 2 semiannual payments) PV = $10,000,000 × 0.45639 (n = 20, i = 4%) = $4,563,900 $4,077,099 + $4,563,900 = $8,640,999

Which of the following accounts uses time value of money concepts to value the account?

Long-term bonds

Required Information #10

Most accounting applications of the time value of money involve the present values of annuities. The initial valuation of long-term bonds is determined by calculating the present value of the periodic stated interest payments and the present value of the lump-sum payment made at maturity. Certain leases require the lessee to compute the present value of future lease payments to value the leased asset and corresponding lease obligation. Similarly, installment notes sometimes require us to calculate the present value of installment payments as the amount at which to record the note. Also, pension plans require the payment of deferred annuities to retirees. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Match each abbreviation on a financial calculator to its function. Instructions

N - Number of periods %I - Interest rate PV - Present value FV - Future value PMT - annuity payment CPT - Compute

FV / (1+i)^n

PV formula

Present Value Table Factor

Present Value / Future Value

Present and future value tables of $1 at 11% are presented below. nPV of $1, FV of $1, PVA of $1, FVA of $1 1 0.90090 1.11000 0.90090 1.0000 2 0.81162 1.23210 1.71252 2.1100 3 0.73119 1.36763 2.44371 3.3421 4 0.65873 1.51807 3.10245 4.7097 5 0.59345 1.68506 3.69590 6.2278 6 0.53464 1.87041 4.23054 7.9129 Lorien, Inc. leased tree excavators under terms of $10,000 down and four equal annual payments of $30,000 on the anniversary date of the lease. The interest rate implicit in the lease is 11%. For what amount would Lorien initially record the asset and lease liability?

Present Value of an Ordinary Annuity = $30,000 × 3.10245* = $93,074 Add the $10,000 down payment already at present value: $93,074 + $10,000 = $103,074 *PVA: n = 4; i = 11%

$1,000 invested today at 10% compounded annually will grow to $1,100 at the end of one year or $1,210 at the end of two years. What is the initial $1,000 referred to as?

Present value

Danielle wants to know how much she should invest now at 5% interest in order to accumulate a sum of $45,000 in four years. She should use a table for the:

Present value of $1. $45,000 × (PV of $1: n = 4, i = 5%) = Amount to Invest

The Sanchez Company purchased a delivery truck on February 1, 2021. The purchase agreement required Sanchez to pay the total amount due of $15,000 on February 1, 2022. Assuming an 8% rate of interest, the calculation of the price of the truck would involve multiplying $15,000 by the:

Present value of $1. The calculation is for the present value today of the $15,000 to be received one year from now.

The Jamison Corporation agrees to pay an employee $10,000 a year for five years beginning three years from today and decides to fund the payments by depositing one lump sum in a savings account today. The company should use which present value concept to determine the required deposit?

Present value of a deferred annuity. The calculation is the amount to be deposited today, the present value, of five equal payments (an annuity), that doesn't start for three years (deferred annuity).

Laura won $5,000,000 in the state lottery, which she has elected to receive at the end of each month over the next 30 years. She will receive 7% interest on unpaid amounts. To determine the amount of her monthly check, she should use a table for the:

Present value of an ordinary annuity of $1. In an ordinary annuity, cash flows occur at the end of each period. In an annuity due, cash flows occur at the beginning of each period.

Initial Investment x Interest Rate x Period of Time

Simple Interest

Multiplying an initial investment times both the applicable interest rate and the period of time for which the money is used is referred to as what?

Simple interest

___ interest is calculated by multiplying an initial investment times the applicable interest rate and the period of time the money is used, whereas ___ interest involves earning interest on the interest.

Simple, compound

Stated Interest Payments

Stated Interest Rate x Face Amount

Required Information #2

The future value of a single amount is the amount of money that a dollar will grow to at some point in the future. It is computed by multiplying the single amount by (1 + i)n, where i is the interest rate and n the number of compounding periods. The Future Value of $1 table allows for the calculation of future value for any single amount by providing the factors for various combinations of i and n.

Required Information #7

The future value of an ordinary annuity (FVA) is the future value of a series of equal-sized cash flows with the first payment taking place at the end of the first compounding period. The last payment will not earn any interest since it is made at the end of the annuity period. The future value of an annuity due (FVAD) is the future value of a series of equal-sized cash flows with the first payment taking place at the beginning of the annuity period (the beginning of the first compounding period).

Assume you borrow $10,000 from the bank and promise to repay the amount in 5 equal installments beginning one year from today. The stated interest rate on the loan is 5%. What is the unknown variable in this problem?

The payment amount

Required Information #3

The present value of a single amount is the amount of money today that is equivalent to a given amount to be received or paid in the future. It is computed by dividing the future amount by (1 + i)n. The Present Value of $1 table simplifies the calculation of the present value of any future amount.

Required Information #8

The present value of an ordinary annuity (PVA) is the present value of a series of equal-sized cash flows with the first payment taking place at the end of the first compounding period. The present value of an annuity due (PVAD) is the present value of a series of equal-sized cash flows with the first payment taking place at the beginning of the annuity period. The present value of a deferred annuity is the present value of a series of equal-sized cash flows with the first payment taking place more than one time period after the date of the agreement. (FV of $1, PV of $1, FVA of $1,PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Required Information #4

There are four variables in the process of adjusting single cash flow amounts for the time value of money: present value (PV), future value (FV), i and n. If we know any three of these, the fourth can be computed easily.

Which concept means that money can be invested today to earn interest and grow to a larger amount in the future?

Time value of money concept

Determine the combined present value as of December 31, 2021, of the following four payments to be received at the end of each of the designated years, assuming an annual interest rate of 8%. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar amount.) Payment - Year Received $7,000 - 2022 7,800 - 2023 9,600 - 2025 11,200 - 2027

Year Received, i, n, Payment, Present Value 2022, 8%, 1, $7,000, $6,482 2023, 8%, 2 $7,800, $6,687 2025, 8%, 4, $9,600, $7,056 2027, 8%, 6, $11,200, $7,058 First payment: $7,000 × 0.92593 = $6,482 n=1 Second payment: 7,800 × 0.85734 = 6,687 n=2 Third payment: 9,600 × 0.73503 = 7,056 n=4 Fourth payment: 11,200 × 0.63017 = 7,058 n=6

The amount of money that a dollar will grow to at some point in the future is known as the

future value.

The amount paid for the use of money for some period of time is referred to as ___.

interest

To solve for the present value of a single sum, you need to know the future value, the number of compounding periods, and the ___ ___.

interest rate

Over a 5-year period, simple interest is ______ compound interest on the same note.

less than

Money and claims to receive money in amounts that are fixed or determinable are called

monetary assets.

An obligation to pay amounts of cash, the amount which is fixed or determinable, is called a

monetary liability.

The formula "future value divided by the quantity (1 + i)n" is the formula for ___ value.

present

The formula PV = $1/(1+i)^n is the formula used to calculate the

present value of $1.

Harold would like to deposit a sum of money today that will grow to $20,000 in year 8. Which table should Harold use when making this calculation?

present value of single amount

On January 1, Gino signs a note payable for $10,000. The note has an interest rate of 3%. If Gino repays $10,300 at the end of year 1, the interest is ______ interest.

simple

The _____ rate of interest on a bond is the interest rate printed on the bond; the ______ rate of interest is the current rate of interest being paid on investments with similar characteristics. (Enter one word per blank)

stated; market

The formula FV = $1(1+i)n is used to calculate

the future value of $1.

The future value of an ordinary annuity table is used when calculating

the future value of a series of payments.

The ___ ___ of money concept means that money invested today will grow to a larger amount in the future.

time value