Test Bank for Intermediate Accounting, Seventeenth Edition
6 – 36
DERIVATIONS — Computational (cont.)
No. Answer Derivation
Accounting and the Time Value of Money
6 – 37
DERIVATIONS — Computational (cont.)
No. Answer Derivation
Test Bank for Intermediate Accounting, Seventeenth Edition
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DERIVATIONS — CPA Adapted
No. Answer Derivation
BRIEF EXERCISES
Accounting and the Time Value of Money
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BE. 6–133—Present and future value concepts.
On the right are six diagrams representing six different present and future value concepts stated
on the left. Identify the diagrams with the concepts by writing the identifying letter of the diagram
on the blank line at the left. Assume n = 4 and i = 8%.
Concept Diagram of Concept
_____ 1. Future value of 1. ? $1
a. | | | | |
_____ 2. Present value of 1.
?
_____ 3. Future value of an annuity $1 $1 $1 $1
due of 1. b. |- – – – | | | |
_____ 4. Future value of an ordinary
annuity of 1. ?
$1 $1 $1 $1
_____ 5. Present value of an ordinary c. | | | |- – – – |
annuity of 1.
_____ 6. Present value of an annuity ? $1 $1 $1 $1
due of 1. d. | | | | |
$1 ?
e. | | | | |
$1 $1 $1 $1 ?
f. | | | | |
BE. 6–134—Compute loan payments. (Tables needed.)
On January 2, 2020, Jensen Company borrowed $150,000 from Lyon Country Bank. The terms
of the loan agreement specified 4 equal annual payments at 6% annual interest. Compute the
amount of each of these payments, assuming they begin on December 31, 2020.
Test Bank for Intermediate Accounting, Seventeenth Edition
6 – 40
BE. 6-135—Present value of an investment in equipment. (Tables needed.)
Find the present value of an investment in equipment if it is expected to provide annual savings of
$50,000 for 10 years and to have a resale value of $125,000 at the end of that period. Assume an
interest rate of 9% and that savings are realized at year end.
EXERCISES
Ex. 6-136—Future value of an annuity due. (Tables needed.)
Accounting and the Time Value of Money
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If $12,000 is deposited annually starting on January 1, 2020 and it earns 9%, how much will
accumulate by December 31, 2029?
Ex. 6-137—Retirement of debt. (Tables needed.)
Steve Milner borrowed $120,000 on July 1, 2020. This amount plus accrued interest at 8%
compounded semiannually is to be repaid in total on July 1, 2030. To retire this debt, Milner plans
to contribute to a debt retirement fund five equal amounts starting on July 1, 2025 and continuing
for the next four years. The fund is expected to earn 6% per annum.
Instructions
Compute how much must be contributed each year by Steve Milner to provide a fund sufficient to
retire the debt on July 1, 2030?
Ex. 6-138—Future value of annuity due. (Tables needed.)
Andrea is 40 years old today and she wishes to accumulate $2,000,000 by her sixty fifth birthday
so she can retire to a beach in Florida. She wishes to accumulate this amount by making equal
deposits on her fortieth through her sixty fourth birthdays. Compute the annual deposit Andrea
must make if the fund will earn 6% interest compounded annually.
Test Bank for Intermediate Accounting, Seventeenth Edition
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Ex. 6-139—Future value of annuity. (Tables needed.)
Linda Ogleby wants to accumulate $40,000 to use for an around the world trip. She plans to
accumulate the desired amount by depositing $5,500 annual-year-end payments into an account
at the National Bank which pays 4% interest, compounded annually.
1. Compute the account balance at the end of the sixth year.
2. Compute the amount of each payment that Linda must make at the end of each of the six
years to accumulate the $40,000.
Ex. 6-140—Future value of annuity. (Tables needed.)
Pearson Corporation having recently issued a $25 million, 10-year bond issue, is required to
make annual year end sinking fund deposits of $1,800,000. The deposits are made on the last
day of each year and yield a return of 5%.
1. Compute the fund balance at the end of the 10 years.
2. Compute the additional annual deposit amount that should have been made at the end of
each of the 10 years to accumulate the $25 million.
Ex. 6-141—Present value of an annuity due. (Tables needed.)
How much must be invested now to receive $60,000 for ten years if the first $60,000 is received
today and the rate is 8%?
Accounting and the Time Value of Money
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Ex. 6-142—Compute the annual rent. (Tables needed.)
Crone Co. has machinery that cost $150,000. It is to be leased for 15 years with rent received at
the beginning of each year. Crone wants a return of 10%. Compute the amount of the annual
rent.
Ex. 6-143—Calculate the market price of a bond. (Tables needed.)
Determine the market price of a $750,000, ten-year, 10% (pays interest semiannually) bond issue
sold to yield an effective rate of 12%.
Ex. 6-144—Calculate the market price of a bond.
On January 1, 2020 Lance Co. issued five-year bonds with a face value of $1,000,000 and a
stated interest rate of 12% payable semiannually on July 1 and January 1. The bonds were sold
to yield 10%. Present value table factors are:
Present value of 1 for 5 periods at 10% .62092
Present value of 1 for 5 periods at 12% .56743
Present value of 1 for 10 periods at 5% .61391
Present value of 1 for 10 periods at 6% .55839
Present value of an ordinary annuity of 1 for 5 periods at 10% 3.79079
Present value of an ordinary annuity of 1 for 5 periods at 12% 3.60478
Present value of an ordinary annuity of 1 for 10 periods at 5% 7.72173
Present value of an ordinary annuity of 1 for 10 periods at 6% 7.36009
Calculate the issue price of the bonds.
Test Bank for Intermediate Accounting, Seventeenth Edition
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Issue price of the bonds $1,077,214
Ex. 6-145—Present value and future value computations. (Tables needed.)
John Rich, an executive VP contemplating retirement on his sixty fifth birthday, decides to create
a fund on a 6% basis that will enable him to withdraw $90,000 per year on July 31, beginning in
2025 and continuing through 2029. To develop this fund, Rich intends to make equal
contributions on July 31 of each of the years 2020–2024.
Instructions
(a) Compute how much the balance of the fund must equal on July 31, 2024, in order for Rich to
satisfy his objective.
(b) Compute the amount of Rich’s contributions to the fund.
Accounting and the Time Value of Money
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PROBLEMS
Pr. 6-146—Present value and future value computations.
Part (a) Compute the amount that a $60,000 investment today would accumulate at 10%
(compound interest) by the end of 6 years.
Part (b) Tom wants to retire at the end of this year (2020). His life expectancy is 20 years from
his retirement. Tom has come to you, his CPA, to learn how much he should deposit on
December 31, 2020 to be able to withdraw $80,000 at the end of each year for the next
20 years, assuming the amount on deposit will earn 8% interest annually.
Part (c) Judy Thomas has a $2,800 overdue debt for medical books and supplies at Joe‘s
Bookstore. She has only $900 in her checking account and doesn’t want her parents to
know about this debt. Joe’s tells her that she may settle the account in one of two ways
since she can’t pay it all now:
1. Pay $900 now and $2,300 when she completes her residency, two years from today.
2. Pay $3,700 one year after completion of residency, three years from today.
Assuming that the cost of money is the only factor in Judy’s decision and that the cost of
money to her is 8%, which alternative should she choose? Your answer must be
supported with calculations.
Pr. 6-147—Annuity with change in interest rate.
Jan Green established a savings account for her son’s college education by making annual
deposits of $10,000 at the beginning of each of six years to a savings account paying 8%. At the
end of the sixth year, the account balance was transferred to a bank paying 10%, and annual
deposits of $10,000 were made at the end of each year from the seventh through the tenth years.
What was the account balance at the end of the tenth year?
Test Bank for Intermediate Accounting, Seventeenth Edition
6 – 46
Solution 6-147
Pr. 6-148— Present value of an ordinary annuity and annuity due.
Jill Morris is presently leasing a small business computer from Eller Office Equipment Company.
The lease requires 10 annual payments of $6,000 at the end of each year and provides the lessor
(Eller) with an 8% return on its investment. You may use the following 8% interest factors:
9 Periods 10 Periods 11 Periods
Future Value of 1 1.99900 2.15892 2.33164
Present Value of 1 .50025 .46319 .42888
Future Value of Ordinary Annuity of 1 12.48756 14.48656 16.64549
Present Value of Ordinary Annuity of 1 6.24689 6.71008 7.13896
Present Value of an Annuity Due of 1 6.74664 7.24689 7.71008
Instructions
(a) Assuming the computer has a ten-year life and will have no salvage value at the expiration of
the lease, what was the original cost of the computer to Eller?
(b) What amount would each payment be if the ten annual payments are to be made at the
beginning of each period?
Accounting and the Time Value of Money
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Pr. 6-149—Finding the implied interest rate.
Bates Company has entered into two lease agreements. In each case the cash equivalent
purchase price of the asset acquired is known and you wish to find the interest rate which is
applicable to the lease payments.
Instructions
Calculate the implied interest rate for the lease payments.
Lease A — Lease A covers office equipment which could be purchased for $252,336. Bates
Company has, however, chosen to lease the equipment for $70,000 per year, payable at the end
of each of the next 5 years.
Lease B — Lease B applies to a machine which can be purchased for $201,212. Bates Company
has chosen to lease the machine for $42,000 per year on a 6-year lease. Payments are due at
the start of each year.
Test Bank for Intermediate Accounting, Seventeenth Edition
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Pr. 6-150—Calculation of unknown rent and interest.
Pine Leasing Company purchased specialized equipment from Wayne Company on December
31, 2019 for $900,000. On the same date, it leased this equipment to Sears Company for 5 years,
the useful life of the equipment. The lease payments begin January 1, 2020 and are made every
6 months until July 1, 2024. Pine Leasing wants to earn 10% annually on its investment.
Various Factors at 10%
Periods Future Present Future Value of an Present Value of an
or Rents Value of $1 Value of $1 Ordinary Annuity Ordinary Annuity
9 2.35795 .42410 13.57948 5.75902
10 2.59374 .38554 15.93742 6.14457
11 2.85312 .35049 18.53117 6.49506
Various Factors at 5%
Periods Future Present Future Value of an Present Value of an
or Rents Value of $1 Value of $1 Ordinary Annuity Ordinary Annuity
9 1.55133 .64461 11.02656 7.10782
10 1.62889 .61391 12.57789 7.72173
11 1.71034 .58468 14.20679 8.30641
Instructions
(a) Calculate the amount of each rent.
(b) How much interest revenue will Pine earn in 2020?
Pr. 6-151—Deferred annuity.
Carey Company owns a plot of land on which buried toxic wastes have been discovered. Since it
will require several years and a considerable sum of money before the property is fully detoxified
and capable of generating revenues, Carey wishes to sell the land now. It has located two
potential buyers: Buyer A, who is willing to pay $700,000 for the land now, and Buyer B, who is
willing to make 20 annual payments of $110,000 each, with the first payment to be made 5 years
from today. Assuming that the appropriate rate of interest is 9%, to whom should Carey sell the
land? Show calculations.
Accounting and the Time Value of Money
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Solution 6-151