ch 6

CHAPTER 6 ACCOUNTING AND THE TIME VALUE OF MONEY IFRS questions are available at the end of this chapter.

TRUE-FALSE —Conceptual Answer F T F T T F F T T T F F F T T T F T F T

No.

Description

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Time value of money. Definition of interest expense. Simple interest. Compound interest. Compound interest. Future value of an ordinary annuity. Present value of an annuity due. Compounding period interest rate. Definition of present value. Future value of a single sum. Determining present value. Present value of a single sum. Annuity due and interest. Annuity due and ordinary annuity. Annuity due and ordinary annuity. Number of compounding periods. Future value of an annuity due factor. Present value of an ordinary annuity. Future value of a deferred annuity. Determining present value of bonds.

MULTIPLE CHOICE—Conceptual Answer a d b a c d b b a d c c b c c

No.

Description

21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. S 35. 35.

Appropriate use of an annuity due table. Time value of money. Present value situations. Definition of interest. Interest variables. Identification of compounding approach. Future value factor. Understanding compound interest tables. Identification of correct compound interest table. Identification of correct compound interest table. Identification of correct compound interest table. Identification of correct compound interest table. Identification of correct compound interest table. Identification of present value of 1 table. Iden Identi tifi fica cati tion on of cor corre rect ct com compo poun und d int intere erest st tabl table. e.

Test Bank for Intermediate Accounting, Fourteenth Edition

6-2

a

S

36. 36.

Iden Identi tifi fica cati tion on of of corr correc ectt comp compou ound nd int inter eres estt tabl table. e.

MULTIPLE CHOICE—Conceptual (cont.) Answer a c a d d a d c a c b d d b c c b c b b b b c c d P S

No. S

37. 37. 38. 38. P 39. 39. P 40. 40. 41. 42. 43. P 44. 44. 45. 46. 47. 48. 49. 50. P 51. 51. 52. 53. 54. 55. 56. 57. 58. P

59. 60. 61.

Description Pres Presen entt val value ue of an annu annuit ity y due due tabl table. e. Defi efiniti nition on of an annu annuiity due. due. Iden Identi tifi fica cati tion on of comp compou ound nd inte intere rest st conc concep ept. t. Iden Identi tifi fica cati tion on of comp compou ound nd inte intere rest st conc concep ept. t. Identification of number of compounding periods. Adjust the interest rate for time periods. Definition of present value. Compo ompoun und d inte intere res st conc concep epts ts.. Difference between or ordinary annuity and annuity due. Future value of 1 and present value of 1 relationship. Identify future value of 1 concept. Determine best bonus option Identify future value of an ordinary annuity Identify future value of an ordinary annuity Futu Future re valu value e of of an an ann annui uity ty due due fac facto tor. r. Determine the timing of rents of an annuity due. Factors of an ordinary annuity and an annuity due. Determine present value of an ordinary annuity. Identification of a future value of of an ordinary annuity of 1. Present value of an ordinary annuity and an annuity due. Difference between an ordinary annuity and an annuity due. Present value of ordinary annuity and present value of annuity due relationship Identify present value of ordinary annuity concept. Determine least costly option. Definition of deferred annuities.

These questions also appear in the Problem-Solving Survival Guide. These questions also appear in the Study Guide.

MULTIPLE CHOICE—Computational Answer a d d c b a b c c d a d b c

No.

Description

62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75.

Calculate the future value of 1. Calculate amount of interest paid. Interest compounded quarterly. Calculate present value of a future amount. Calculate a future value. Calculate a future value of an annuity due. Calculate a future value. Calculate a future value. Calculate present value of a future amount. Calculate present value of a future amount. Calculate present value of an annuity due. Calculate the future value of 1. Present value of a single sum. Present value of a single sum, unknown number of periods.

Accounting and the Time Value of Money c

76.

6-3

Future value of a single sum.

MULTIPLE CHOICE—Computational (cont.) Answer b b c d c a c a b c c d d b d d a b c d a b c d a a d c d a b b c a b b b c d a b d b b c b a

No. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123.

Description Present value of a single sum. Present value of a single sum, unknown number of periods. Future value of a single sum. Calculate the present value of 1. Calculate the future value of 1. Calculate the present value of 1. Calculate interest rate. Calculate number of years. Calculate the future value of 1. Calculate the present value of 1. Calculate the present value of 1. Calculate the present value of 1 and present value of an ordinary annuity. Calculate number if years. Calculate the amount of annual deposit. Calculate the amount of annual deposit. Calculate the amount of annual deposit. Present value of an ordinary annuity. Present value of an annuity due. Future value of an ordinary annuity. Future value of a annuity due. Present value of an ordinary annuity. Present value of an annuity due. Future value of an ordinary annuity. Future value of an annuity due. Calculate future value of an annuity due. Calculate future value of of an ordinary annuity. Calculate future value of an annuity due. Calculate annual deposit for annuity due. Calculate co cost of of ma machine pu purchased on in installment. Calculate present value of an ordinary annuity. Calculate present value of an annuity due. Calculate co cost of of ma machine pu purchased on in installment. Calculate cost of machine purchased on installment. Calc Calcul ulat ate e the the annu annual al rent rents s of leas leased ed equi equipm pmen ent. t. Calculate present value of an investment in equipment. Calculate proceeds from issuance of bonds. Calculate proceeds from issuance of bonds. Calculate present value of an ordinary annuity. Calculate interest rate. Calculate present value of an annuity due. Calculate effective interest rate. Calculate present value of an ordinary annuity. Calculate present value of an annuity due. Calculate annual interest rate. Calculate interest rate. Calculate annual lease payment. Calculate selling price of bonds.


6-4

MULTIPLE CHOICE—CPA Adapted Answer c d c a b a a d b

No. 124. 125. 126. 127. 128. 129. 130. 131. 132.

Description Calculate interest expense of bonds. Identification of of co correct co compound in interest ta table. Calculate interest revenue of a zero-interest-bearing note. Appropriate use of an ordinary annuity table. Calculate annual deposit of annuity due. Calculate the present value of a note. Calculate the present value of a note. Determine the issue price of a bond. Determine the acquisition cost of a franchise.

EXERCISES Item E6-133 E6-134 E6-135 E6-136 E6-137 E6-138 E6-139 E6-140

Description Present an and fu future va value co concepts. Compute estimated goodwill. Present value of an investment in equipment. Future va value of of an annuity due. Present value of an annuity due. Compute the annual rent. Calculate the market price of a bond. Calculate the market price of a bond.

PROBLEMS Item P6-141 P6-142 P6-1 P6-143 43 P6-144 P6-145 P6-146

Description Present va value an and future va value co computations. Annuity with change in interest rate. Pres Presen entt value alue of ordi ordina nary ry annu annuiity and and annu annuiity due. due. Finding th the im implied in interest ra rate. Calculation of unknown ren rent and interest. Deferred an annuity.

CHAPTER LEARNING OBJECTIVES 1. 2. 3. 4. 5. 6. 7. 8.

Identify Identify accountin accounting g topics topics where the the time time value of of money is is relevant. relevant. Distinguish Distinguish between between simple simple and compoun compound d interest interest.. Use appro appropri priate ate compo compound und inter interest est table tables. s. Identify Identify variabl variables es fundamenta fundamentall to solvin solving g interest interest problems problems.. Solve Solve futur future e and prese present nt value value of 1 prob problem lems. s. Solve future future value value of ordinary ordinary and and annuity annuity due due problems problems.. Solve present present value value of ordinary ordinary and annuity annuity due problems. problems. Solve present present value value problems problems related related to to deferred deferred annuities annuities and and bonds. bonds.

Accounting and the Time Value of Money

6-5

SUMMARY OF LEARNING OBJECTIVES BY QUESTIONS Ite

Ty

Ite

Ty

Ite

1.

TF

2.

TF

21.

3.

TF

4.

TF

5.

6. 7. 8.

TF TF TF

27. 28. 29.

MC MC MC

30. 31. 32.

9.

TF

10. 11. 12. 43. P 44. 45.

P

P

39.

MC

TF TF TF MC MC MC

46. 47. 48. 65. 66. 68.

MC MC MC MC MC MC

69. 70. 71. 73. 74. 75.

13. 14. 16. 17.

TF TF TF TF

49. 50. P 51. 52.

MC MC MC NC

53. 67. 90. 91.

15. 18. 53. 54. 55. 56.

TF TF MC MC MC MC

57. 58. 59. 60. 72. 88.

MC MC MC MC MC MC

104. 105. 106. 107. 108. 109.

19.

TF

20.

TF

61.

Note:

40.

TF = True-False MC = Multiple Choice

Ty

Ite

Ty

Ite

Learning Objective 1 MC 22. MC 23. Learning Objective 2 TF 26. MC 62. Learning Objective 3 S MC 33. MC 36. S MC 34. MC 37. S P MC 35. MC 38. Learning Objective 4 MC 41. MC 42. Learning Objective 5 MC 76. MC 82. MC 77. MC 83. MC 78. MC 84. MC 79. MC 85. MC 80. MC 86. MC 81. MC 87. Learning Objective 6 MC 92. MC 96. MC 93. MC 97. MC 94. MC 98. MC 95. MC 99. Learning Objective 7 MC 110. MC 116. MC 111. MC 117. MC 112. MC 118. MC 113. MC 119. MC 114. MC 120. MC 115. MC 121. Learning Objective 8 MC 123. MC 146.

E = Exercise P = Problem

Ty

Ite

Ty

MC

24.

MC

MC

63.

MC MC MC

64. 125.

MC MC

MC MC MC MC MC MC

88. 89. 124. 126. 133. 134.

MC MC MC MC MC MC MC MC MC MC

Ite

Typ

25.

MC

124.

MC

MC MC MC MC E E

135. 141.

E P

100. 101. 102. 103.

MC MC MC MC

136. 142.

E P

122. 127. 128. 137. 138. 139.

MC MC MC E E E

140. 141. 143. 144. 145.

E P P P P

MC

P

6-6


TRUE-FALSE —Conceptual 1. The time value value of money refers refers to the fact that a dollar dollar received received today is worth worth less than a dollar promised at some time in the future. 2. Interest is the excess cash received or repaid over and above the amount lent or borrowed. 3. Simple Simple interest interest is computed computed on princi principal pal and on any interes interestt earned that has not been withdrawn. 4. Compou Compound nd intere interest, st, rather rather than than simple simple interest interest,, must must be used used to properl properly y evalua evaluate te longlongterm investment proposals. 5. Compound Compound interest interest uses the accumulate accumulated d balance at each year year end to compute interest interest in the succeeding year. 6. The future future value of an ordinary ordinary annuit annuity y table is used used when when paymen payments ts are invest invested ed at the beginning of each period. 7. The present present value of an annuity annuity due table table is used when payments payments are made at the the end of each period. 8. If the compounding compounding period period is less than one year, year, the annual interest interest rate rate must be converted converted to the compounding period interest rate by dividing the annual rate by the number of compounding periods per year. 9. Present Present value is the value value now of a future sum or sums sums discounted discounted assuming assuming compound compound interest. 10. The future future value of a single sum is determined determined by multiplyin multiplying g the future value factor factor by its present value. 11. In determin determining ing present present value, value, a compan company y moves moves backward backward in time time using using a proces process s of accumulation. 12. The unknown unknown present value is always always a larger amount amount than the known future future value because because dollars received currently are worth more than dollars to be received in the future. 13. The rents that that comprise comprise an annuity annuity due earn no interest interest during during the period in which which they are originally deposited. 14. If two annuities annuities have have the same number number of rents with with the same dollar dollar amount, but one is an annuity due and one is an ordinary annuity, the future value of the annuity due will be greater than the future value of the ordinary annuity. 15. If two annuities annuities have have the same number number of rents with with the same dollar dollar amount, but one is an annuity due and one is an ordinary annuity, the present value of the annuity due will be greater than the present value of the ordinary annuity. 16. The number number of compounding compounding periods will will always be one less than the number number of rents when computing the future value of an ordinary annuity.


6-7

17. The future future value value of an annuity annuity due factor factor is found found by multip multiply lying ing the future future value of an ordinary annuity factor by 1 minus the interest rate. 18. The presen presentt value of an ordina ordinary ry annuity annuity is the present present value of a series series of equal rents rents withdrawn at equal intervals. 19. 19. The The futu future re valu value e of a defe deferr rred ed annu annuit ity y is less than than the the futu future re valu value e of an annu annuit ity y not not deferred. 20. At the date of issue, issue, bond buyers buyers determin determine e the present present value value of the bonds’ bonds’ cash cash flows flows using the market interest rate.

True False Answers— Conceptual Item 1. 2. 3. 4. 5.

Ans. F T F T T

Item 6. 7. 8. 9. 10.

Ans. F F T T T

Item 11. 12. 13. 14. 15.

Ans. F F F T T

Item 16. 17. 18. 19. 20.

Ans. T F T F T

MULTIPLE CHOICE—Conceptual 21. 21.

Whic Which h of the the foll follow owin ing g tran transa sact ctio ions ns would would requir require e the the use use of the prese present nt value value of an annuity due concept in order to calculate the present value of the asset obtained or liability owed at the date of incurrence? a. A capital capital lease lease is entered entered into into with the initia initiall lease paymen paymentt due upon the signing signing of the lease agreement. b. A capital capital lease is entered entered into into with the initial initial lease lease payment payment due one month subsesubsequent to the signing of the lease agreement. c. A ten-year ten-year 8% bond is is issued issued on January January 2 with with interest interest payable payable semiannually semiannually on July 1 and January 1 yielding 7%. d. A ten-year ten-year 8% bond is is issued issued on January January 2 with with interest interest payable payable semiannually semiannually on July 1 and January 1 yielding 9%.

22. 22.

What What bes bestt desc descri ribe bes s the the time time val value ue of of money money? ? a. The interes interestt rate rate charg charged ed on a loan. loan. b. Accounts Accounts receiv receivable able that that are are determin determined ed uncollec uncollectible. tible. c. An inve investm stment ent in a chec checkin king g accoun account. t. d. The rela relatio tionsh nship ip betwe between en time time and money money..

23. 23.

Whic Which h of the follo followi wing ng situat situatio ions ns does does not not base base an acco accoun unti ting ng measur measure e on presen presentt values? a. Pensions. b. Prep Prepai aid d insur insuran ance ce.. c. Leases. d. Sink Sinkiing fun funds ds..

6-8


24.

Wha What is interest? a. Paymen Paymentt for for the the use use of of mone money. y. b. An equi equity ty inve invest stme ment nt.. c. Retu Return rn on capi capita tal. l. d. Loan.

25.

What What is NOT NOT a vari variabl able e that that is cons conside idered red in in interes interestt comput computati ations ons? ? a. Principal. b. Inte Intere rest st rate rate.. c. Assets. d. Time.

26.

If you you invest invest $50,000 $50,000 to earn earn 8% interest, interest, which which of the the follow following ing compoundi compounding ng approaches approaches would return the lowest amount after one year? a. Daily. b. Monthly. c. Quarterly rly. d. Annually lly.

27.

Which Which facto factorr would would be great greater er — the the present present valu value e of $1 for for 10 period periods s at 8% per per period period or the future value of $1 for 10 periods at 8% per period? a. Present Present value value of $1 for for 10 period periods s at 8% per per period. period. b. Future Future value value of of $1 for 10 10 periods periods at at 8% per peri period. od. c. The The fac facto tors rs are are the the sam same. e. d. Need Need more more inf infor orma mati tion on..

28.

Which Which of the the followi following ng tables tables would would show show the small smallest est value value for for an interes interestt rate rate of 5% for six periods? a. Futu Future re valu value e of of 1 b. Pres Presen entt val value ue of 1 c. Future Future valu value e of an an ordin ordinary ary annuity annuity of 1 d. Presen Presentt value value of an an ordina ordinary ry annui annuity ty of 1

29. 29.

Whic Which h table table would would you you use use to dete determ rmin ine e how much much you would would need need to have have depos deposit ited ed three years ago at 10% compounded annually in order to have $1,000 today? a. Future Future valu value e of 1 or prese present nt valu value e of 1 b. Future Future value value of of an annuit annuity y due due of 1 c. Future Future valu value e of an an ordin ordinary ary annuity annuity of 1 d. Presen Presentt value value of an an ordina ordinary ry annui annuity ty of 1

30. 30.

Whic Which h table table woul would d you you use to determ determin ine e how much much must must be depo deposi site ted d now in order order to provide for 5 annual withdrawals at the beginning of each year, starting one year hence? a. Future Future valu value e of an ordi ordinary nary annuity annuity of 1 b. Future Future value value of of an annuit annuity y due due of 1 c. Presen Presentt value value of an an annui annuity ty due due of of 1 d. None one of thes these e

31.

Which Which table table has has a facto factorr of 1.000 1.00000 00 for for 1 period period at at every every inte interes restt rate? rate? a. Futu Future re valu value e of of 1 b. Pres Presen entt val value ue of 1 c. Future Future valu value e of an an ordin ordinary ary annuity annuity of 1 d. Presen Presentt value value of an an ordina ordinary ry annui annuity ty of 1


6-9

32.

Which table would show the largest largest factor factor for an interes interestt rate rate of 8% for for five five periods? periods? a. Future Future valu value e of an ordi ordinary nary annuity annuity of 1 b. Presen Presentt value value of an an ordina ordinary ry annui annuity ty of 1 c. Future Future value value of of an annuit annuity y due due of 1 d. Presen Presentt value value of an an annui annuity ty due due of of 1

33.

Which of the the following following tables tables would show the smalle smallest st factor factor for for an interes interestt rate rate of 10% for for six periods? a. Future Future valu value e of an ordi ordinary nary annuity annuity of 1 b. Presen Presentt value value of an an ordina ordinary ry annui annuity ty of 1 c. Future Future value value of of an annuit annuity y due due of 1 d. Presen Presentt value value of an an annui annuity ty due due of of 1

34.

The figur figure e .94232 .94232 is taken taken from from the colum column n marked marked 2% and and the row mark marked ed three three period periods s in a certain interest table. From what interest table is this figure taken? a. Futu Future re valu value e of of 1 b. Futu Future re val value ue of of annu annuit ity y of 1 c. Pres Presen entt val value ue of 1 d. Pres Presen entt valu value e of ann annui uity ty of of 1

S

35.

Which of the the following following tables tables would show the largest largest value for an interest interest rate rate of 10% for for 8 periods? a. Futu Future re amo amoun untt of 1 tabl table. e. b. Pres Presen entt valu value e of 1 tabl table. e. c. Future Future amoun amountt of an ordin ordinary ary annui annuity ty of 1 table table.. d. Present Present value value of an ordinary ordinary annuity annuity of 1 table. table.

S

36. 36.

On June June 1, 2012 2012,, Pitts Pitts Comp Compan any y sold some some equip equipme ment nt to Ganno Gannon n Compan Company. y. The two two compan companies ies entere entered d into into an instal installme lment nt sales sales contra contract ct at a rate rate of 8%. The contra contract ct required 8 equal annual payments with the first payment due on June 1, 2012. What type of compound interest table is appropriate for this situation? a. Presen Presentt value value of an an annuit annuity y due of of 1 table. table. b. Present Present value value of an ordinary ordinary annuity annuity of 1 table. table. c. Future Future amoun amountt of an ordin ordinary ary annui annuity ty of 1 table table.. d. Futu Future re amo amoun untt of 1 tabl table. e.

S

37.

Which of the the following following transaction transactions s would would best best use the present present value of an annuity annuity due of 1 table? a. Fernet Fernetti, ti, Inc. Inc. rents a truck truck for 5 years years with with annual rental rental payment payments s of $20,00 $20,000 0 to be made at the beginning of each year. b. Edmiston Edmiston Co. rents rents a warehouse warehouse for for 7 years with with annual rental rental payments payments of $120,000 $120,000 to be made at the end of each year. c. Durant, Durant, Inc. borrows borrows $20,000 $20,000 and has agreed agreed to pay pay back the the principal principal plus plus interest interest in three years. d. Babbitt, Babbitt, Inc. Inc. wants to deposit deposit a lump lump sum to accumula accumulate te $50,000 $50,000 for the construc construction tion of a new parking lot in 4 years.

6 - 10


P

38.

A series series of equal equal recei receipts pts at at equal equal interva intervals ls of time time when when each each receipt receipt is rece receive ived d at the beginning of each time period is called an a. ordi ordina nary ry ann annui uity ty.. b. annu annuit ity y in arr arrea ears rs.. c. annuity due. d. unea unearn rned ed rec recei eipt pt..

P

39.

In the the time time diagr diagram am belo below, w, whic which h concep conceptt is bein being g depict depicted? ed?

0

1 $1

2 $1

3 $1

4 $1

PV

a. b. c. d. P

Presen Presentt value value of an ordi ordinary nary annuit annuity y Presen Presentt value value of an an annui annuity ty due Future Future value value of of an ordina ordinary ry annu annuity ity Future Future value value of of an annuit annuity y due due

40.

On Decemb December er 1, 2012, 2012, Richa Richards rds Compa Company ny sold sold some mach machine inery ry to Flemi Fleming ng Compan Company. y. The two companies entered into an installment sales contract at a predetermined interest rate. The contract required four equal annual payments with the first payment due on December 1, 2012, the date of the sale. What present value concept is appropriate for this situation? a. Future Future amoun amountt of an annui annuity ty of 1 for for four peri periods ods b. Future Future amount amount of 1 for four four perio periods ds c. Present Present value value of an ordinary ordinary annuity annuity of 1 for four periods periods d. Present Present value value of an annuity annuity due of 1 for four periods. periods.

41.

An amount amount is is deposite deposited d for eight years at 8%. 8%. If compoundin compounding g occurs occurs quarterl quarterly, y, then then the the table value is found at a. 8% for for eig eight ht peri period ods. s. b. 2% for for eig eight ht peri period ods. s. c. 8% for for 32 32 per perio iods ds.. d. 2% for for 32 32 per perio iods ds..

42.

If the the number number of of period periods s is know known, n, the the intere interest st rate rate is determ determine ined d by a. dividing dividing the future future value value by the present present value value and looking looking for the quotien quotientt in the future future value of 1 table. b. divi dividi ding ng the the futu future re valu value e by the pres presen entt valu value e and and look lookin ing g for for the the quot quotie ient nt in the the present value of 1 table. c. dividing dividing the present present value value by the future future value value and looking looking for the quotient quotient in in the future future value of 1 table. d. multip multiply lying ing the present present value value by the future future value and looking looking for the product product in the present value of 1 table.


P

6 - 11

43.

Present va value is is a. the value value now now of of a futu future re amou amount. nt. b. the amount amount that that must be be invested invested now to produce produce a known known future value. value. c. always always smal smaller ler than than the the futu future re valu value. e. d. all all of of thes these. e.

44. 44.

Whic Which h of the the foll follow owin ing g stat statem emen ents ts is is true true? ? a. The higher higher the the discount discount rate, rate, the the higher higher the present present value. value. b. The process process of accumul accumulating ating interest interest on interes interestt is referred referred to as discounti discounting. ng. c. If money money is wort worth h 10% 10% comp compou ound nded ed annual annually ly,, $1,1 $1,100 00 due one one year year from today today is equivalent to $1,000 today. d. If a single single sum is is due on December December 31, 31, 2012, the the present present value of of that sum sum decreases decreases as the date draws closer to December 31, 2012.

45.

What What is the the primar primary y differ differenc ence e between between an ordin ordinary ary annu annuity ity and and an annuit annuity y due? due? a. The timing timing of of the the perio periodic dic paym payment ent.. b. The The int inter eres estt rate rate.. c. Annuit Annuity y due only only relat relates es to pres present ent valu values. es. d. Ordinary Ordinary annuity annuity only relates relates to present present values. values.

46.

What is the the relations relationship hip between between the future future value value of one and the the present present value of one? one? a. The present present value of one equals equals the future future value value of one plus plus one. b. The present present value value of one one equals one plus plus future value factor factor for for n-1 periods periods.. c. The present present value of one equals equals one divided divided by the future future value value of of one. d. The present present value value of one one equals one plus plus the future future value value factor factor for n+1 n+1 value value

47.

Peter Peter invest invests s $100,00 $100,000 0 in a 3-year 3-year certifi certificat cate e of deposit deposit earni earning ng 3.5% 3.5% at his local local bank. bank. Whic Which h time time valu value e conc concep eptt would would be used used to dete determ rmin ine e the the matu maturi rity ty valu value e of the the certificate? a. Pres Presen entt val value ue of one. one. b. Futu Future re val value ue of of one. one. c. Presen Presentt value value of an an annui annuity ty due. due. d. Future Future valu value e of an an ordin ordinary ary annuity annuity..

48.

Jerry Jerry recent recently ly was offer offered ed a positio position n with a major major account accounting ing firm. firm. The firm firm offere offered d Jerry either a signing bonus of $23,000 payable on the first day of work or a signing bonus of $26,000 payable after one year of employment. Assuming that the relevant interest rate is 10%, which option should Jerry choose? a. The The optio options ns are are equiv equival alen ent. t. b. Insuff Insuffici icient ent infor informat mation ion to deter determin mine. e. c. The signing signing bonus of of $23,000 $23,000 payable payable on the the first first day of work. work. d. The signing signing bonus of of $26,000 $26,000 payable payable after after one year of employme employment. nt.

49. 49.

If Jeth Jethro ro want wanted ed to save save a set set amount amount each each month month in order order to buy a new pick pick-up -up truc truck k when the new models are next available, which time value concept would be used to determine the monthly payment? a. Pres Presen entt val value ue of one. one. b. Futu Future re val value ue of of one. one. c. Presen Presentt value value of an an annui annuity ty due. due. d. Future Future valu value e of an an ordin ordinary ary annuity annuity..

6 - 12

P


50.

Bett Betty y wants ants to know now how how much much she she shoul hould d begi begin n savin aving g eac each mon month to fund und her her retirement. What kind of problem is this? a. Pres Presen entt val value ue of one. one. b. Future Future valu value e of an an ordin ordinary ary annuity annuity.. c. Pres Presen entt value value of an an ordi ordina nary ry.. d. Futu Future re val value ue of of one. one.

51

If the the interes interestt rate rate is 10%, 10%, the the fact factor or for for the futu future re value value of of annuit annuity y due of of 1 for n = 5, i = 10% is equal to the factor for the future value of an ordinary annuity of 1 for n = 5, i = 10% a. plus 1.10. b. minus 1. 1.10. c. mult multip iplilied ed by by 1.1 1.10. 0. d. divi divide ded d by by 1.10 1.10..

52. 52.

Whic Which h of of the the foll follow owin ing g is true true? ? a. Rents occur at at the beginnin beginning g of each period period of an an ordinary ordinary annuity. annuity. b. Rents occur at the the end of each each period period of of an annuity annuity due. due. c. Rents occur at the beginning beginning of each each period period of an annuity annuity due. due. d. None one of of the these se..

53.

Whi Which st statement is is false? a. The factor factor for the futur future e value of an annuity annuity due due is found found by multiply multiplying ing the ordinar ordinary y annuity table value by one plus the interest rate. b. The factor factor for the the present present value of an annuity annuity due is is found by multiply multiplying ing the ordinary ordinary annuity table value by one minus the interest rate. c. The factor factor for the the future future value value of an annuity annuity due is is found by subtractin subtracting g 1.00000 1.00000 from the ordinary annuity table value for one more period. d. The factor factor for the the present present value value of an annuit annuity y due is found by adding adding 1.0000 1.00000 0 to the ordinary annuity table value for one less period.

54.

Al Darby Darby wants wants to withdraw withdraw $20,0 $20,000 00 (inclu (includin ding g principa principal) l) from an inves investme tment nt fund fund at the end of each year for five years. How should he compute his required initial investment at the beginning of the first year if the fund earns 10% compounded annually? a. $20,000 $20,000 times the future future value value of a 5-year, 5-year, 10% ordinar ordinary y annuity annuity of 1. b. $20,000 $20,000 divided divided by the future future value value of a 5-year 5-year,, 10% ordinary ordinary annuity annuity of 1. c. $20,000 $20,000 times the present present value value of a 5-year 5-year,, 10% ordinary ordinary annuity annuity of of 1. d. $20,000 $20,000 divided divided by the present present value of of a 5-year, 5-year, 10% ordinary ordinary annuity annuity of 1.

55.

Sue Gray Gray wants wants to to invest invest a cert certain ain sum sum of mone money y at the the end of each each year year for for five five years. years. The investment will earn 6% compounded annually. At the end of five years, she will need a total of $40,000 accumulated. How should she compute her required annual investment? a. $40,000 $40,000 times the future future value value of a 5-year, 5-year, 6% ordinary ordinary annuity annuity of 1. b. $40,000 $40,000 divided divided by the future future value value of a 5-year 5-year,, 6% ordinary ordinary annuity annuity of of 1. c. $40,000 $40,000 times the present present value value of a 5-year 5-year,, 6% ordinary ordinary annuity annuity of 1. d. $40,000 $40,000 divided divided by the present present value of of a 5-year, 5-year, 6% ordinary ordinary annuity annuity of 1.


6 - 13

56. 56.

An accou account ntan antt wish wishes es to find find the prese present nt value value of an annui annuity ty of $1 payab payable le at the the beginning beginning of each period at 10% for eight periods. The accountant accountant has only one present value table which shows the present value of an annuity of $1 payable at the end of each period. To compute the present value, the accountant would use the present value factor in the 10% column for a. seven even per perio iods ds.. b. eight eight perio periods ds and and multip multiply ly by (1 + .10). .10). c. eigh eightt per perio iods ds.. d. nine nine period periods s and and multip multiply ly by (1 – .10) .10)..

57.

If an annui annuity ty due and and an ordina ordinary ry annuit annuity y have the the same same number number of equal equal payment payments s and the same interest rates, then a. the presen presentt value of the annuity annuity due is less less than the present present value value of the ordinary ordinary annuity. b. the present present value value of the annuity annuity due is greate greaterr than the present present value value of the ordinary ordinary annuity. c. the future future value of of the annuity annuity due is equal equal to the future future value value of the ordinary ordinary annuity. annuity. d. the future future value of of the annuity annuity due is less less than the future future value value of the ordinary ordinary annuity annuity..

58.

What What is the relat relation ionshi ship p between between the the present present valu value e factor factor of an ordin ordinary ary annui annuity ty and the the present value factor of an annuity due for the same interest rate? a. The ordinary ordinary annuity annuity factor factor is is not related related to the annuity annuity due factor factor.. b. The annuity annuity due due factor factor equals equals one plus plus the ordinary ordinary annuity annuity factor factor for for n−1 periods. c. The ordinary ordinary annuity annuity factor factor equals equals one one plus the the annuity annuity due factor factor for for n+1 periods periods.. d. The annuity annuity due factor factor equals equals the ordinary ordinary annuity annuity factor factor for n+1 n+1 periods minus minus one. one.

59. 59.

Paul Paula a purc purcha hase sed d a hous house e for for $300 $300,0 ,000 00.. Afte Afterr prov provid idin ing g a 20% 20% down down payme payment nt,, she she borrowed the balance from the local savings and loan under a 30-year 6% mortgage loan requiring equal monthly installments at the end of each month. Which time value concept would be used to determine the monthly payment? a. Pres Presen entt val value ue of one. one. b. Futu Future re val value ue of of one. one. c. Presen Presentt value value of an ordi ordinary nary annuit annuity. y. d. Future Future valu value e of an an ordin ordinary ary annuity annuity..

60.

Stemw Stemway ay require requires s a new manuf manufact acturi uring ng facilit facility. y. Manage Managemen mentt found three three locati locations ons;; all of which would provide needed capacity, the only difference is the price. Location A may be purchased for $500,000. Location B may be acquired with a down payment of $100,000 and annual payments at the end of each of the next twenty years of $50,000. Location C requir requires es $40,00 $40,000 0 paymen payments ts at the beginn beginning ing of each each of the next next twenty twenty-fiv -five e years. years. Assuming Stemway's borrowing costs are 8% per annum, which option is the least costly to the company? a. Location A. A. b. Location B. B. c. Location C. d. Loca Locati tion on A and and Loc Locat atio ion n B.

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61.


Whic Which h of of the the foll follow owin ing g is is false? a. The future future value value of a deferred deferred annuity is is the same as the the future future value of an annuity annuity not not deferred. b. A deferred deferred annuity annuity is an annuity annuity in which the rents rents begin begin after a specifi specified ed number of periods periods.. c. To compute compute the present present value of a deferr deferred ed annuity, annuity, we compute compute the the present present value value of an ordinary annuity of 1 for the entire period and subtract the present value of the rents which were not received during the deferral period. d. If the first first rent is is received received at the end end of the sixth sixth period, period, it means means the ordinary ordinary annuit annuity y is deferred for six periods.

Multiple Choice Answers —Conceptual Item

21. 22. 23. 24. 25. 26.

Ans.

a d b a c d

Item

27. 28. 29. 30. 31. 32.

Ans.

b b a d c c

Item

33. 34. 35. 36. 37. 38.

Ans.

b c c a a c

Item

39. 40. 41. 42. 43. 44.

Ans.

a d d a d c

Item

45. 46. 47. 48. 49. 50.

Ans.

Item

Ans.

Item

Ans.

a c b d d b

51. 52. 53. 54. 55. 56.

c c b c b b

57. 58. 59. 60. 61.

b b c c d

Solution to Multiple Choice question for which the answer is “none of these.” 30. 30. Pres Presen entt val value ue of an an Ordi Ordina nary ry Ann Annui uity ty of 1. 1.

MULTIPLE CHOICE—Computational 62.

Assume Assume ABC ABC Company Company depos deposits its $50,0 $50,000 00 with with First First Natio National nal Bank Bank in an accoun accountt earning earning interest at 6% per annum, compounded semi-annually. How much will ABC have in the account after five years if interest is reinvested? a. $67,196. b. $50,000. c. $65,000. d. $66,912.

63.

Charli Charlie e Corp. Corp. is purchas purchasing ing new new equipme equipment nt with with a cash cost cost of $150 $150,00 ,000 0 for an assem assembly bly line. The manufacturer has offered to accept $34,440 payment at the end of each of the next six years. How much interest will Charlie Corp. pay over the term of the loan? a. $34,440. b. $150,000. c. $184,440. d. $56,640.

64.

If a saving savings s account account pays pays interes interestt at 4% compounded compounded quarter quarterly, ly, then then the amount of $1 left on deposit for 8 years would be found in a table using a. 8 per periiods ods at at 4% 4%. b. 8 per periiods ods at at 1% 1%. c. 32 peri period ods s at at 4%. 4%. d. 32 peri period ods s at at 1%. 1%.


6 - 15

Items 65 through 68 apply to the appropriate use of interest tables. Given below are the future value factors for 1 at 8% for one to five periods. Each of the items 65 to 68 is based on 8% interest compounded annually. Periods 1 2 3 4 5

Future Value of 1 at 8% 1.080 1.166 1.260 1.360 1.469

65.

What amount should should be deposited deposited in in a bank bank account account today today to to grow grow to $10,000 $10,000 three three years years from today? a. $10, $10,00 000 0 × 1.2 1.260 60 b. $10, $10,00 000 0 × 1.26 1.260 0 ×3 c. $10, $10,00 000 0 ÷ 1.26 1.260 0 d. $10, $10,00 000 0 ÷ 1.08 1.080 0 ×3

66.

If $3,000 $3,000 is put in a savings savings account account today, today, what amount will be be available available three years from today? a. $3,0 $3,000 00 ÷ 1. 1.260 260 b. $3,0 $3,000 00 × 1.2 1.260 60 c. $3,0 $3,000 00 × 1.0 1.080 80 × 3 d. ($3,000 ($3,000 × 1.080) 1.080) + ($3,000 ($3,000 × 1.166) 1.166) + ($3,000 ($3,000 × 1.260) 1.260)

67.

What What amount amount will will be in a bank bank accoun accountt three three years years from from now if $6,00 $6,000 0 is invest invested ed each each year for four years with the first investment to be made today? a. ($6,000 ($6,000 × 1.260) 1.260) + ($6,000 ($6,000 × 1.166) 1.166) + ($6,000 ($6,000 × 1.080) 1.080) + $6,000 b. $6,0 $6,000 00 × 1.3 1.360 60 × 4 c. ($6,000 ($6,000 × 1.080) 1.080) + ($6,000 ($6,000 × 1.166) 1.166) + ($6,000 ($6,000 × 1.260) + ($6,000 ($6,000 × 1.360) 1.360) d. $6,0 $6,000 00 × 1.0 1.080 80 × 4

68.

If $4,000 $4,000 is put put in a savings savings accou account nt today, today, what what amoun amountt will will be availab available le six year years s from now? a. $4,0 $4,000 00 × 1.0 1.080 80 × 6 b. $4,0 $4,000 00 × 1.0 1.080 80 × 1.4 1.469 69 c. $4,0 $4,000 00 × 1.1 1.166 66 × 3 d. $4,0 $4,000 00 × 1.2 1.260 60 × 2

Items 69 through 72 apply to the appropriate use of present value tables. Given below are the present value factors for $1.00 discounted at 10% for one to five periods. Each of the items 69 to 72 is based on 10% interest compounded annually. Present Value of $1 Periods Discounted at 10% per Period 1 0.909 2 0.826 3 0.751 4 0.683 5 0.621

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69. 69.

If an indiv individ idual ual put put $4,000 $4,000 in a savi saving ngs s accoun accountt today, today, what what amoun amountt of cash cash woul would d be available two years from today? a. $4,0 $4,000 00 × 0.8 0.826 26 b. $4,0 $4,000 00 × 0.8 0.826 26 × 2 c. $4,0 $4,000 00 ÷ 0.82 0.826 6 d. $4,0 $4,000 00 ÷ 0.9 0.909 09 × 2

70.

What What is the the present present valu value e today today of $6,00 $6,000 0 to be recei received ved six six years years from from today today? ? a. $6,0 $6,000 00 × 0.9 0.909 09 × 6 b. $6,0 $6,000 00 × 0.7 0.751 51 × 2 c. $6,0 $6,000 00 × 0.6 0.621 21 × 0.90 0.909 9 d. $6,0 $6,000 00 × 0.6 0.683 83 × 3

71. 71.

What What amou amount nt shou should ld be depos deposit ited ed in a bank bank today today to to grow to $3,0 $3,000 00 three three years years from from today? a. $3,0 $3,000 00 ÷ 0.7 0.751 51 b. $3,0 $3,000 00 × 0.9 0.909 09 × 3 c. ($3,000 ($3,000 × 0.909) 0.909) + ($3,000 ($3,000 × 0.826) 0.826) + ($3,000 ($3,000 × 0.751) 0.751) d. $3,0 $3,000 00 × 0.7 0.751 51

72. 72.

What What amoun amountt should should an indi indivi vidu dual al have have in a bank bank accou account nt today today befor before e withdr ithdraw awal al if $5,000 is needed each year for four years with the first withdrawal to be made today and each subsequent withdrawal at one-year intervals? (The balance in the bank account should be zero after the fourth withdrawal.) a. $5,000 + ($5,000 ($5,000 × 0.909) 0.909) + ($5,000 ($5,000 × 0.826) 0.826) + ($5,000 ($5,000 × 0.751) 0.751) b. $5,0 $5,000 00 ÷ 0.6 0.683 83 × 4 c. ($5,000 ($5,000 × 0.909) 0.909) + ($5,000 ($5,000 × 0.826) 0.826) + ($5,000 ($5,000 × 0.751) + ($5,000 ($5,000 × 0.683) 0.683) d. $5,0 $5,000 00 ÷ 0.9 0.909 09 × 4

73.

At the the end of two two years, years, what what will will be the balance balance in a saving savings s account account paying paying 6% annuall annually y if $10,000 is deposited today? The future value of one at 6% for one period is 1.06. a. $10,000 b. $10,600 c. $11,200 d. $11,236

74.

Mordica Mordica Company Company will receive receive $250,000 $250,000 in 7 years. years. If the appropri appropriate ate interes interestt rate rate is 10%, the present value of the $250,000 receipt is a. $127,500. b. $128,290. c. $377,500. d. $487,180.

75.

Dunston Dunston Company Company will receiv receive e $200,000 $200,000 in in a future future year. year. IfIf the future receipt receipt is discounted discounted at an interest rate of 10%, its present value is $102,632. In how many years is the $200,000 received? a. 5 years b. 6 years c. 7 years d. 8 years


6 - 17

76.

Milner Milner Compa Company ny will will invest invest $400,00 $400,000 0 today. today. The invest investmen mentt will earn earn 6% for 5 years, years, with with no funds withdrawn. In 5 years, the amount in the investment fund is a. $400,000. b. $520,000. c. $535,292. d. $536,116.

77.

Barber Barber Compa Company ny will will receive receive $800,0 $800,000 00 in 7 years. years. If the the appropri appropriate ate interes interestt rate is 10%, 10%, the present value of the $800,000 receipt is a. $408,000. b. $410,528. c. $1,208,000. d. $1,5 $1,558 58,,976. 976.

78.

Barkley Barkley Company Company will will receive receive $300,0 $300,000 00 in a future future year. year. If the future future receipt receipt is disco discounted unted at an interest rate of 8%, its present value is $189,051. In how many years is the $300,000 received? a. 5 years b. 6 years c. 7 years d. 8 years

79.

Altman Altman Company Company will will invest invest $500,000 $500,000 today. today. The invest investment ment will earn earn 6% for 5 years, years, with with no funds withdrawn. In 5 years, the amount in the investment fund is a. $500,000. b. $650,000. c. $669,115. d. $670,145.

80.

John John Jones Jones won a lottery lottery that that will will pay him $2,00 $2,000,0 0,000 00 after after twenty twenty years years.. Assumin Assuming g an appropriate interest rate is 5% compounded annually, what is the present value of this amount? a. $2,0 $2,000 00,,000. 000. b. $5,3 $5,306 06,,600. 600. c. $24, $24,92 924, 4,42 420. 0. d. $753,780.

81. 81.

Angi Angie e inve invest sted ed $100, $100,00 000 0 she she rece receiv ived ed from from her grandm grandmot othe herr toda today y in a fund that that is expected to earn 10% per annum. To what amount should the investment grow in five years if interest is compounded semi-annually? a. $155,134. b. $161,050. c. $162,890. d. $177,156.

82. 82.

Bell Bella a requ requir ires es $120, $120,00 000 0 in four four year years s to purch purchas ase e a new home. home. What What amount amount must must be invested today in an investment that earns 6% interest, compounded annually? a. $95,051. b. $98,724. c. $145,337. d. $151,497.

6 - 18


83. 83.

What What intere interest st rate rate (the (the neares nearestt perc percen ent) t) must must Charl Charlie ie earn on a $150 $150,0 ,000 00 inve invest stme ment nt today so that he will have $380,000 after 12 years? a. 6%. b. 7%. c. 8%. d. 9%.

84.

Ethan Ethan has $80,0 $80,000 00 to invest invest today today at an annu annual al interes interestt rate of 4%. 4%. Approx Approxima imatel tely y how many years will it take before the investment grows to $162,000? a. 18 years. b. 20 years. c. 16 years. d. 11 years.

85.

Jane Jane wants wants to set aside aside funds funds to take take an around around the worl world d cruise cruise in four four years. years. Assumi Assuming ng that Jane has $8,000 to invest today in an account expected to earn 6% per annum, how much will she have to spend on her vacation? a. $6,336. b. $10,100. c. $34,997. d. $10,706.

86. 86.

Jane Jane want wants s to set set aside aside funds funds to take an aroun around d the world world cruis cruise e in four four year years. s. Jane Jane expects expects that she will need $10,000 for her dream vacation. vacation. If she is able to earn 8% per annum on an investment, how much will she have to set aside today so that she will have sufficient funds available? a. $2,219. b. $13,604. c. $7,350. d. $6,806.

87. 87.

What What would ould you pay pay for for an inve invest stme ment nt that that pays pays you $3,0 $3,000 00,0 ,000 00 afte afterr fort forty y year years? s? Assume that the relevant interest rate for this type of investment investment is 6%. a. $93,540. b. $935,400. c. $291,660. d. $311,010.

88.

What What would would you you pay for for an invest investmen mentt that pays pays you you $20,00 $20,000 0 at the end end of each each year year for for the next ten years and then returns a maturity value of $300,000 after ten years? Assume that the relevant interest rate for this type of investment is 8%. a. $138,958. b. $134,202. c. $144,936. d. $273,158.


6 - 19

89.

Anna Anna has $30,00 $30,000 0 to invest invest.. She requi requires res $50,0 $50,000 00 for for a down paym payment ent for for a house. house. If she she is able to invest invest at 6%, how many years will it be before she will accumulate the desired balance? a. 6 years. b. 7 years. c. 8 years. d. 9 years.

90.

Lucy and and Fred Fred want want to begin begin saving saving for their their baby's baby's college college education education.. They estimate estimate that that they will need $200,000 in eighteen years. If they are able to earn 6% per annum, how much must be deposited at the beginning of each of the next eighteen years to fund the education? a. $6,471. b. $6,105. c. $11,111. d. $5,924.

91.

Lucy and and Fred Fred want want to begin begin saving saving for their their baby's baby's college college education education.. They estimate estimate that that they will need $300,000 in eighteen years. If they are able to earn 5% per annum, how much must be deposited at the end of each of the next eighteen years to fund the education? a. $11,618. b. $25,664. c. $24,823. d. $10,664.

92. 92.

Jane Jane want wants s to set set aside aside funds funds to take take an arou around nd the worl world d crui cruise se in four four years. years. Jane Jane expects expects that she will need $10,000 for her dream vacation. vacation. If she is able to earn 8% per annum on an investment, how much will she need to set aside at the beginning of each year to accumulate sufficient funds? a. $2,219. b. $13,604. c. $7,350. d. $2,055.

93. 93.

Pear Pearso son n Corp Corpor orat atio ion n make makes s an inve invest stme ment nt today today (Janu (January ary 1, 2012 2012). ). They They will will rece receiv ive e $6,000 every December 31st for the next six years (2012 – 2017). If Pearson wants to earn 12% on the investment, what is the most they should invest on January 1, 2012? a. $24,668. b. $27,629. c. $48,691. d. $54,534.

94. 94.

Garr Garret etso son n Corp Corpor orat atio ion n will will receiv receive e $8,0 $8,000 00 today today (Jan (Janua uary ry 1, 2012 2012), ), and also also on each each January 1st for the next five years (2013 – 2017). What is the present value of the six $8,000 receipts, assuming a 12% interest rate? a. $32,891. b. $36,838. c. $64,922. d. $72,712.

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95.

Spencer Spencer Corporati Corporation on will will invest invest $15,000 $15,000 every December December 31st 31st for the the next next six six years years (2012 (2012 – 2017). If Spencer will earn 12% on the investment, what amount will be in the investment fund on December 31, 2017? a. $61,671. b. $69,072. c. $121,728. d. $136,335.

96.

Tipson Tipson Corp Corporat oration ion will will invest invest $15,0 $15,000 00 every every Januar January y 1st for for the next next six years years (2012 (2012 – 2017). If Linton will earn 12% on the investment, what amount will be in the investment fund on December 31, 2017? a. $61,671 b. $69,072. c. $121,728. d. $136,335.

97. 97.

Hill Hiller er Corp Corpor orat atio ion n make makes s an invest investme ment nt today today (Jan (Janua uary ry 1, 2012 2012). ). They will will rece receiv ive e $40,000 every December 31st for the next six years (2012 – 2017). If Hiller wants to earn 12% on the investment, what is the most they should invest on January 1, 2012? a. $164,456. b. $184,191. c. $324,608. d. $363,560.

98. 98.

Sona Sonata ta Corpo Corporat ratio ion n will will receiv receive e $20, $20,00 000 0 toda today y (Jan (Janua uary ry 1, 2012 2012), ), and also also on each each January 1st for the next five years (2013 – 2017). What is the present value of the six $40,000 receipts, assuming a 12% interest rate? a. $164,456. b. $184,191. c. $324,608. d. $363,560.

99.

Renfro Renfro Corporati Corporation on will will invest invest $50,000 $50,000 every December December 31st 31st for for the the next next six years (2012 – 2017). If Renfro will earn 12% on the investment, what amount will be in the investment fund on December 31, 2017? a. $205,570 b. $230,240. c. $405,760. d. $454,450.

100. 100.

Vannoy Vannoy Corpo Corporat ration ion will will invest invest $30,00 $30,000 0 every Janu January ary 1st 1st for the next next six years years (2012 (2012 – 2017). If Wagner will earn 12% on the investment, what amount will be in the investment fund on December 31, 2017? a. $123,342. b. $138,144. c. $243,456. d. $272,670.

Accounting and the Time Value of Money 101. 101.

6 - 21

On Januar January y 1, 2012, 2012, Kline Kline Compa Company ny decid decided ed to begi begin n accu accumu mula lati ting ng a fund fund for asset asset replacement five years later. The company plans to make five annual deposits of $40,000 at 9% each January 1 beginning in 2012. What will be the balance in the fund, within $10, on January 1, 2017 (one year after the last deposit)? The following 9% interest factors may be used. Present Value of Future Value of Ordinary An Annuity Ordinary An Annuity 4 periods 3.2397 4.5731 5 periods 3.8897 5.9847 6 periods 4.4859 7.5233 a. b. c. d.

$260,932 $239,388 $218,000 $200,000

Use the following 8% interest factors for questions 102 through 105.

7 periods 8 periods 9 periods

Present Value of Ordinary An Annuity 5.2064 5.7466 6.2469

Future Value of Ordinary An Annuity 8.92280 10.63663 12.48756

102.

What will be the the balance balance on Septembe Septemberr 1, 2018 in a fund which which is accumulate accumulated d by making making $10,000 annual deposits each September 1 beginning in 2011, with the last deposit being made on September 1, 2018? The fund pays interest at 8% compounded annually. a. $106,366 b. $89,229 c. $75,600 d. $57,466

103. 103.

If $6,000 $6,000 is deposi deposited ted annual annually ly starti starting ng on January January 1, 2012 2012 and it earns earns 8%, what what will will the balance be on December 31, 2019? a. $53,537 b. $57,820 c. $63,820 d. $68,925

104. 104.

Korm Korman an Compa Company ny wishe wishes s to accum accumul ulat ate e $400 $400,0 ,000 00 by May May 1, 2020 2020 by making making 8 equa equall annual annual deposi deposits ts beginn beginning ing May 1, 2012 2012 to a fund fund paying paying 8% intere interest st compou compounde nded d annually. What is the required amount of each deposit? a. $69,606 b. $37,606 c. $34,820 d. $40,312

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105. 105.

What What amoun amountt should should be record recorded ed as the cost cost of a machin machine e purc purcha hase sed d Decemb December er 31, 2012, which is to be financed by making 8 annual payments of $8,000 each beginning December 31, 2013? The applicable interest rate is 8%. a. $56,000 b. $49,975 c. $85,093 d. $45,973

106. 106.

How How much much must must be depos deposit ited ed on Janu Januar ary y 1, 2012 2012 in a savi saving ngs s acco accoun untt pay paying ing 6% annually in order to make annual withdrawals of $25,000 at the end of the years 2012 and 2013? The present value of one at 6% for one period is .9434. a. $45,835 b. $47,175 c. $50,000 d. $22,250

107. 107.

How much much must must be inves invested ted now now to receiv receive e $20,000 $20,000 for for 15 years years if the firs firstt $20,000 $20,000 is received today and the rate is 9%? Present Value of Periods Ordinary Annuity at 9% 14 7.78615 15 8.06069 16 8.31256 a. $161,214 b. $175,723 c. $300,000 d. $146,250

108. 108.

Jenks Jenks Compa Company ny financ financed ed the purch purchase ase of a machin machine e by making making paymen payments ts of $10,00 $10,000 0 at the end of each of five years. The appropriate rate of interest was 8%. The future value of one for five periods at 8% is 1.46933. The future value of an ordinary annuity for five periods at 8% is 5.8666. The present value of an ordinary annuity for five periods at 8% is 3.99271. What was the cost of the machine to Jenks? a. $14,794 b. $39,927 c. $50,000 d. $58,667

109. 109.

A machine machine is purc purchas hased ed by makin making g payment payments s of $6,000 $6,000 at the the begin beginning ning of of each each of the next five years. The interest rate was 10%. The future value of an ordinary annuity of 1 for five periods is 6.10510. The present value of an ordinary annuity of 1 for five periods is 3.79079. What was the cost of the machine? a. $40,294 b. $36,631 c. $25,019 d. $22,745


6 - 23

110. 110.

Lane Lane Co. has has a mach machin ine e that cost cost $300, $300,00 000. 0. It is to be leased leased for 20 year years s with with rent received at the beginning of each year. Lane wants a return of 10%. Calculate the amount of the annual rent. Present Value of Period Ordinary Annuity 19 8.36492 20 8.51356 21 8.64869 a. $32,034 b. $35,864 c. $44,592 d. $35,238

111. 111.

Find Find the presen presentt value value of an invest investmen mentt in plant plant and equipm equipment ent if it is expe expecte cted d to provide provide annual earnings of $26,000 for 15 years and to have a resale value of $50,000 at the end of that period. Assume a 10% rate and earnings at year end. The present value of 1 at 10% for 15 periods is .23939. The present value of an ordinary annuity at 10% for 15 periods is 7.60608. The future value of 1 at 10% for 15 periods is 4.17725. a. $197,758 b. $209,728 c. $247,758 d. $401,970

112. 112.

On January January 2, 2012, 2012, Wine Wine Corpor Corporati ation on wishes wishes to issue issue $3,00 $3,000,0 0,000 00 (par value value)) of its 8%, 10-year bonds. The bonds pay interest annually on January 1. The current yield rate on such bonds is 10%. Using the interest factors below, compute the amount that Wine will realize from the sale (issuance) of the bonds. Present value of 1 at 8% for 10 periods Present value of 1 at 10% for 10 periods Pres Presen entt val value ue of an ordi ordina nary ry annu annuit ity y at at 8% 8% for for 10 peri period ods s Pres Presen entt val value ue of of an an ordi ordina nary ry ann annui uity ty at at 10% 10% for for 10 peri period ods s a. b. c. d.

113. 113.

0.4632 0.3855 6.71 6.7101 01 6.14 6.1446 46

$3,000,000 $2,631,204 $3,000,018 $3,318,078

The marke markett price price of a $500,0 $500,000, 00, ten-y ten-year, ear, 12% 12% (pays (pays interest interest semia semiannu nnuall ally) y) bond issue issue sold to yield an effective rate of 10% is a. $561,445. b. $562,311. c. $566,635. d. $936,180.

6 - 24


114. 114.

John John won a lotter lottery y that that will will pay him him $150,00 $150,000 0 at the end end of each each of the next next twent twenty y years. years. Assuming an appropriate interest rate is 8% compounded annually, what is the present value of this amount? a. $1,5 $1,590 90,,540. 540. b. $32,183. c. $1,472,723. d. $6,8 $6,864 64,,294. 294.

115.

Jonas won a lotter lottery y that will will pay him $200,000 $200,000 at the the end of each each of the the next next twenty twenty years. years. Zebra Finance has offered to purchase the payment stream for $2,718,000. What interest rate (to the nearest percent) was used to determine the amount of the payment? a. 7%. b. 6%. c. 5%. d. 4%.

116. 116.

Jame James s leases leases a ski ski chalet chalet to his best best friend friend,, Jane Janet. t. The leas lease e term term is five five years years with $16,000 annual payments due at the beginning of each year. What is the present value of the payments discounted at 8% per annum? a. $68,994. b. $63,884. c. $61,077. d. $57,990.

117.

Jeremy is in the process process of purchasi purchasing ng a car. car. The The list list price price of the car car is $36,000. $36,000. If Jeremy Jeremy pays cash for the car, the dealer will reduce the price by 10%. Otherwise, Otherwise, the dealer will provide financing where Jeremy must pay $7,706 at the end of each of the next five years. Compute the effective interest rate to the nearest percent that Jeremy would pay if he chooses to make the five annual payments? a. 5%. b. 6%. c. 7%. d. 8%.

118. 118.

What What would would you you pay for for an invest investmen mentt that pays pays you you $15,00 $15,000 0 at the end end of each each year year for for the next twenty years? Assume that the relevant interest rate for this type of investment is 12%. a. $125,487. b. $1,0 $1,080 80,,786. 786. c. $15,550. d. $112,042.

119. 119.

What What would would you pay pay for an inves investme tment nt that that pays pays you $20,00 $20,000 0 at the begin beginnin ning g of each year year for the next next ten years? years? Assume Assume that the releva relevant nt interest interest rate for this type of investment is 10%. a. $122,890. b. $135,180. c. $129,902. d. $142,892.


6 - 25

120. 120.

Zigg Ziggy y is cons consid ider erin ing g purc purcha hasi sing ng a new new car. car. The cash cash purc purcha hase se pric price e for for the the car car is $33,600. What is the annual interest rate if Ziggy is required to make annual payments of $7,800 at the end of the next five years? a. 4%. b. 5%. c. 6%. d. 7%.

121.

Charlie Charlie Corp. Corp. is purchasing purchasing new new equipme equipment nt with with a cash cost of $200,000 $200,000 for the the assembly assembly line. The manufacturer has offered to accept $45,920 payments at the end of each of the next six years. What is the interest rate that Charlie Corp. will be paying? a. 8%. b. 9%. c. 10%. d. 11%.

122. 122.

Jere Jeremy my Leasin Leasing g purc purcha hase ses s and and then then leas leases es small small airc aircra raft ft to inte intere rest sted ed partie parties. s. The company is currently determining the required rental for a small aircraft that cost them $600,000. If the lease is for twenty years and annual lease payments are required to be made at the end of each year, what will be the annual rental if Jeremy wants to earn a return of 10%? a. $64,070. b. $70,476. c. $10,476. d. $30,314.

123. 123.

Stech Stech Co. Co. is issuin issuing g $6.5 milli million on 12% bond bonds s in a private private plac placeme ement nt on July July 1, 2012. 2012. Each Each $1,000 bond pays interest semi-annually on December 31 and June 30 of each year. The bonds mature in ten years. At the time of issuance, the market interest rate for similar types of bonds was 8%. What is the expected selling price of the bonds? a. $8,2 $8,266 66,,764. 764. b. $13, $13,56 566, 6,99 992. 2. c. $8,244,598. d. $8,3 $8,310 10,,962. 962.

Multiple Choice Answers— Computational Item

62. 63. 64. 65. 66. 67. 68. 69. 70.

Ans.

a d d c b a b c c

Item

71. 72. 73. 74. 75. 76. 77. 78. 79.

Ans.

d a d b c c b b c

Item

80. 81. 82. 83. 84. 85. 86. 87. 88.

Ans.

d c a c a b c c d

Item

89. 90. 91. 92. 93. 94. 95. 96. 97.

Ans.

Item

Ans.

Item

Ans.

Item

Ans.

d b d d a b c d a

98. 99. 100. 101. 102. 103. 104. 105. 106.

b c d a a d c d a

107. 108. 109. 110. 111. 112. 113. 114. 115.

b b c a b b b c d

116. 117. 118. 119. 120. 121. 122. 123.

a b d b b c b a

6 - 26


MULTIPLE CHOICE—CPA Adapted 124. 124.

On January January 1, 1, 2012, 2012, Gore Co. Co. sold sold to Cey Corp Corp.. $600,00 $600,000 0 of its 10% 10% bonds bonds for for $531,17 $531,177 7 to yield 12%. Interest is payable semiannually on January 1 and July 1. What amount should Gore report as interest expense for the six months ended June 30, 2012? a. $26,559 b. $30,000 c. $31,871 d. $36,000

125. 125.

On May May 1, 2012, 2012, a comp company any purc purchas hased ed a new mach machine ine whic which h it does does not have have to to pay for for until May 1, 2014. The total payment on May 1, 2014 will include both principal and interest. Assuming interest at a 10% rate, the cost of the machine would be the total payment multiplied by what time value of money factor? a. Futu Future re val value ue of of annu annuit ity y of 1 b. Futu Future re valu value e of of 1 c. Pres Presen entt valu value e of ann annui uity ty of of 1 d. Pres Presen entt val value ue of 1

126. 126.

On January January 1, 2012, 2012, Ball Ball Co. exchan exchanged ged equipm equipment ent for for a $200,0 $200,000 00 zero-i zero-inte nteres rest-b t-bear earing ing note due on January 1, 2015. The prevailing rate of interest for a note of this type at January 1, 2012 was 10%. The present value of $1 at 10% for three periods is 0.75. What amount of interest revenue should be included in Abel's 2013 income statement? a. $0 b. $15,000 c. $16,500 d. $20,000

127. 127.

For whic which h of the follow following ing transa transacti ctions ons would would the the use of the prese present nt value value of an ordina ordinary ry annuity concept be appropriate in calculating the present value of the asset obtained or the liability owed at the date of incurrence? a. A capi capita tall leas lease e is ente entere red d into into with ith the the init initia iall leas lease e paym paymen entt due due one one mont month h subsequent to the signing of the lease agreement. b. A capital capital lease lease is entered entered into into with the initia initiall lease paymen paymentt due upon the signing signing of the lease agreement. c. A ten-year ten-year 8% bond is issued issued on January January 2 with with interes interestt payable payable semiann semiannual ually ly on January 2 and July 1 yielding 7%. d. A ten-year ten-year 8% bond is issued issued on January January 2 with with interes interestt payable payable semiann semiannual ually ly on January 2 and July 1 yielding 9%.

Accounting and the Time Value of Money 128. 128.

6 - 27

On January January 15, 15, 2012, 2012, Dolan Dolan Corp. Corp. adopt adopted ed a plan to accum accumula ulate te funds funds for for environm environment ental al improvements beginning July 1, 2016, at an estimated cost of $5,000,000. Dolan plans to make four equal annual deposits in a fund that will earn interest at 10% compounded annually. The first deposit was made on July 1, 2012. Future value factors are as follows: Future value of 1 at 10% for 5 periods Future value of ordinary annuity of 1 at 10% for 4 periods Future value of annuity due of 1 at 10% for 4 periods

1.61 4.64 5.11

Dolan should make four annual deposits of a. $889,522. b. $978,474. c. $1,077,586. d. $1,2 $1,250 50,,000. 000. 129. 129.

On Decemb December er 30, 2012, 2012, AGH, AGH, Inc. Inc. purcha purchased sed a machin machine e from Grant Grant Corp. Corp. in excha exchange nge for a zero-interest-bearing note requiring eight payments of $70,000. The first payment was made on December December 30, 2012, and the others are due annually annually on December December 30. At date of issuance, the prevailing rate of interest for this type of note was 11%. Present value factors are as follows: Present Value of Ordinary Present Value of Period Annuity of 1 at 11% Annuity Due of 1 at 11% 7 4.712 5.231 8 5.146 5.712 On AGH's December 31, 2012 balance sheet, the net note payable to Grant is a. $329,840. b. $360,220. c. $366,485. d. $399,840.

130. 130.

On January January 1, 2012, 2012, Ott Ott Co. sold sold goods goods to Flynn Flynn Company Company.. Flynn Flynn signed signed a zero-int zero-intere ereststbearing note requiring payment of $90,000 annually for seven years. The first payment was made on January 1, 2012. The prevailing rate of interest for this type of note at date of issuance was 10%. Information on present value factors is as follows: Period 6 7

Present Value of 1 at 10% .5645 .5132

Ott should record sales revenue in January 2012 of a. $481,972. b. $438,156. c. $391,977. d. $321,300.

Present Value of Ordinary Annuity of 1 at 10% 4.3553 4.8684

6 - 28


131. 131.

On Januar January y 1, 2012, 2012, Haley Haley Co. issu issued ed ten-ye ten-year ar bonds bonds with with a face amount amount of $3,0 $3,000, 00,000 000 and a stated interest rate of 8% payable annually on January 1. The bonds were priced to yield 10%. Present value factors are as follows: At 8% At 10% Present value of 1 for 10 periods 0.463 0.386 Present value of an ordinary annuity of 1 for 10 periods 6.710 6.145 The total issue price of the bonds was a. $3,0 $3,000 00,,000. 000. b. $2,9 $2,940 40,,000. 000. c. $2,760,000. d. $2,6 $2,632 32,,800. 800.

132. 132.

On July July 1, 2012, 2012, Ed Wynn Wynne e signed signed an agree agreeme ment nt to opera operate te as a fran franch chis isee ee of Kwik Kwik Foods, Inc., for an initial franchise fee of $240,000. Of this amount, $80,000 was paid when when the the agre agreem emen entt was sign signed ed and and the the bala balanc nce e is payabl payable e in four four equa equall annu annual al payments of $40,000 beginning July 1, 2013. The agreement provides that the down payment is not refundable and no future services are required of the franchisor. Wynne's credit rating indicates that he can borrow money at 14% for a loan of this type. Information on present and future value factors is as follows: Present value of 1 at 14% for 4 periods Future value of 1 at 14% for 4 periods Present va value of of an ord ordiinary annuity of of 1 at at 14% for 4 perio riods Wynne should record the acquisition cost of the franchise on July 1, 2012 at a. $174,400. b. $196,400. c. $240,000. d. $270,400.

Multiple Choice Answers— CPA Adapted Item

Ans.

Item

Ans.

Item

Ans.

Item

Ans.

Item

Ans.

124. 125.

c d

126. 127.

c a

128. 129.

b a

130. 131.

a d

132.

b

DERIVATIONS — Computational No.

Answer

Derivation

62.

a

$50,000 × 1.34392 = $67,196.

63.

d

($34,440 × 6) − $150,000 = $56,640.

64.

d

4 × 8 = 32 periods; 4% ÷ 4 = 1%.

65.

c

1.260 × PV = $10,000; PV = $10,000 ÷ 1.260.

66.

b

1.260 × $3,000.

0.59 1.69 2.91


No.

Answer

Derivation

67.

a

($6,000 × 1.260) + ($6,000 × 1.166) + ($6,000 × 1.080) + $6,000.

68.

b

$4,000 × (1.080)6 or $4,000 × 1.469 × 1.080.

69.

c

0.826 × PV = $4,000; PV = $4,000 ÷ 0.826.

70.

c

$6,000 × 0.621 × 0.909.

71.

d

$3,000 × 0.751.

72.

a

$5,000 + ($5,000 × 0.909) + ($5,000 × 0.826) + ($5,000 × 0.751).

73.

d

$10,000 × (1.06)2 = $11,236.

74.

b

$250,000 × 0.51316 = $128,290.

75.

c

$102,632 ÷ $200,000 = 0.51316; 0,51316 is PV factor for 7 years.

76.

c

$400,000 × 1.33823 = $535,292.

77.

b

$800,000 × 0.51316 = $410,528.

78.

b

$189,051 ÷ $300,000 = 0.63017; 0.63017 is PV factor for 6 years.

79.

c

$500,000 × 1.33823 = $669,115.

80.

d

$2,000,000 × .37689 = $753,780.

81.

c

$100,000 × 1.62890 = $162,890.

82.

a

$120,000 × .79209 = $95,051.

83.

c

$150,000 ÷ $380,000 = .39474; .39474 is PV factor for 8%.

84.

a

$162,000 ÷ $80,000 = 2.025; 2.025 is FV factor for 18 years.

85.

b

$8,000 × 1.26248 = $10,100.

86.

c

$10,000 × .73503 = $7,350.

87.

c

$3,000,000 × .09722 = $291,660.

88.

d

($20,000 × 6.71008) + ($300,000 × .46319) = $273,158.

89.

d

$50,000 ÷ $30,000 = 1.66667; 1.66667 is FV factor for 9 years.

90.

b

$200,000 ÷ (30.90565 × 1.06) = $6,105.

91.

d

$300,000 ÷ 28.13279 = $10,664.

6 - 29

6 - 30

No.


Answer

Derivation

92.

d

$10,000 ÷ (4.50611 × 1.08) = $2,055.

93.

a

$6,000 × 4.11141 = $24,668.

94.

b

$8,000 × 4.60478 = $36,838.

95.

c

$15,000 × 8.11519 = $121,728.

96.

d

$15,000 × 8.11519 × 1.12 = $136,335.

97.

a

$40,000 × 4.11141 = $164,456.

98.

b

$40,000 × 4.60478 = $184,191.

99.

c

$50,000 × 8.11519 = $405,760.

100.

d

$30,000 × 8.11519 × 1.12 = $272,670.

101. 101.

a

$40, $40,00 000 0 × (7.5 (7.523 233 3 – 1) = $260 $260,9 ,932 32 or $40, $40,00 000 0 × 5.98 5.9847 47 × 1.09 1.09..

102.

a

$10,000 × 10.63663 = $106,366.

103.

d

$6,000 × (12.48756 – 1) = $68,925 or $6,000 × 10.63663 × 1.08.

104.

c

(10.63663 × 1.08) × R = $400,000; R = $400,000 ÷ 11.48756 = $34,820.

105.

d

$8,000 × 5.7466 = $45,973.

106.

a

($25,000 × 0.9434) + [$25,000 × (0.9434)2] = $45,835.

107.

b

$20,000 × (7.78615 + 1) = $175,723 or $20,000 × 8.06069 × 1.09.

108.

b

$10,000 × 3.99271 = $39,927.

109.

c

$6,000 × (3.79079 × 1.10) = $6,000 × 4.16987 = $25,019.

110.

a

$300,000 = R × (8.51356 × 1.10); R = $300,000 ÷ 9.36492 = $32,034.

111.

b

($26,000 × 7.60608) + ($50,000 × .23939) = $209,728.

112.

b

$3,000,000 × .08 = $240,000 (annual interest payment) ($240,000 × 6.1446) + ($3,000,000 × 0.3855) = $2,631,204.

113.

b

$500,000 × .06 = $30,000 (semiannual interest payment) ($30,000 × 12.46221) + ($500,000 × .37689) = $562,311.

114.

c

$150,000 × 9.81815 = $1,472,723.

115.

d

$2,718,000 ÷ $200,000 = 13.59; 13.59 is PV factor for 4%.


No.

Answer

116.

a

$16,000 × 4.31214 = $68,994.

117.

b

($36,000 × .90) ÷ $7,706 = 4.20438, 4.20438 is PV factor for 6%.

118.

d

$15,000 × 7.46944 = $112,042.

119.

b

$20,000 × 6.75902 = $135,180.

120.

b

$33,600 ÷ $7,800 = 4.30769; 4.30769 is PV factor for 5%.

121.

c

$200,000 ÷ $45,920 = 4.35540; 4.35540 is PV factor for 10%.

122.

b

$600,000 ÷ 8.51356 = $70,476.

123.

a

($6,500,000 × .45639) + ($390,000 × 13.59033) = $8,266,764.

6 - 31

Derivation

DERIVATIONS — CPA Adapted No.

Answer

Derivation

124.

c

$531,177 × .06 = $31,871.

125.

d

Conceptual.

126.

c

$200,000 × .75 = $150,000 (present value of note) $150,000 × 1.10 = $165,000; $165,000 × 0.10 = $16,500.

127.

a

Conceptual.

128.

b

5.11 × R = $5,000,000; R = $5,000,000 ÷ 5.11 = $978,474.

129.

a

$70,000 × 4.712 = $329,840 or ($70,000 × 5.712) – $70,000 = $329,840.

130.

a

$90,000 × (4.8684 × 1.1) = $481,972.

131.

d

$3,000,000 × .08 = $240,000 ($240,000 × 6.145) + ($3,000,000 × 0.386) = $2,632,800.

132.

b

($40,000 × 2.91) + $80,000 = $196,400.

6 - 32


EXERCISES Ex. 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 _____ 1.

Diagram of Concept

Future value of 1.

? a.

_____ 2. _____ 3.

|

|

|

|

|

$1

$1

? $1

|- - - - |

|

|

|

? $1

$1

$1

$1

|

|

|

|- - - - |

?

$1

$1

$1

$1

|

|

|

|

|

Present value of 1. Future value of an annuity

$1

due of 1. _____ 4.

$1

b.

Future value of an ordinary annuity of 1.

_____ 5.

Present value of an ordinary annuity of 1.

_____ 6.

Present value of an annuity

c.

due of 1.

d.

$1 e.

f.

?

|

|

|

|

|

$1

$1

$1

$1

?

|

|

|

|

|

Solution 6-133

1. e

2. a

3. f

4. b

5. d

6. c

needed.) Ex. 6-134—Compute estimated goodwill. (Tables needed.) Compute estimated goodwill if it is found by discounting excess earnings at 12% compounded quarterly. Excess annual earnings of $16,000 are expected for 8 years. Solution 6-134

Present value of $4,000 for 32 periods at 3% ($4,000 × 20.38877) = $81,555.


6 - 33

Ex. 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 $20,000 for 10 years and to have a resale value of $50,000 at the end of that period. Assume an interest rate of 9% and that savings are realized at year end. Solution 6-135

Present value of $20,000 for 10 periods at 9% (6.41766 × $20,000) = $128,353 Present value of $50,000 discounted for 10 periods at 9% (.42241 × $50,000) = 21,121 Present value of investment in equipment $149,474 annuity due. (Tables needed.) Ex. 6-136—Future value of an annuity If $6,000 is deposited annually starting on January 1, 2012 and it earns 9%, how much will accumulate by December 31, 2021? Solution 6-136

Future value of an annuity due of $6,000 for 10 periods at 9% ($6,000 × 15.19293 × 1.09) = $99,362. Ex. 6-137—Present value of an annuity due.(Tables needed.)

How much must be invested now to receive $25,000 for ten years if the first $25,000 is received today and the rate is 8%? Solution 6-137

Present value of an annuity due of $25,000 for ten periods at 8% ($25,000 × 7.24689) = $181,172. Ex. 6-138—Compute the annual rent. (Tables needed.)

Crone Co. has machinery that cost $90,000. 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. Solution 6-138

Present value factor for an annuity due for 15 periods at 10% (1.10 × 7.60608) = 8.36669 $90,000 ÷ 8.36669 = $10,757. Ex. 6-139—Calculate market price of a bond. (Tables needed.)

Determine the market price of a $300,000, ten-year, 10% (pays interest semiannually) bond issue sold to yield an effective rate of 12%.

6 - 34


Solution 6-139

Present value of $15,000 for 20 periods at 6% ($15,000 × 11.46992) = Present Present value of $300,000 $300,000 discounted discounted for 20 periods periods at 6% ($300,000 ($300,000 × .31180) .31180) = Market price of the bond issue

$172,049 93,540 $265,589

Ex. 6-140—Calculate market price of a bond.

On January 1, 2012 Lance Co. issued five-year bonds with a face value of $500,000 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. Solution 6-140

Present Present value value of $500,000 $500,000 discounted discounted for 10 periods periods at 5% 5% ($500,00 ($500,000 0 × .61391) .61391) = Present value of $30,000 for 10 periods at 5% ($30,000 × 7.72173) = Issue price of the bonds

$306,955 $306,955 231,652 $538,607

PROBLEMS Pr. 6-141—Present value and future value computations.

Part Part (a) (a) Comp Comput ute e the the amou amount nt that that a $30, $30,00 000 0 inve invest stme ment nt toda today y would ould accu accumu mula late te at 10% 10% (compound interest) by the end of 6 years. Part (b) Tom wants wants to retire at the the end of this year year (2012). His His life expecta expectancy ncy is 20 years years from his retirement. Tom has come to you, his CPA, to learn how much he should deposit on December 31, 2012 to be able to withdraw $50,000 at the end of each year for the next 20 years, assuming the amount on deposit will earn 8% interest annually. Part Part (c) (c) Judy Judy Thom Thomas as has a $1,8 $1,800 00 overd overdue ue debt debt for for medi medica call book books s and and supp supplilies es at Joe' Joe's s Bookstore. She has only $600 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 $600 now and and $1,500 $1,500 when she complete completes s her residency residency,, two years years from today. today. 2. Pay $2,400 $2,400 one year year after after completion completion of residency, residency, three three years years from from today. today. Assuming that the cost of money is the only factor 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.


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Solution 6-141

Part (a) (a) Future value of $30,000 $30,000 compoun compounded ded @ 10% 10% for 6 years years ($30,000 × 1.77156) = $53,147. Part (b) Present Present value of a $50,000 $50,000 ordinary ordinary annuity annuity discounte discounted d @ 8% for 20 years years ($50,000 × 9.81815) = $490,908. Part Part (c) (c) Alte Altern rnat ativ ive e1 Present value of $1,500 discounted @ 8% for 2 years ($1,500 × .85734) = Present value of $1,500 now = Present value of $600 now = Present value of Alternative 1

$1,286 600 $1,886

Alternative 2 Pres Presen entt val value ue of $2,4 $2,400 00 disc discou ount nted ed @ 8% 8% for for 3 yea years rs ($2, ($2,40 400 0 × .793 .79383 83))

$1,9 $1,905 05

On the present value basis, Alternative 1 is preferable. Pr. 6-142—Annuity with change in interest rate.

Jan Green established a savings account for her son's college education by making annual deposits deposits of $8,000 at the beginning beginning of each of six years to a savings account account paying 8%. At the end of the sixth year, the account balance was transferred to a bank paying 10%, and annual deposits of $8,000 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? Solution 6-142

Years Years 1-6: 1-6:

Future Future value value of of annuity annuity due due of $8,00 $8,000 0 for 6 perio periods ds at 8%: 8%: (7.33592 × 1.08) × $8,000 = $63,382

Years 7-10: 7-10: Future value of of $63,382 $63,382 for 4 periods periods at 10%: 1.4641 × $63,382 = $92,798 Future value of ordinary annuity of $8,000 for 4 periods at 10%: 4.6410 × $8,000 = $37,128 Sum in bank at end of tenth year: $37,128 + $92,798 = $129,926 Pr. 6-143—Present value of an ordinary annuity due.

Jill Morris is presently leasing a small business computer from Eller Office Equipment Company. The lease requires 10 annual payments of $8,000 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: Future Value of 1 Present Value of 1 Future Value of Ordinary Annuity of 1 Present Value of Ordinary Annuity of 1 Present Value of Annuity Due of 1

9 Periods 1.99900 .50025 12.48756 6.24689 6.74664

10 Periods 2.15892 .46319 14.48656 6.71008 7.24689

11 Periods 2.33164 .42888 16.64549 7.13896 7.71008

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Pr. 6-143 (cont.) Instructions (a) Assuming Assuming the computer computer has a ten-yea ten-yearr life and will have have no salvage salvage value at the expirat expiration ion of the lease, what was the original cost of the computer to Eller?

(b) What What amount amount would would each payment payment be if the ten annual annual paymen payments ts are to be made at the beginning of each period? Solution 6-143

(a) Present Present value value of an ordinary ordinary annuity annuity of $8,000 at 8% for 10 years is is 6.71008 × $8,000 = (b) Present Present value value factor factor for an annuity annuity due of $8,000 $8,000 at 8% for 10 years years is 7.24689; $53,681 ÷ 7.24689 =

$53,681 $7,407

Pr. 6-144—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. pa yments. Instructions Calculate the implied interest rate for the lease payments.

Lease A — Lease A covers office equipment which could be purchased for $108,144. Bates Company has, however, chosen to lease the equipment for $30,000 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 $114,978. Bates Company has chosen to lease the machine for $24,000 per year on a 6-year lease. Payments are due at the start of each year. Solution 6-144

Lease A — Calculation of the Implied Interest Rate: $30,000 × (factor for Present Value of Ordinary Annuity for 5 yrs.) = $108,144 Factor for Present Value of Ordinary Annuity for 5 yrs. = $108,144 ÷ $30,000 = 3.6048 The 3.6048 factor implies a 12% interest rate. Lease B — Calculation of the Implied Interest Rate: $24,000 × (factor for Present Value of Annuity Due for 6 yrs.) = $114,978 Factor for Present Value of Annuity Due Due for 6 yrs. = $114,978 ÷ $24,000 = 4.79075 The 4.79075 factor implies a 10% interest rate (present value of an annuity due table).


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Pr. 6-145—Calculation of unknown rent and interest.

Pine Leasing Company Company purchased purchased specialized specialized equipment equipment from Wayne Company on December December 31, 2011 for $600,000. 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, 2012 and are made every 6 months until July 1, 2016. Pine Leasing wants to earn 10% annually on its investment. Various Factors at 10% Periods or Rents 9 10 11

Periods or Rents 9 10 11

Future Value of $1 2.35795 2.59374 2.85312

Present Value of $1 .42410 .38554 .35049

Future Value of an Ordinary Annuity 13.57948 15.93743 18.53117

Present Value of an Ordinary Annuity 5.75902 6.14457 6.49506

Future Value of $1 1.55133 1.62889 1.71034

Various Factors at 5% Present Future Value of an Value of $1 Ordinary Annuity .64461 11.02656 .61391 12.57789 .58468 14.20679

Present Value of an Ordinary Annuity 7.10782 7.72173 8.30641

Instructions (a) Calculate Calculate the amount amount of of each rent. rent. (b) How much interes interestt revenue will will Pine earn in in 2012?

Solution 6-145

(a) Calculation Calculation of rent: rent: 7.72173 7.72173 × 1.05 = 8.10782 (present value of a 10-rent annuity due at 5%.) $600,000 ÷ 8.10782 = $74,003. (b) Interest Interest Revenue Revenue during 2012: Rent No. 1 2 None

Cash Received $74,003 74,003 None

Date 1/1/12 7/1/12 12/31/12 Total

Interest Revenue $ -026,300 23,915 (Accrual) $50,215

Lease Receivable $525,997 478,294

Pr. 6-146—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 potential buyers: Buyer Buyer A, who is willing willing to pay $480,000 for the land now, and Buyer B, who is willing to make 20 annual payments of $75,000 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.

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Solution 6-146

Buyer Buyer A. The present present value value of the the purchase purchase price price is $480,00 $480,000. 0. Buyer Buyer B. The present present value of the purchase purchase price price is: is: Present value of ordinary annuity of $75,000 for 24 periods at 9% Less Less pres present ent value value of ordina ordinary ry annuit annuity y of $75,00 $75,000 0 for for 4 peri periods ods (defer (deferred red)) at at 9% Difference Multiplied by annual payments Present value of payments Conclusion: Carey should sell to Buyer B.

9.70661 3.2397 3.23972 2 6.46689 × $75,000 $485,017


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IFRS QUESTIONS True / False

1. IFRS does not not intend to issue issue detailed guidance guidance on the selection selection of a discount discount rate when the time value of money is required to determine cash flows. 2. Under IAS 37 and the establishment establishment of estimate estimate provisions, provisions, discounting discounting is required where where the time value of money is material. 3. Under Under IFRS, the rate implici implicitt in the lease lease is general generally ly used to discou discount nt minimum minimum lease payments. 4. Under IFRS, IFRS, the discount discount rate should reflect reflect risks for which which future cash flow estimates estimates have been adjusted. 5. Under Under IFRS, if an estima estimate te is being being develope developed d for a large large number number of items with with varied varied outcomes, then the expected value method is used. Answers to True / False questions: 1. True 2. True 3. True 4. False 5. True

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Multiple Choice Questions:

1.

Underwood Underwood Company Company maintains maintains its accounting accounting records records using using IFRS. IFRS. The company company recently recently signed a lease for a new office building, for a lease period of 10 years. Under the lease agreement, agreement, a security security deposit of $20,000 is made, with the deposit to be returned at the expiration of the lease, with interest compounded at 10% per year. What amount will the company receive at the time the lease expires? a. b. c. d.

$51,875. $40,000. $122,892. $27,711.

Calculation: Future value of $20,000 @ 10% for 10 years ($20,000 × 2.59374) = $51,875 Use the following information to answer questions 2 & 3. Martin Martin Indust Industrie ries s mainta maintains ins its accoun accountin ting g record records s using using IFRS. IFRS. The compan company y purcha purchases ses equipment with a price of $300,000. The manufacturer has offered a payment plan that would allow Martin to make 10 equal annual payments of $36,987, with the first payment due one year after the purchase. 2.

How much much total total inte interes restt will will Mart Martin in pay pay on on this this paym payment ent plan plan? ? a. b. c. d.

$69,870 $36,987 $120,000 $30,000

Calculation: Total interest = Total payments—amount owed today $369,870 (10 × $36,987) − $300,000 = $69,870. 3.

Martin Martin could could borrow borrow $300 $300,00 ,000 0 from its its bank to to finance finance the the purchas purchase e at an annual annual rate rate of 6%. Should Martin borrow from the bank or use the manufactur manufacturer's er's payment payment plan to pay for the equipment? a. Borr Borrow ow from from the the ban bank. k. b. Use Use the manu manufac factur turer' er's s paymen paymentt plan. plan. c. The The rate rates s for for both both the bank bank and and manu manufa fact ctur urer er are the same, same, so Mart Martin in would would be indifferent. d. There is not not enough enough informat information ion to to answer answer this this question question..

Calculation: Martin should use the manufacturer's payment plan, since it is about a 4% rate as compared to the bank's 6% rate. PV − OA9, i% = $300,000 ÷ $36,987 = 8.11096; Inspection of the10 period row reveals a rate of about 4%.

Accounting and the Time Value of Money 4.

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Bart Barton on Compa ompany ny,, a comp compan any y who main mainta tain ins s its its acco accoun untting ing reco record rds s usin using g IFRS, manufactures furniture. Barton sells a $75,000 order to Save-A Lot Furniture in exchange for a zero-interest-bearing note due from the customer in two years. Since there is no stated interest rate on the note, the controller uses the current market rate of 8% to derive the present value factor. Based on this information and the incorporation of the time value of money, which of the following would be recorded by Barton to recognize this sale? a. b. c. d.

A credit credit to to Discoun Discountt on Notes Notes Receivable Receivable for $10,699 $10,699.. A credi creditt to Sale Sales s Reven Revenue ue for for $75,00 $75,000. 0. A debit debit to Note Notes s Recei Receivab vable le for for $64,30 $64,301. 1. A debit debit to Discount Discount on on Notes Notes Receiv Receivable able for for $6,000. $6,000.

Rationale: Notes Receivable 75,000 Sales Revenue 64,301 Discount on Notes Receivable 10,699 $75,000 × PV (8%, 2) = $75,000 × .85734 = $64,301 5.

Moor Moore e Indu Indust stri ries es manu manufa fact ctur ures es exerc exercis ise e equi equipm pmen ent. t. Rece Recent ntly ly the the vice vice pres presid iden entt of operat operation ions s of the company company has requested requested construc constructio tion n of a new plant to meet meet the increasing demand for the company's exercise equipment. After a careful evaluation of the request, the board of directors has decided to raise funds for the new plant by issuing $2,000,000 of 11% bonds on March 1, 2012, due on March 1, 2027, with interest payable each March 1 and September 1. At the time of issuance, the market interest rate for similar financial instruments is 10%. What is the selling price of the bonds? a. b. c. d.

$2,220,000 $1,269,776 $2,153,730 $1,690,970

Calculations: Formula for the interest payments: PV − OA = R (PVF − OAn, i) PV − OA = $110,000 (PVF − OA30, 5%) PV − OA = $110,000 (15.37245) PV − OA = $1,690,970 Formula for the principal: PV = FV (PVFn, i) PV = $2,000,000 (PVF30, 5%) PV = $2,000,000 (0.23138) PV = $462,760 The selling price of the bonds = $1,690,970 + $462,760 = $2,153,730.

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6.


Reegan Reegan Compa Company ny owns owns a trade trade name name that that was purch purchase ased d in an acqui acquisit sition ion of Hami Hamilto lton n Company. Company. The trade name has a book value of $3,500,000, but according according to GAAP, it is assessed for impairment on an annual basis. To perform this impairment test, Reegan must estimate the fair value of the trade name. It has developed the following cash flow estima estimates tes relate related d to the trade trade name name based based on intern internal al inform informati ation. on. Each Each cash cash flow flow estimate reflects Reegan's estimate of annual cash flows over the next 7 years. The trade name is assumed to have no residual value after the 7 years. (Assume the cash flows occur at the end of each year.) Probability As Assessment 30% 50% 20%

Cash Fl Flow Es Estimate $480,000 730,000 850,000

Reegan determines that the appropriate discount rate for this estimation is 6%. To the nearest dollar, what is the estimated fair value of the trade name? a. b. c. d.

$3,500,000 $ 679,000 $2,060,000 $3,790,436

Calculations: This exercise determines the present value of an ordinary annuity of expected cash flows as a fair value estimate. Cash Flow Probability Expected Estimate $480,000 730,000 850,000

×

Assessme Asse ssment nt 30% 50% 20%

=

Cash Flow $144,000 365,000 170,000 $679,000

(n = 7, l = 6%) $679,000 7.

• •

PV Factor, Present Value ×

×

5.58238 5.58238 = $3,790,436 $3,790,436

Jamiso Jamison n Company Company uses uses IFRS IFRS for its finan financia ciall reportin reporting. g. It produc produces es machin machines es that that sell globally. All sales are accompanied by a one-year warranty. At the end of the year, the company has the following data: 2,000 units were sold during the year. The trend over the past five years has been that 4% of the machines were defective in some way and had to be repaired. Of this 4%, half required a full replacement at a cost of $3,000 per unit and half were able to be repaired at an average cost of $300.

What is the expected value of the warranty cost provision? a. b. c. d.

$240,000 $132,000 $264,000 $120,000

Calculation: (2,000 × 4% × 50% × $3,000) + (2,000 × 4% × 50% × $300) = $120,000 + $12,000 = $132,000

Accounting and the Time Value of Money 8.

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Maxim Maxim Compan Company y leased leased an office office under under a five-y five-year ear contra contract, ct, whic which h has been accou accounte nted d for as an operating lease. Faced with the downturn in the economy, the viable company decided to sub-lease the office. However, they have had no luck with this effort and the landlord will not allow the lease to be cancelled. The payments are $6,000 per year and there there are four years years left left on the lease. lease. The company' company's s most most recent recent interest interest rate for financing financing from a bank is 6%. The risk-free risk-free rate on government government bonds is 4%. What is the provision for the lease under IFRS? a. b. c. d.

$21,780 $22,572 $24,000 $20,791

Calculation: PV $6,000 (4 years, 6%) = $6,000 × 3.46511 = $20,791 9.

Dolphi Dolphin n Company Company lease leased d an office office under under a six-yea six-yearr contrac contract, t, which which has been been accoun accounted ted for as an operating lease. Faced with the downturn in the economy, the viable company decided to sub-lease the office. However, they have had no luck with this effort and the landlord will not allow the lease to be cancelled. The payments are $10,000 per year and there there are five years years left left on the lease. lease. The company' company's s most most recent recent interest interest rate rate for financing financing from a bank is 9%. The risk-free risk-free rate on government government bonds is 5%. What is the provision for the lease under IFRS? a. b. c. d.

$50,000 $44,519 $38,897 $43,295

Calculation: PV $10,000 (5 years, 9%) = $10,000 × 3.88965 = $38,897 10

Tech Techtr tron onic ics, s, a tech techno nolo logy gy compan company y that that uses uses IFRS for for its its fina financ ncia iall repo report rtin ing, g, has been been found to have polluted the property surrounding its plant. The property is leaded for 12 years and Techtronics has agreed that when the lease expires, the pollution will be remediated before transfer back to its owner. The lease has a renewal option for another 8 years. If this option is exercised, the cleanup will be done at the end of the renewal period. There is a 70% chance that the lease will not be renewed and the cleanup will cost $180,000. There is 30% chance that the lease will be renewed and the cleanup costs will be $375,000 at the end of the 20 years. If you assume that these estimates are derived from best estimates of likely outcomes and the risk-free rate is 5%, the expected present value of the cleanup provision is: a. b. c. d.

$238,500 $112,562 $277,500 $226,575

Calculation: ($180,000 × 70% × 0.55684) + ($375,000 × 30% × 0.37689) = $70,162 + $42,400 = $112,562

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Answers to Multiple Choice. 1. a 2. a 3. b 4. a 5. c 6. d 7. b 8. d 9. c 10. b

ch 6

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