Solution Manual for Financial Accounting Tools for Business Decision Making, 7th Edition Paul D. Kimmel .doc

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APPENDIX D

Time Value of Money Learning Objectives 1. 2. 3. 4. 5. 6. 7. 8.

Distinguish between simple and compound interest. Solve for future value of a single amount. Solve for future value of an annuity. Identify the variables fundamental to solving present value problems. Solve for present value of a single amount. Solve for present value of an annuity. Compute the present value of notes and bonds. Use a financial calculator to solve time value of money problems.

Summary of Questions by Learning Objectives and Bloom’s Taxonomy Item

LO

BT

Item

LO

BT

Item

LO

BT

Item

LO

BT

Item

LO

BT

18.

6

AP

25.

8

AP

19.

6, 7

AP

26.

8

AP

20.

5

AN

27.

8

AP

21.

5

AN

28.

8

AP

22.

6

AN

23.

6

AN

24.

8

AP

Brief Exercises  1.

2

AP

 8.

5, 6

AP

 2.

2, 3

C

 9.

5

AP

 3.

2

AP

10.

5

AP

 4.

3

AP

11.

6

AP

 5.

2, 3

AP

12.

6

AP

 6.

2

AP

13.

 7.

5, 6

C

5, 6, 7

AP

14. 15. 16. 17.

5, 6, 7

AP

5, 6, 7

AP

5, 6, 7

AP

6, 7

AP

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SOLUTIONS TO BRIEF EXERCISES BRIEF EXERCISE D-1 (a) Interest = p X i X n I = $8,000 X .05 X 12 years I = $4,800 Accumulated amount = $8,000 + $4,800 = $12,800 (b) Future value factor for 12 periods at 5% is 1.79586 (from Table 1) Accumulated amount = $8,000 X 1.79586 = $14,366.88 BRIEF EXERCISE D-2 (a)

(b) (1) A B

6% 4%

3 periods 8 periods

(b) (2) A B

5% 3%

(a) 8 periods 12 periods

BRIEF EXERCISE D-3 FV = p X FV of 1 factor = $9,200 X 1.60103 = $14,729.48 BRIEF EXERCISE D-4 FV of an annuity of 1 = p X FV of an annuity factor = $78,000 X 12.57789 = $981,075.42

D-2

Copyright © 2013 John Wiley & Sons, Inc.   Kimmel, Financial Accounting,7/e, Solutions Manual    (For Instructor Use Only)

Full file at http://testbankinstant.CH/Solution-Manual-for-FinancialAccounting-Tools-for-Business-Decision-Making,-7th-Edition-Paul-D.KimmelBRIEF EXERCISE D-5

FV = p X FV of 1 factor + (p X FV of an annuity factor) = ($6,000 X 2.02582) + ($1,000 X 25.64541) = $12,154.92 + $25,645.41 = $37,800.33 BRIEF EXERCISE D-6 FV = p X FV of 1 factor = $34,000 X 1.53862 = $52,313.08 BRIEF EXERCISE D-7 (1)

(a) A B C

(2) A B C

(b)

12% 10% 3% 12% 10% 4%

  6 periods 11 periods 18 periods

20 periods  5 periods  8 periods

BRIEF EXERCISE D-8 (a)

i = 10%

? 0

1

2

3

4

$28,000 5

6

7

8

9

Discount rate from Table 3 is .42410 (9 periods at 10%). Present value of $28,000 to be received in 9 years discounted at 10% is therefore $11,874.80 ($28,000 X .42410). download full file at http://testbankinstant.com

D-4

Copyright © 2013 John Wiley & Sons, Inc.   Kimmel, Financial Accounting,7/e, Solutions Manual    (For Instructor Use Only)

Full file at http://testbankinstant.CH/Solution-Manual-for-FinancialAccounting-Tools-for-Business-Decision-Making,-7th-Edition-Paul-D.KimmelBRIEF EXERCISE D-8 (Continued) (b)

i = 9% ?

$28,000 $28,000 $28,000 $28,000 $28,000 $28,000

0

1

2

3

4

5

6

Discount rate from Table 4 is 4.48592 (6 periods at 9%). Present value of 6 payments of $28,000 each discounted at 9% is therefore $125,605.76 ($28,000 X 4.48592).

BRIEF EXERCISE D-9 i = 9%

? 0

1

2

$750,000

3

4

5

Discount rate from Table 3 is .64993 (5 periods at 9%). Present value of $750,000 to be received in 5 years discounted at 9% is therefore $487,447.50 ($750,000 X .64993). Elmdale Company should therefore invest $487,447.50 to have $750,000 in five years. BRIEF EXERCISE D-10 i = 10%

? 0

1

2

3

4

$480,000 5

6

7

8

Discount rate from Table 3 is .46651 (8 periods at 10%). Present value of $480,000 to be received in 8 years discounted at 10% is therefore $223,924.80 download full file at http://testbankinstant.com

($480,000 X .46651). Orear Company should invest $223,924.80 to have $480,000 in eight years.

D-6

Copyright © 2013 John Wiley & Sons, Inc.   Kimmel, Financial Accounting,7/e, Solutions Manual    (For Instructor Use Only)

Full file at http://testbankinstant.CH/Solution-Manual-for-FinancialAccounting-Tools-for-Business-Decision-Making,-7th-Edition-Paul-D.KimmelBRIEF EXERCISE D-11

i = 5% ?

$45,000 $45,000 $45,000 $45,000

0

1

2

3

$45,000 $45,000

4

14

15

Discount rate from Table 4 is 10.37966. Present value of 15 payments of $45,000 each discounted at 5% is therefore $467,084.70 ($45,000 X 10.37966). Dayton Company should pay $467,084.70 for this annuity contract.

BRIEF EXERCISE D-12 i = 8% ?

$90,000

$90,000

$90,000

$90,000

$90,000

$90,000

0

1

2

3

4

5

6

Discount rate from Table 4 is 4.62288. Present value of 6 payments of $90,000 each discounted at 8% is therefore $416,059.20 ($90,000 X 4.62288). Nolasko Enterprises invested $416,059.20 to earn $90,000 per year for six years.

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BRIEF EXERCISE D-13

Diagram for Principal

i = 4%

?

0

1

2

3

$300,000

4

19

20

i = 4% Diagram for Interest

?

0

$13,500 $13,500 $13,500 $13,500

1

2

3

4

$13,500 $13,500

19

20

Present value of principal to be received at maturity: $300,000 X 0.45639 (PV of $1 due in 20 periods at 4% from Table 3)................................................................ $136,917.00 Present value of interest to be received periodically over the term of the bonds: $13,500 X 13.59033 (PV of $1 due each period for 20 periods at 4% from Table 4).......................................................................... 183,469.45 Present value of bonds................................................................. $320,386.45 BRIEF EXERCISE D-14 The bonds will sell at a discount (for less than $300,000). This may be proven as follows: Present value of principal to be received at maturity: $300,000 X .37689 (PV of $1 due in 20 periods at 5% from Table 3)................................................................ $113,067.00 Present value of interest to be received periodically over the term of the bonds: $13,500 X 12.46221 (PV of $1 due each period for 20 periods at 5% from Table 4).......................................................................... 168,239.83 Present value of bonds................................................................. $281,306.83

D-8

Copyright © 2013 John Wiley & Sons, Inc.   Kimmel, Financial Accounting,7/e, Solutions Manual    (For Instructor Use Only)

Full file at http://testbankinstant.CH/Solution-Manual-for-FinancialAccounting-Tools-for-Business-Decision-Making,-7th-Edition-Paul-D.KimmelBRIEF EXERCISE D-15

Diagram for Principal

i = 8%

?

0

1

2

$64,000

3

4

5

6

i = 8% Diagram for Interest

?

$3,840

$3,840

$3,840

$3,840

$3,840

$3,840

0

1

2

3

4

5

6

Present value of principal to be received at maturity: $64,000 X .63017 (PV of $1 due in 6 periods at 8% from Table 3).............................................................. Present value of interest to be received annually over the term of the note: $3,840 X 4.62288 (PV of $1 due each period for 6 periods at 8% from Table 4).................................................................. Present value of note received...................................................

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$40,330.88

17,751.86 $58,082.74

BRIEF EXERCISE D-16

Diagram for Principal

i = 5%

?

0

1

2

3

$2,600,000

4

14

15

16

i = 5% Diagram for Interest

?

$117,000 $117,000 $117,000 $117,000

0

1

2

3

4

$117,000$117,000 $117,000

14

15

Present value of principal to be received at maturity: $2,600,000 X 0.45811 (PV of $1 due in 16 periods at 5% from Table 3).............................................................. Present value of interest to be received periodically over the term of the bonds: $117,000 X 10.83777 (PV of $1 due each period for 16 periods at 5% from Table 4)......................................................................... Present value of bonds and cash proceeds..............................

16

$1,191,086*

 1,268,019 $2,459,105

BRIEF EXERCISE D-17 i = 10% ?

4

0 5

$3,300 $3,300 $3,300 $3,300 $3,300 $3,300 $3,300 $3,300

1 6

2 7

Discount rate from Table 4 is 5.33493. Present value of 8 payments of $3,300 each discounted at 10% is therefore $17,605.27 ($3,300 X 5.33493). Phil Emley should not purchase the tire retreading machine because the present value of the future cash flows is less than the $18,000 purchase price of the retreading machine. D-10

Copyright © 2013 John Wiley & Sons, Inc.   Kimmel, Financial Accounting,7/e, Solutions Manual    (For Instructor Use Only)

Full file at http://testbankinstant.CH/Solution-Manual-for-FinancialAccounting-Tools-for-Business-Decision-Making,-7th-Edition-Paul-D.KimmelBRIEF EXERCISE D-18

i = 4% ?

$46,850

$46,850

$46,850

$46,850

$46,850

$46,850

0

1

2

3

4

9

10

Discount rate from Table 4 is 8.11090. Present value of 10 payments of $46,850 each discounted at 4% is therefore $379,995.66 ($46,850 X 8.11090). Jamison Company should receive $379,995.66 from the issuance of the note.

BRIEF EXERCISE D-19 i = 10% ?

$38,000

$40,000

$50,000

0

1

2

3

To determine the present value of the future cash flows, discount the future cash flows at 10%, using Table 3. Year 1 ($38,000 X .90909) = Year 2 ($40,000 X .82645) = Year 3 ($50,000 X .75132) = Present value of future cash flows

$ 34,545.42 33,058.00 37,566.00 $105,169.42

To achieve a minimum rate of return of 10%, Pendley Company should pay no more than $105,169.42. If Pendley pays less than $105,169.42, its rate of return will be greater than 10%.

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BRIEF EXERCISE D-20 i=?

$4,172.65

0

1

2

3

$10,000

4

14

15

Present value = Future value X Present value of 1 factor $4,172.65 = $10,000 X Present value of 1 factor Present value of 1 factor = $4,172.65 ÷ $10,000 = .41727 The .41727 for 15 periods is found in the 6% column. Barbara Oxford will receive a 6% return.

BRIEF EXERCISE D-21 $25,490

i = 10%

$80,000

n=? Present value = Future value X Present value of 1 factor $25,490 = $80,000 X Present value of 1 factor Present value of 1 factor = $25,490 ÷ $80,000 = .31863 The .31863 at 10% is found in the 12 years row. Blake Mohr therefore must wait 12 years to receive $80,000.

D-12

Copyright © 2013 John Wiley & Sons, Inc.   Kimmel, Financial Accounting,7/e, Solutions Manual    (For Instructor Use Only)

Full file at http://testbankinstant.CH/Solution-Manual-for-FinancialAccounting-Tools-for-Business-Decision-Making,-7th-Edition-Paul-D.KimmelBRIEF EXERCISE D-22

i=? ?

0

$1,000 $1,000 $1,000 $1,000 $1,000 $1,000

$9,128.55

1

2

3

4

5

6

$1,000 $1,000

19

20

Present value = Annuity amount X Present value of an annuity factor $9,128.55 = $1,000 X Present value of an annuity factor Present value of an annuity factor = $9,128.55 ÷ $1,000 = 9.12855

The 9.12855 for 20 periods is found in the 9% column. Amanda Tevis will therefore earn a rate of return of 9%.

BRIEF EXERCISE D-23 i = 11% $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $5,146.12

n=?

Present value = Annuity amount X Present value of an annuity factor $5,146.12 = $1,000 X Present value of an annuity factor Present value of an annuity factor = $5,146.12 ÷ $1,000 = 5.14612

The 5.14612 at an interest rate of 11% is shown in the 8-year row. Therefore, Kelly will receive 8 payments.

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BRIEF EXERCISE D-24 10

?

–18,000

0

50,000

N

I/YR.

PV

PMT

FV

10.76%

BRIEF EXERCISE D-25 10

?

60,000

–8,860

0

N

I/YR.

PV

PMT

FV

7.80%

BRIEF EXERCISE D-26 40

?

178,000

–8,400

0

N

I/YR.

PV

PMT

FV

3.55% (semiannual)

D-14

Copyright © 2013 John Wiley & Sons, Inc.   Kimmel, Financial Accounting,7/e, Solutions Manual    (For Instructor Use Only)

Full file at http://testbankinstant.CH/Solution-Manual-for-FinancialAccounting-Tools-for-Business-Decision-Making,-7th-Edition-Paul-D.KimmelBRIEF EXERCISE D-27 (a) Inputs:

7

6.9

?

–16,000

0

N

I

PV

PMT

FV

Answer:

86,530.07

(b) Inputs:

Answer:

10

8.65

?

14,000

200,000

N

I

PV

PMT

FV

–178,491.52

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BRIEF EXERCISE D-28 (a) Note—set payments at 12 per year. Inputs: 96 7.8 N

I

42,000

?

0

PV

PMT

FV

Answer:

–589.48

(b) Note—set payments to 1 per year. Inputs: 5 7.25 N Answer:

D-16

I

8,000

?

0

PV

PMT

FV

–1,964.20

Copyright © 2013 John Wiley & Sons, Inc.   Kimmel, Financial Accounting,7/e, Solutions Manual    (For Instructor Use Only)