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Appendix B

Applying Present and Future Values

QUICK STUDIES

Quick Study B-1 (10 minutes)

1.

2.

3.

4.

2%

12%

3%

1%

Quick Study B-2 (10 minutes)

In Table B.1, where n = 15 and p = $2,745/$10,000 = 0.2745, the i = 9%.

Quick Study B-3 (10 minutes)

In Table B.1, where i = 6% and p = $6,651/$10,000 = 0.6651, the n = 7.

Quick Study B-4 (10 minutes)

In Table B.1, where n = 5 and i = 9%, the p = 0.6499.

Amount willing to pay today: 0.6499 x $140,000 = $90,986

Quick Study B-5 (10 minutes)

In Table B.2, where n = 10 and i = 12%, the f = 3.1058.

Cash proceeds at liquidation: 3.1058 x $630,000 = $1,956,654

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Quick Study B-6 (10 minutes)

In Table B.3, where n = 6 and i = 7%, the p = 4.7665.

Amount willing to pay for the project: 4.7665 x $150,000 = $714,975

Quick Study B-7 (10 minutes)

In Table B.4, where n = 30 and i = 10%, the f = 164.494.

Ending value of the investment program: 164.494 x $1,500 = $246,741

EXERCISES

Exercise B-1 (10 minutes)

In Table B.2, where i = 12% and f = $96,463/$10,000 = 9.6463, the n = 20

(implies the investor must wait 20 years before payment).

Exercise B-2 (10 minutes)

In Table B.2, where n = 25 and f = $108,347/$10,000 = 10.8347, the i = 10%

(investor must earn 10% interest to achieve investment goal).

Exercise B-3 (10 minutes)

In Table B.3, where n = 8 and p = $57,466/$10,000 = 5.7466, the i = 8%

(investor must earn 8% interest to achieve investment goal).

Exercise B-4 (10 minutes)

In Table B.3, where i = 10% and p = $82,014/$10,000 = 8.2014, the n = 18

(investor expects 18 annual payments to be received).

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Exercise B-5 (10 minutes)

In Table B.4, where n = 40 and f = $154,762/$1,000 = 154.762, the i = 6%

(investor must earn a 6% rate of interest).

Exercise B-6 (10 minutes)

In Table B.4, where i = 8% and f = $303,243/$10,000 = 30.3243, the n = 16

(investor must make 16 annual payments to achieve investment goal).

Exercise B-7 (10 minutes)

Interest rate per period = 12% annual / 12 months per year = 1% per month

Using Table B.3, where n = 40 and i = 1%, the p = 32.8347. This means:

Loan balance ............$16,417.35 (present value of loan = 32.8347 x $500)

Down payment .......... 6,500.00 (cash)

Total cost ..................$22,917.35

Exercise B-8 (15 minutes)

Semiannual interest payment = $500,000 x 10% x 1/2 = $25,000

Using Table B.1, where n = 30 and i = 4%, the p = 0.3083 (Principal payment)

Using Table B.3, where n = 30 and i = 4%, the p = 17.2920 (Interest payments)

0.3083 x $500,000 =

17.2920 x $ 25,000 =

$154,150 present value of maturity amount

432,300 present value of interest payments

$586,450 cash proceeds

Exercise B-9 (15 minutes)

In Table B.1, where n = 6 and i = 10%, the p = 0.5645.

Present value of investment = $606,773 x .5645 = $342,523

Exercise B-10 (15 minutes)

1. $90,000 x 0.6651 (using Table B.1, i = 6%, n = 7) = $59,859.

2. $20,000 x 2.4869 (using Table B.3, i = 10%, n = 3) = $49,738.

©McGraw-Hill Companies, 2008

Solutions Manual, Appendix B

719

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Exercise B-11 (15 minutes)

Amount borrowed = present value of $20,000 at 10% for 3 years

= $20,000 x 0.7513 (using Table B.1, i = 10%, n = 3)

= $15,026

Exercise B-12 (10 minutes)

Single Future

Payment

a. $40,000

b.

75,000

c.

52,000

d.

18,000

e.

63,000

f.

89,000

Number of

Periods

3

7

9

2

8

5

Exercise B-13 (25 minutes)

1.

First Annuity

Future

Payment

First payment ........ $5,000

Second payment ...

5,000

Third payment .......

5,000

Fourth payment ....

5,000

Fifth payment ........

5,000

Sixth payment .......

5,000

Total borrowed .....

Interest Rate

4%

8

10

4

6

2

Number of

Periods

1

2

3

4

5

6

Table B.1

Value

0.8890

0.5835

0.4241

0.9246

0.6274

0.9057

Amount

Borrowed

$35,560

$43,763

$22,053

$16,643

$39,526

$80,607

Interest

Rate

6%

6

6

6

6

6

Table B.1

Value

0.9434

0.8900

0.8396

0.7921

0.7473

0.7050

Amount

Borrowed

$ 4,717

4,450

4,198

3,961

3,737

3,525

$24,588

Interest

Rate

6%

6

6

6

Table B.1

Value

0.9434

0.8900

0.8396

0.7921

Amount

Borrowed

$ 7,076

6,675

6,297

5,941

$25,989

Second Annuity

First payment ........

Second payment ...

Third payment .......

Fourth payment ....

Total borrowed .....

Future

Payment

$7,500

7,500

7,500

7,500

Number of

Periods

1

2

3

4

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Exercise B-13 (Continued)

2.

First Annuity

Payment size ....................................... $ 5,000

Number of payments ..........................

6

Interest rate .........................................

6%

Value from Table B.3 .......................... 4.9173

Present value of the annuity ............. $24,587

(difference from part (1) due to rounding)

Second Annuity

Payment size ....................................... $ 7,500

Number of payments ..........................

4

Interest rate .........................................

6%

Value from Table B.3 .......................... 3.4651

Present value of the annuity ............. $25,988

(difference from part (1) due to rounding)

Exercise B-14 (30 minutes)

1. Present value of the annuity

Payment size ....................................... $13,000

Number of payments ..........................

4

Interest rate .........................................

4% (semiannual)

Value from Table B.3 .......................... 3.6299

Present value of the annuity ............. $47,189

2. Present value of the annuity

Payment size ....................................... $13,000

Number of payments ..........................

4

Interest rate .........................................

6% (semiannual)

Value from Table B.3 .......................... 3.4651

Present value of the annuity ............. $45,046

3. Present value of the annuity

Payment size ....................................... $13,000

Number of payments ..........................

4

Interest rate .........................................

8% (semiannual)

Value from Table B.3 .......................... 3.3121

Present value of the annuity ............. $43,057

©McGraw-Hill Companies, 2008

Solutions Manual, Appendix B

721

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Exercise B-15 (15 minutes)

10 years x 4 quarters = 40 interest periods

8% annual / 4 quarters per year = 2% per quarter

In Table B.2, where n = 40 and i = 2%, the f = 2.2080.

Total accumulation = 2.2080 x $7,200 = $15,897.60

Exercise B-16 (15 minutes)

12% annual / 12 months per year = 1% per month

2.5 years x 12 months per year = 30 total months

In Table B.4, where n = 30 and i = 1%, the f = 34.7849.

Total accumulation = 34.7849 x $50 = $1,739.25

Exercise B-17 (15 minutes)

10 years x 4 quarters per year = 40 total quarters

12% annual / 4 quarters per year = 3% per quarter

In Table B.2, where n = 40 and i = 3%, the f = 3.2620.

In Table B.4, where n = 40 and i = 3%, the f = 75.4013.

3.2620 x $100,000 =

75.4013 x $50,000 =

$ 326,200 future value of initial investment

3,770,065 future value of periodic investments

$4,096,265 future value of fund

Exercise B-18 (15 minutes)

In Table B.2, where n = 9 and i = 7%, the f = 1.8385.

Future value of investment = $163,170 x 1.8385 = $299,988

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Exercise B-19 (20 minutes)

a.

b.

(1)

(2)

(3)

OR

(1)

(2)

(3)

Present Value of a single amount.

Multiply $10,000 by p from Table B.1.

Use Table B.1, periods = 8 and interest rate = 4%.

(1)

(2)

(3)

OR

(1)

(2)

Future Value of an Annuity.

Divide $10,000 by f from Table B.4.

Use Table B.4, periods = 8 and interest rate = 4%.

Future Value of a single amount.

Divide $10,000 by f from Table B.2.

Use Table B.2, periods = 8 and interest rate = 4%.

(3)

Present Value of an Annuity.

Multiply $10,000 by p from Table B.1 and then divide by p from

Table B.3.

Use Tables B.1 and B.3, periods = 8 and interest rate = 4%.

c.

(1)

(2)

(3)

Future Value of an Annuity.

Multiply $4,000 by f from Table B.4.

Use Table B.4, periods = 40 and interest = 8%.

d.

(1)

(2)

(3)

Present Value of an Annuity.

Multiply $30,000 by p from Table B.3.

Use Table B.3, periods = 20 and interest = 10%.

[Note: Students must recognize the present value of $225,000

received today is $225,000.]

©McGraw-Hill Companies, 2008

Solutions Manual, Appendix B

723

Appendix B

Applying Present and Future Values

QUICK STUDIES

Quick Study B-1 (10 minutes)

1.

2.

3.

4.

2%

12%

3%

1%

Quick Study B-2 (10 minutes)

In Table B.1, where n = 15 and p = $2,745/$10,000 = 0.2745, the i = 9%.

Quick Study B-3 (10 minutes)

In Table B.1, where i = 6% and p = $6,651/$10,000 = 0.6651, the n = 7.

Quick Study B-4 (10 minutes)

In Table B.1, where n = 5 and i = 9%, the p = 0.6499.

Amount willing to pay today: 0.6499 x $140,000 = $90,986

Quick Study B-5 (10 minutes)

In Table B.2, where n = 10 and i = 12%, the f = 3.1058.

Cash proceeds at liquidation: 3.1058 x $630,000 = $1,956,654

©McGraw-Hill Companies, 2008

Solutions Manual, Appendix B

717

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Quick Study B-6 (10 minutes)

In Table B.3, where n = 6 and i = 7%, the p = 4.7665.

Amount willing to pay for the project: 4.7665 x $150,000 = $714,975

Quick Study B-7 (10 minutes)

In Table B.4, where n = 30 and i = 10%, the f = 164.494.

Ending value of the investment program: 164.494 x $1,500 = $246,741

EXERCISES

Exercise B-1 (10 minutes)

In Table B.2, where i = 12% and f = $96,463/$10,000 = 9.6463, the n = 20

(implies the investor must wait 20 years before payment).

Exercise B-2 (10 minutes)

In Table B.2, where n = 25 and f = $108,347/$10,000 = 10.8347, the i = 10%

(investor must earn 10% interest to achieve investment goal).

Exercise B-3 (10 minutes)

In Table B.3, where n = 8 and p = $57,466/$10,000 = 5.7466, the i = 8%

(investor must earn 8% interest to achieve investment goal).

Exercise B-4 (10 minutes)

In Table B.3, where i = 10% and p = $82,014/$10,000 = 8.2014, the n = 18

(investor expects 18 annual payments to be received).

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Exercise B-5 (10 minutes)

In Table B.4, where n = 40 and f = $154,762/$1,000 = 154.762, the i = 6%

(investor must earn a 6% rate of interest).

Exercise B-6 (10 minutes)

In Table B.4, where i = 8% and f = $303,243/$10,000 = 30.3243, the n = 16

(investor must make 16 annual payments to achieve investment goal).

Exercise B-7 (10 minutes)

Interest rate per period = 12% annual / 12 months per year = 1% per month

Using Table B.3, where n = 40 and i = 1%, the p = 32.8347. This means:

Loan balance ............$16,417.35 (present value of loan = 32.8347 x $500)

Down payment .......... 6,500.00 (cash)

Total cost ..................$22,917.35

Exercise B-8 (15 minutes)

Semiannual interest payment = $500,000 x 10% x 1/2 = $25,000

Using Table B.1, where n = 30 and i = 4%, the p = 0.3083 (Principal payment)

Using Table B.3, where n = 30 and i = 4%, the p = 17.2920 (Interest payments)

0.3083 x $500,000 =

17.2920 x $ 25,000 =

$154,150 present value of maturity amount

432,300 present value of interest payments

$586,450 cash proceeds

Exercise B-9 (15 minutes)

In Table B.1, where n = 6 and i = 10%, the p = 0.5645.

Present value of investment = $606,773 x .5645 = $342,523

Exercise B-10 (15 minutes)

1. $90,000 x 0.6651 (using Table B.1, i = 6%, n = 7) = $59,859.

2. $20,000 x 2.4869 (using Table B.3, i = 10%, n = 3) = $49,738.

©McGraw-Hill Companies, 2008

Solutions Manual, Appendix B

719

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Exercise B-11 (15 minutes)

Amount borrowed = present value of $20,000 at 10% for 3 years

= $20,000 x 0.7513 (using Table B.1, i = 10%, n = 3)

= $15,026

Exercise B-12 (10 minutes)

Single Future

Payment

a. $40,000

b.

75,000

c.

52,000

d.

18,000

e.

63,000

f.

89,000

Number of

Periods

3

7

9

2

8

5

Exercise B-13 (25 minutes)

1.

First Annuity

Future

Payment

First payment ........ $5,000

Second payment ...

5,000

Third payment .......

5,000

Fourth payment ....

5,000

Fifth payment ........

5,000

Sixth payment .......

5,000

Total borrowed .....

Interest Rate

4%

8

10

4

6

2

Number of

Periods

1

2

3

4

5

6

Table B.1

Value

0.8890

0.5835

0.4241

0.9246

0.6274

0.9057

Amount

Borrowed

$35,560

$43,763

$22,053

$16,643

$39,526

$80,607

Interest

Rate

6%

6

6

6

6

6

Table B.1

Value

0.9434

0.8900

0.8396

0.7921

0.7473

0.7050

Amount

Borrowed

$ 4,717

4,450

4,198

3,961

3,737

3,525

$24,588

Interest

Rate

6%

6

6

6

Table B.1

Value

0.9434

0.8900

0.8396

0.7921

Amount

Borrowed

$ 7,076

6,675

6,297

5,941

$25,989

Second Annuity

First payment ........

Second payment ...

Third payment .......

Fourth payment ....

Total borrowed .....

Future

Payment

$7,500

7,500

7,500

7,500

Number of

Periods

1

2

3

4

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Exercise B-13 (Continued)

2.

First Annuity

Payment size ....................................... $ 5,000

Number of payments ..........................

6

Interest rate .........................................

6%

Value from Table B.3 .......................... 4.9173

Present value of the annuity ............. $24,587

(difference from part (1) due to rounding)

Second Annuity

Payment size ....................................... $ 7,500

Number of payments ..........................

4

Interest rate .........................................

6%

Value from Table B.3 .......................... 3.4651

Present value of the annuity ............. $25,988

(difference from part (1) due to rounding)

Exercise B-14 (30 minutes)

1. Present value of the annuity

Payment size ....................................... $13,000

Number of payments ..........................

4

Interest rate .........................................

4% (semiannual)

Value from Table B.3 .......................... 3.6299

Present value of the annuity ............. $47,189

2. Present value of the annuity

Payment size ....................................... $13,000

Number of payments ..........................

4

Interest rate .........................................

6% (semiannual)

Value from Table B.3 .......................... 3.4651

Present value of the annuity ............. $45,046

3. Present value of the annuity

Payment size ....................................... $13,000

Number of payments ..........................

4

Interest rate .........................................

8% (semiannual)

Value from Table B.3 .......................... 3.3121

Present value of the annuity ............. $43,057

©McGraw-Hill Companies, 2008

Solutions Manual, Appendix B

721

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Exercise B-15 (15 minutes)

10 years x 4 quarters = 40 interest periods

8% annual / 4 quarters per year = 2% per quarter

In Table B.2, where n = 40 and i = 2%, the f = 2.2080.

Total accumulation = 2.2080 x $7,200 = $15,897.60

Exercise B-16 (15 minutes)

12% annual / 12 months per year = 1% per month

2.5 years x 12 months per year = 30 total months

In Table B.4, where n = 30 and i = 1%, the f = 34.7849.

Total accumulation = 34.7849 x $50 = $1,739.25

Exercise B-17 (15 minutes)

10 years x 4 quarters per year = 40 total quarters

12% annual / 4 quarters per year = 3% per quarter

In Table B.2, where n = 40 and i = 3%, the f = 3.2620.

In Table B.4, where n = 40 and i = 3%, the f = 75.4013.

3.2620 x $100,000 =

75.4013 x $50,000 =

$ 326,200 future value of initial investment

3,770,065 future value of periodic investments

$4,096,265 future value of fund

Exercise B-18 (15 minutes)

In Table B.2, where n = 9 and i = 7%, the f = 1.8385.

Future value of investment = $163,170 x 1.8385 = $299,988

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Financial Accounting, 4th Edition

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Exercise B-19 (20 minutes)

a.

b.

(1)

(2)

(3)

OR

(1)

(2)

(3)

Present Value of a single amount.

Multiply $10,000 by p from Table B.1.

Use Table B.1, periods = 8 and interest rate = 4%.

(1)

(2)

(3)

OR

(1)

(2)

Future Value of an Annuity.

Divide $10,000 by f from Table B.4.

Use Table B.4, periods = 8 and interest rate = 4%.

Future Value of a single amount.

Divide $10,000 by f from Table B.2.

Use Table B.2, periods = 8 and interest rate = 4%.

(3)

Present Value of an Annuity.

Multiply $10,000 by p from Table B.1 and then divide by p from

Table B.3.

Use Tables B.1 and B.3, periods = 8 and interest rate = 4%.

c.

(1)

(2)

(3)

Future Value of an Annuity.

Multiply $4,000 by f from Table B.4.

Use Table B.4, periods = 40 and interest = 8%.

d.

(1)

(2)

(3)

Present Value of an Annuity.

Multiply $30,000 by p from Table B.3.

Use Table B.3, periods = 20 and interest = 10%.

[Note: Students must recognize the present value of $225,000

received today is $225,000.]

©McGraw-Hill Companies, 2008

Solutions Manual, Appendix B

723

## Solution manual advanced accounting 4e by jeter

## Solution manual advanced accounting 4e by jeter

## Solution manual financial accounting 4e by wild appendi xe

## Solution manual financial accounting 4e by wild appendix b

## Solution manual financial accounting 4e by wild appendix c

## Solution manual financial accounting 4e by wild appendix d

## Solution manual financial accounting 4e by wild chapter01

## Solution manual financial accounting 4e by wild chapter02

## Solution manual financial accounting 4e by wild chapter03

## Solution manual financial accounting 4e by wild chapter04

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