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Solution manual financial accounting 4e by wild appendi xb chapter

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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

©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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718

Financial Accounting, 4th Edition


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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

©McGraw-Hill Companies, 2008
720

Financial Accounting, 4th Edition


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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

©McGraw-Hill Companies, 2008
722

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



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