INSTRUCTOR’S SOLUTIONS
MANUAL
Kelly Halliday
Georgian College
Ali R. Hassanlou
Kwantlen Polytechnic University
Contemporary Business Mathematics
with Canadian Applications
Thirteenth Edition
S. A. Hummelbrunner
Kelly Halliday
Georgian College
Ali R. Hassanlou
Kwantlen Polytechnic University
ISBN 978-0-13-789689-9
.
, Contents
PART ONE Mathematics Fundamentals and Business Applications
Chapter 1: Review of Arithmetic 1
Chapter 2: Review of Basic Algebra 35
Chapter 3: Ratio, Proportion, and Percent 91
Chapter 4: Linear Systems 135
Chapter 5: Cost-Volume-Profit Analysis and Break-Even 193
PART TWO Mathematics of Business and Management
Chapter 6: Trade Discount, Cash Discount, Markup, and Markdown 225
Chapter 7: Simple Interest 263
Chapter 8: Simple Interest Applications 289
PART THREE Mathematics of Finance and Investment
Chapter 9: Compound Interest—Future Value and Present Value 335
Chapter 10: Compound Interest—Further Topics 379
Chapter 11: Ordinary Simple Annuities 415
Chapter 12: Ordinary General Annuities 455
Chapter 13: Annuities Due, Deferred Annuities, and Perpetuities 493
Chapter 14: Amortization of Loans, Including Residential Mortgages 545
Chapter 15: Bond Valuation and Sinking Funds 611
Chapter 16: Investment Decision Applications 669
, I’ll expand on the topics related to "Taxation of Business Entities," providing a more detailed exploration. This overview will cover fundamental concepts, applications, and implications relevant to the study of business taxation.---### Overview of Business
Entities#### 1. Types of Business EntitiesBusiness entities can be categorized based on ownership structure and tax treatment. Understanding these types is crucial for determining tax obligations and benefits.- **Sole Proprietorships**: - Owned by a single
individual, this is the simplest form of business entity. Income is reported on the owner’s personal tax return (Form 1040, Schedule C), which simplifies tax filing but also means personal liability for debts and obligations.- **Partnerships**: - Consisting of two
or more individuals, partnerships do not pay federal income taxes. Instead, they are considered pass-through entities, meaning income is taxed at the partners' individual rates. Form 1065 is used to report partnership income, while partners receive Schedule K-1
to report their share on their returns.- **Corporations**: - Corporations are separate legal entities that provide limited liability protection to their owners (shareholders). C-Corporations face double taxation: once at the corporate level on profits and again at the
individual level when dividends are distributed. S-Corporations, on the other hand, are pass-through entities but have restrictions on ownership and number of shareholders.- **Limited Liability Companies (LLCs)**: - LLCs combine the flexibility of
partnerships with the liability protection of corporations. An LLC can choose to be taxed as a sole proprietorship, partnership, or corporation, allowing for strategic tax planning. ### 2. Tax Implications of Each Entity TypeUnderstanding the tax implications of
each entity type is critical for effective business planning.- **Sole Proprietorships**: - Income is taxed at the owner’s individual tax rate. All profits and losses are reported on the owner’s tax return. This simplicity, however, can expose owners to significant
personal risk.- **Partnerships**: - Each partner reports their share of income and losses on their personal returns, allowing for loss deductions. Partners are also subject to self-employment taxes on their share of the income, which can significantly impact tax
liability.- **Corporations**: - C-Corporations are taxed at the corporate tax rate (currently 21%). Dividends are taxed again at the shareholder level. S-Corporations avoid double taxation, but there are restrictions on the number and type of shareholders.-
**Limited Liability Companies (LLCs)**: - By default, single-member LLCs are treated as sole proprietorships for tax purposes, while multi-member LLCs are treated as partnerships. However, they can elect to be taxed as a corporation if beneficial.### Key
Tax Concepts#### 1. Income RecognitionIncome recognition is a fundamental principle in taxation, determining when income must be reported.- **Cash vs. Accrual Accounting**: - Businesses can choose between cash and accrual methods. Cash accounting
recognizes income when received and expenses when paid, making it straightforward. Accrual accounting recognizes income when earned and expenses when incurred, aligning revenue with the period it relates to, but can complicate cash flow
management.#### 2. DeductionsDeductions reduce taxable income, directly impacting tax liability.- **Ordinary and Necessary Expenses**: - The IRS allows deductions for expenses that are ordinary (common in the industry) and necessary (helpful and
appropriate for the business). Common deductions include rent, utilities, salaries, and professional fees.- **Limits on Deductions**: - Certain expenses, such as meals and entertainment, have specific limits (e.g., meals are typically only 50% deductible).
Understanding these limits is vital for effective tax planning.#### 3. Tax CreditsTax credits directly reduce the tax liability, providing a dollar-for-dollar reduction of taxes owed.- **Types of Tax Credits**: - Examples include the Research and Development
(R&D) tax credit, which encourages innovation, and the Work Opportunity Tax Credit (WOTC) for hiring individuals from certain target groups.### Specific Business Entity Taxation#### 1. PartnershipsPartnerships are a popular choice for many businesses
due to their flexible structure.- **Pass-Through Taxation**: - Income is reported on individual partners’ returns, preventing double taxation. However, partners must pay self-employment taxes on their earnings.- **Distributions and Basis**: - When a partner
receives a distribution, it is generally tax-free to the extent of their basis in the partnership. Understanding how basis is calculated is critical for accurate tax reporting.#### 2. CorporationsCorporate taxation can be complex due to double taxation and various
regulations.- **C-Corporations**: - Taxed at the corporate rate, profits are taxed at the entity level, and dividends are taxed at the shareholder level. Corporations can reinvest profits to defer taxation, but shareholders may face immediate tax consequences
upon dividend distribution.
- **S-Corporations**: - Limited to 100 shareholders and certain types of stock, S-Corps can only have eligible domestic individuals as shareholders. They provide the benefits of limited liability and pass-through taxation, making
PART ONE Mathematics Fundamentals and Business Applications
Chapter 1 Review of Arithmetic
Exercise 1.1
A. 1. 12 6 3 12 2 14
2. (38 6) 2 (24 6) 2 18 2 9
3. (7 4)5 2 115 2 55 2 53
4. 53 2 4 15 8 23
5. 6(7 2) 3(5 3) 6(5) 3(2) 30 6 24
20 16 4 1
6. 0.2
15 5 20 5
7. 4(8 5)2 5(3 22 ) 4(3)2 5(3 4) 4(9) 5(7) 36 35 1
8. (3 4 2)2 (2 2 72 ) (12 2)2 (2 2 49)
102 (2 98) 100 96 4
9. 250(1 0.08)10 250(2.158925) 539.73
10. (1 0.04)4 1 1.169859 1 0.17
11. 30 600 2500 12 600 18, 000 2500 7200 8300
12.
1[(1 0.40)(1 0.25)(1 0.05)] 1[(0.6)(0.75)(0.95)] 1[0.4275] 0.5725 0.57
,
13. 15 7 6(2 3) 3
15 7 6(5) 3
15 7 30 3
15 7 10
18
14. 16 2 4 6(4 2)
8 4 6(6)
32 36
68
15. (1 0.7) 4 20 5
(0.3) 4 4
(0.3) 16
15.7
16. 50[(1 0.2)(1 0.175)(1 0.04)]
50[(0.8)(0.825)(0.96)]
50[(0.6336)]
31.68
17. 7a 6[4 (3a 6)]
7a 6[4 3a 6]
7a 6[2 3a]
7a 12 18a
25a 12
18. 6a 4b 2(16 2a b)
6a 4b 32 4a 2b
2a 6b 32
I’ll expand on the topics related to "Taxation of Business Entities," providing a more detailed exploration. This overview will cover fundamental concepts, applications, and implications relevant to the study of business taxation.---### Overview of Business
Entities#### 1. Types of Business EntitiesBusiness entities can be categorized based on ownership structure and tax treatment. Understanding these types is crucial for determining tax obligations and benefits.- **Sole Proprietorships**: - Owned by a single
individual, this is the simplest form of business entity. Income is reported on the owner’s personal tax return (Form 1040, Schedule C), which simplifies tax filing but also means personal liability for debts and obligations.- **Partnerships**: - Consisting of two or
more individuals, partnerships do not pay federal income taxes. Instead, they are considered pass-through entities, meaning income is taxed at the partners' individual rates. Form 1065 is used to report partnership income, while partners receive Schedule K-1 to
report their share on their returns.- **Corporations**: - Corporations are separate legal entities that provide limited liability protection to their owners (shareholders). C-Corporations face double taxation: once at the corporate level on profits and again at the
individual level when dividends are distributed. S-Corporations, on the other hand, are pass-through entities but have restrictions on ownership and number of shareholders.- **Limited Liability Companies (LLCs)**: - LLCs combine the flexibility of partnerships
with the liability protection of corporations. An LLC can choose to be taxed as a sole proprietorship, partnership, or corporation, allowing for strategic tax planning. ### 2. Tax Implications of Each Entity TypeUnderstanding the tax implications of each entity type
is critical for effective business planning.- **Sole Proprietorships**: - Income is taxed at the owner’s individual tax rate. All profits and losses are reported on the owner’s tax return. This simplicity, however, can expose owners to significant personal risk.-
**Partnerships**: - Each partner reports their share of income and losses on their personal returns, allowing for loss deductions. Partners are also subject to self-employment taxes on their share of the income, which can significantly impact tax liability.-
**Corporations**: - C-Corporations are taxed at the corporate tax rate (currently 21%). Dividends are taxed again at the shareholder level. S-Corporations avoid double taxation, but there are restrictions on the number and type of shareholders.- **Limited Liability
Companies (LLCs)**: - By default, single-member LLCs are treated as sole proprietorships for tax purposes, while multi-member LLCs are treated as partnerships. However, they can elect to be taxed as a corporation if beneficial.### Key Tax Concepts#### 1.
Income RecognitionIncome recognition is a fundamental principle in taxation, determining when income must be reported.- **Cash vs. Accrual Accounting**: - Businesses can choose between cash and accrual methods. Cash accounting recognizes income when
received and expenses when paid, making it straightforward. Accrual accounting recognizes income when earned and expenses when incurred, aligning revenue with the period it relates to, but can complicate cash flow management.#### 2. DeductionsDeductions
reduce taxable income, directly impacting tax liability.- **Ordinary and Necessary Expenses**: - The IRS allows deductions for expenses that are ordinary (common in the industry) and necessary (helpful and appropriate for the business). Common deductions
include rent, utilities, salaries, and professional fees.- **Limits on Deductions**: - Certain expenses, such as meals and entertainment, have specific limits (e.g., meals are typically only 50% deductible). Understanding these limits is vital for effective tax
planning.#### 3. Tax CreditsTax credits directly reduce the tax liability, providing a dollar-for-dollar reduction of taxes owed.- **Types of Tax Credits**: - Examples include the Research and Development (R&D) tax credit, which encourages innovation, and the
Work Opportunity Tax Credit (WOTC) for hiring individuals from certain target groups.### Specific Business Entity Taxation#### 1. PartnershipsPartnerships are a popular choice for many businesses due to their flexible structure.- **Pass-Through Taxation**: -
Income is reported on individual partners’ returns, preventing double taxation. However, partners must pay self-employment taxes on their earnings.- **Distributions and Basis**: - When a partner receives a distribution, it is generally tax-free to the extent of their
basis in the partnership. Understanding how basis is calculated is critical for accurate tax reporting.#### 2. CorporationsCorporate taxation can be complex due to double taxation and various regulations.- **C-Corporations**: - Taxed at the corporate rate, profits
are taxed at the entity level, and dividends are taxed at the shareholder level. Corporations can reinvest profits to defer taxation, but shareholders may face immediate tax consequences upon dividend distribution.
- **S-Corporations**: - Limited to 100 shareholders and certain types of stock, S-Corps can only have eligible domestic individuals as shareholders. They provide the benefits of limited liability and pass-through taxation, making
MANUAL
Kelly Halliday
Georgian College
Ali R. Hassanlou
Kwantlen Polytechnic University
Contemporary Business Mathematics
with Canadian Applications
Thirteenth Edition
S. A. Hummelbrunner
Kelly Halliday
Georgian College
Ali R. Hassanlou
Kwantlen Polytechnic University
ISBN 978-0-13-789689-9
.
, Contents
PART ONE Mathematics Fundamentals and Business Applications
Chapter 1: Review of Arithmetic 1
Chapter 2: Review of Basic Algebra 35
Chapter 3: Ratio, Proportion, and Percent 91
Chapter 4: Linear Systems 135
Chapter 5: Cost-Volume-Profit Analysis and Break-Even 193
PART TWO Mathematics of Business and Management
Chapter 6: Trade Discount, Cash Discount, Markup, and Markdown 225
Chapter 7: Simple Interest 263
Chapter 8: Simple Interest Applications 289
PART THREE Mathematics of Finance and Investment
Chapter 9: Compound Interest—Future Value and Present Value 335
Chapter 10: Compound Interest—Further Topics 379
Chapter 11: Ordinary Simple Annuities 415
Chapter 12: Ordinary General Annuities 455
Chapter 13: Annuities Due, Deferred Annuities, and Perpetuities 493
Chapter 14: Amortization of Loans, Including Residential Mortgages 545
Chapter 15: Bond Valuation and Sinking Funds 611
Chapter 16: Investment Decision Applications 669
, I’ll expand on the topics related to "Taxation of Business Entities," providing a more detailed exploration. This overview will cover fundamental concepts, applications, and implications relevant to the study of business taxation.---### Overview of Business
Entities#### 1. Types of Business EntitiesBusiness entities can be categorized based on ownership structure and tax treatment. Understanding these types is crucial for determining tax obligations and benefits.- **Sole Proprietorships**: - Owned by a single
individual, this is the simplest form of business entity. Income is reported on the owner’s personal tax return (Form 1040, Schedule C), which simplifies tax filing but also means personal liability for debts and obligations.- **Partnerships**: - Consisting of two
or more individuals, partnerships do not pay federal income taxes. Instead, they are considered pass-through entities, meaning income is taxed at the partners' individual rates. Form 1065 is used to report partnership income, while partners receive Schedule K-1
to report their share on their returns.- **Corporations**: - Corporations are separate legal entities that provide limited liability protection to their owners (shareholders). C-Corporations face double taxation: once at the corporate level on profits and again at the
individual level when dividends are distributed. S-Corporations, on the other hand, are pass-through entities but have restrictions on ownership and number of shareholders.- **Limited Liability Companies (LLCs)**: - LLCs combine the flexibility of
partnerships with the liability protection of corporations. An LLC can choose to be taxed as a sole proprietorship, partnership, or corporation, allowing for strategic tax planning. ### 2. Tax Implications of Each Entity TypeUnderstanding the tax implications of
each entity type is critical for effective business planning.- **Sole Proprietorships**: - Income is taxed at the owner’s individual tax rate. All profits and losses are reported on the owner’s tax return. This simplicity, however, can expose owners to significant
personal risk.- **Partnerships**: - Each partner reports their share of income and losses on their personal returns, allowing for loss deductions. Partners are also subject to self-employment taxes on their share of the income, which can significantly impact tax
liability.- **Corporations**: - C-Corporations are taxed at the corporate tax rate (currently 21%). Dividends are taxed again at the shareholder level. S-Corporations avoid double taxation, but there are restrictions on the number and type of shareholders.-
**Limited Liability Companies (LLCs)**: - By default, single-member LLCs are treated as sole proprietorships for tax purposes, while multi-member LLCs are treated as partnerships. However, they can elect to be taxed as a corporation if beneficial.### Key
Tax Concepts#### 1. Income RecognitionIncome recognition is a fundamental principle in taxation, determining when income must be reported.- **Cash vs. Accrual Accounting**: - Businesses can choose between cash and accrual methods. Cash accounting
recognizes income when received and expenses when paid, making it straightforward. Accrual accounting recognizes income when earned and expenses when incurred, aligning revenue with the period it relates to, but can complicate cash flow
management.#### 2. DeductionsDeductions reduce taxable income, directly impacting tax liability.- **Ordinary and Necessary Expenses**: - The IRS allows deductions for expenses that are ordinary (common in the industry) and necessary (helpful and
appropriate for the business). Common deductions include rent, utilities, salaries, and professional fees.- **Limits on Deductions**: - Certain expenses, such as meals and entertainment, have specific limits (e.g., meals are typically only 50% deductible).
Understanding these limits is vital for effective tax planning.#### 3. Tax CreditsTax credits directly reduce the tax liability, providing a dollar-for-dollar reduction of taxes owed.- **Types of Tax Credits**: - Examples include the Research and Development
(R&D) tax credit, which encourages innovation, and the Work Opportunity Tax Credit (WOTC) for hiring individuals from certain target groups.### Specific Business Entity Taxation#### 1. PartnershipsPartnerships are a popular choice for many businesses
due to their flexible structure.- **Pass-Through Taxation**: - Income is reported on individual partners’ returns, preventing double taxation. However, partners must pay self-employment taxes on their earnings.- **Distributions and Basis**: - When a partner
receives a distribution, it is generally tax-free to the extent of their basis in the partnership. Understanding how basis is calculated is critical for accurate tax reporting.#### 2. CorporationsCorporate taxation can be complex due to double taxation and various
regulations.- **C-Corporations**: - Taxed at the corporate rate, profits are taxed at the entity level, and dividends are taxed at the shareholder level. Corporations can reinvest profits to defer taxation, but shareholders may face immediate tax consequences
upon dividend distribution.
- **S-Corporations**: - Limited to 100 shareholders and certain types of stock, S-Corps can only have eligible domestic individuals as shareholders. They provide the benefits of limited liability and pass-through taxation, making
PART ONE Mathematics Fundamentals and Business Applications
Chapter 1 Review of Arithmetic
Exercise 1.1
A. 1. 12 6 3 12 2 14
2. (38 6) 2 (24 6) 2 18 2 9
3. (7 4)5 2 115 2 55 2 53
4. 53 2 4 15 8 23
5. 6(7 2) 3(5 3) 6(5) 3(2) 30 6 24
20 16 4 1
6. 0.2
15 5 20 5
7. 4(8 5)2 5(3 22 ) 4(3)2 5(3 4) 4(9) 5(7) 36 35 1
8. (3 4 2)2 (2 2 72 ) (12 2)2 (2 2 49)
102 (2 98) 100 96 4
9. 250(1 0.08)10 250(2.158925) 539.73
10. (1 0.04)4 1 1.169859 1 0.17
11. 30 600 2500 12 600 18, 000 2500 7200 8300
12.
1[(1 0.40)(1 0.25)(1 0.05)] 1[(0.6)(0.75)(0.95)] 1[0.4275] 0.5725 0.57
,
13. 15 7 6(2 3) 3
15 7 6(5) 3
15 7 30 3
15 7 10
18
14. 16 2 4 6(4 2)
8 4 6(6)
32 36
68
15. (1 0.7) 4 20 5
(0.3) 4 4
(0.3) 16
15.7
16. 50[(1 0.2)(1 0.175)(1 0.04)]
50[(0.8)(0.825)(0.96)]
50[(0.6336)]
31.68
17. 7a 6[4 (3a 6)]
7a 6[4 3a 6]
7a 6[2 3a]
7a 12 18a
25a 12
18. 6a 4b 2(16 2a b)
6a 4b 32 4a 2b
2a 6b 32
I’ll expand on the topics related to "Taxation of Business Entities," providing a more detailed exploration. This overview will cover fundamental concepts, applications, and implications relevant to the study of business taxation.---### Overview of Business
Entities#### 1. Types of Business EntitiesBusiness entities can be categorized based on ownership structure and tax treatment. Understanding these types is crucial for determining tax obligations and benefits.- **Sole Proprietorships**: - Owned by a single
individual, this is the simplest form of business entity. Income is reported on the owner’s personal tax return (Form 1040, Schedule C), which simplifies tax filing but also means personal liability for debts and obligations.- **Partnerships**: - Consisting of two or
more individuals, partnerships do not pay federal income taxes. Instead, they are considered pass-through entities, meaning income is taxed at the partners' individual rates. Form 1065 is used to report partnership income, while partners receive Schedule K-1 to
report their share on their returns.- **Corporations**: - Corporations are separate legal entities that provide limited liability protection to their owners (shareholders). C-Corporations face double taxation: once at the corporate level on profits and again at the
individual level when dividends are distributed. S-Corporations, on the other hand, are pass-through entities but have restrictions on ownership and number of shareholders.- **Limited Liability Companies (LLCs)**: - LLCs combine the flexibility of partnerships
with the liability protection of corporations. An LLC can choose to be taxed as a sole proprietorship, partnership, or corporation, allowing for strategic tax planning. ### 2. Tax Implications of Each Entity TypeUnderstanding the tax implications of each entity type
is critical for effective business planning.- **Sole Proprietorships**: - Income is taxed at the owner’s individual tax rate. All profits and losses are reported on the owner’s tax return. This simplicity, however, can expose owners to significant personal risk.-
**Partnerships**: - Each partner reports their share of income and losses on their personal returns, allowing for loss deductions. Partners are also subject to self-employment taxes on their share of the income, which can significantly impact tax liability.-
**Corporations**: - C-Corporations are taxed at the corporate tax rate (currently 21%). Dividends are taxed again at the shareholder level. S-Corporations avoid double taxation, but there are restrictions on the number and type of shareholders.- **Limited Liability
Companies (LLCs)**: - By default, single-member LLCs are treated as sole proprietorships for tax purposes, while multi-member LLCs are treated as partnerships. However, they can elect to be taxed as a corporation if beneficial.### Key Tax Concepts#### 1.
Income RecognitionIncome recognition is a fundamental principle in taxation, determining when income must be reported.- **Cash vs. Accrual Accounting**: - Businesses can choose between cash and accrual methods. Cash accounting recognizes income when
received and expenses when paid, making it straightforward. Accrual accounting recognizes income when earned and expenses when incurred, aligning revenue with the period it relates to, but can complicate cash flow management.#### 2. DeductionsDeductions
reduce taxable income, directly impacting tax liability.- **Ordinary and Necessary Expenses**: - The IRS allows deductions for expenses that are ordinary (common in the industry) and necessary (helpful and appropriate for the business). Common deductions
include rent, utilities, salaries, and professional fees.- **Limits on Deductions**: - Certain expenses, such as meals and entertainment, have specific limits (e.g., meals are typically only 50% deductible). Understanding these limits is vital for effective tax
planning.#### 3. Tax CreditsTax credits directly reduce the tax liability, providing a dollar-for-dollar reduction of taxes owed.- **Types of Tax Credits**: - Examples include the Research and Development (R&D) tax credit, which encourages innovation, and the
Work Opportunity Tax Credit (WOTC) for hiring individuals from certain target groups.### Specific Business Entity Taxation#### 1. PartnershipsPartnerships are a popular choice for many businesses due to their flexible structure.- **Pass-Through Taxation**: -
Income is reported on individual partners’ returns, preventing double taxation. However, partners must pay self-employment taxes on their earnings.- **Distributions and Basis**: - When a partner receives a distribution, it is generally tax-free to the extent of their
basis in the partnership. Understanding how basis is calculated is critical for accurate tax reporting.#### 2. CorporationsCorporate taxation can be complex due to double taxation and various regulations.- **C-Corporations**: - Taxed at the corporate rate, profits
are taxed at the entity level, and dividends are taxed at the shareholder level. Corporations can reinvest profits to defer taxation, but shareholders may face immediate tax consequences upon dividend distribution.
- **S-Corporations**: - Limited to 100 shareholders and certain types of stock, S-Corps can only have eligible domestic individuals as shareholders. They provide the benefits of limited liability and pass-through taxation, making
