tax - definition, types, provisions under Income Tax Act to save tax, Minimization of tax using Linear Programming with examples

1. Investments and Tax Savings
Subject: Operations Research
Suresh Sundar

2. Tax
What?
A fee charged/levied upon an
individual/organization by the Government at
National/State/Local level on a
product/income/activity
Why?
To finance various public and government
expenditures(infrastructure, police, military,
education, public welfare)

3. Types
Direct taxes:
Cannot be transferred to another
person/organization (taxpayer has to bear it)
Eg: income, corporate, wealth
Indirect taxes:
Can be transferred to another
person/organization
Eg: sales, service, excise

4. Tax Deductions and Exemptions
BASIS FOR COMPARISON DEDUCTION EXEMPTION
Meaning Deduction means subtraction i.e. an amount that is eligible to reduce taxable
income.
Exemption means exclusion, i.e. if certain income is exempt from tax then it will
not contribute to the total income of a person.
What is it? Concession Relaxation
Concept The amount of deduction is first included in the gross income and then deducted
from it to arrive at the net income.
The exempted income is not considered as a part of total income, the whole
amount is an exemption for the taxpayer.
Income is Tax deductible Tax free
Objective To promote savings and investments of the general public. To boost that particular section in which tax is exempted.
Sections Section 80 C to 80 U deals with deduction Section 10 deals with exemptions
Allowable to Specific persons All the persons
Conditional Yes No

5. For firms, domestic companies and corporates flat 30% is
charged with additional surcharges if applicable.

6. Exemptions under Section 10
• House Rent Allowance
• Leave Travel Allowance
• Transport Allowance
• High Altitude Allowance
• Special Compensatory Allowance
• Agricultural income

7. Deductions under Section
80C,CCC,CCD(max 1,50,000)
• EPF, PPF, NSC
• LIC premium
• Home loan principle
• Children tuition fees
• Tax-free FD, PO-Time Deposits
• Sukanya Samriddhi Yojana
• Medical insurance
Section 80CCD(1): NPS (max 1,00,000)
Section 80CCD(2): NPS (additional 50,000)
Section 80D + Section 80CCD = 2,00,000

8. Other sections
• 80CCG- RGESS (50% of amt. invested or 25,000
whichever is lower, GI<12 lakhs)
• 80D- Medical insurance premium (max of 60,000 plus
5,000 for preventive check-up
• 80E- education loan for higher studies (no limit, upto
8years)
• 80EE- Interest on home loan for 1st time buyers(50,000)
• 80G- Donation towards social causes(100%)
• 80GG- House rent paid
• 80TTA- Interest on SB A/c (max10,000)
• 24- Accrued interest of home loan (upto 2,00,000)

9. Linear programming
‘Linear’ – linear relationship among variables in
a model.
Change in one variable will cause a proportional
change in another variable
‘Programming’ – mathematical modelling to find
desired optimum results (economic allocation of
limited resources by choosing a particular
course of action)

10. What?
• A mathematical technique to find the best
possible solution or optimization(maximizat
ion/minimization) of a linear function with
certain linear inequalities(constraints) relating
to some situation.
• A mathematical model for allocating limited
resources to obtain maximum profit or
minimum cost

11. Why and How?
• Objectives of business: Maximize the profits
Minimize the costs
• LP uses linear algebraic relationships to
represent firm’s decisions, given a business
objective and a resource constraints
• Model Formulation Steps:
1)Clearly define decision variables
2)Construct the objective function
3)Formulate the constraints

12. Methods To Solve LPP
• The Graphical Method (Minimization &
Maximization)
• The Simplex Method(Minimization &
Maximization)
1)Two Phase Model
2)The Big M Method
For Minimization

13. Standardization
TYPES OF CONSTRAINTS EXTRA VARIABLE NEEDED
Less than or equal to (≤) A slack variable added
Greater than or equal to (≥) A surplus variable is subtracted & an
artificial variable is added
Equal to (=) Only an artificial variable is added
Slack Variable: Represents the quantity of unused resource
Surplus Variable : Represents amount by which solution exceed a resource

14. The Simplex Method
• It examines corner points of the feasible
region, using matrix row operations, until an
optimal solution is found
• Minimization : E.g :Minimizing the cost of
production, time, taxes etc
• Maximization E.g :Maximizing the profits,
return on investment etc

15. Case 1
• Mr Raghu is working in a private firm and his CTC was Rs.5,50,000.
His total annual expenses were Rs.3,00,000 and he realized that he
has to pay Rs.22,500 as Income Tax every year as per the new tax
slabs, since he is keeping all his savings in the bank account itself.
He went to an investment consultant to get advice about how to
save the tax. The consultant made him aware of the different
investment options and avenues available in which a person can
invest to save taxes considerably. And also considering his age,
savings, expenses, risk bearing capacity he suggested an investment
policy to Raghu which is as follows.
• Total savings amount available for investment is Rs.2,50,000
• Amount to be kept in savings account for emergency cash purpose
should be Rs.50,000
• Atleast 40% of the remaining amount should be invested in Equity
Linked Savings Schemes as it gives more returns.

16. • Only Rs.50,000 or less should be invested in tax free bank
deposits or Term deposits
• The Government norms as per section 80C of IT act is one can
get a tax exemption for Rs.1,50,000 in all these avenues and
an additional Rs.50,000 by investing in New Pension Scheme.
• How can Raghu invest in these investment avenues so that his
returns are maximum by minimizing the taxes?
Tax saving scheme ROI (%)
ELSS 18
ULIP 10
NPS 9.5
FD 8

17. Objective function:
MaxZ=0.18X1+0.10X2+0.095X3+0.08X4
Subject to constrains,
X1+X2+X3+X4=2,00,000
X1≥60,000
X4≤50,000
X1, X2, X3, X4≥0

18. Case 2
Mrs. Shruthi’s annual income is Rs.8,00,000 and
she has a 5 year old daughter. She wants to
invest her excess money after expenses in
different investment options as shown below in
order to reduce maximum taxes.
Scheme % Tax reduction
Housing loan 50
Mutual Funds 20
Sukanya Samriddhi Yogana 15
LIC 15

19. Her savings after expenses is 5,00,000. she
doesn’t want to invest not more than 1,00,000
including SSY and LIC. The maximum investment
limit under Section 80C for the last three
investments should be 1,50,000. How can she
diversify her savings in order to get maximum
tax reduction?

20. Objective function:
MaxZ= 0.50X1+0.20X2+0.15X3+0.15X4
Subject to constraints,
X1+X2+X3+X4= 5,00,000
X3+X4≤1,00,000
X2+X3+X4≤1,50,000
X1, X2, X3, X4≥0

21. Case 3
The following data shows the annual income and
expenditure of a person and how to save maximum
tax possible by making use of various deductions
and exemptions
CTC- 10,00,000
Expenses- 3,00,000
Tax free limit- 2,50,000
Taxable income(before deductions)-
7,50,000(@20%)
Tax- 1,50,000

22. Investments
Section 80C:
Home loan principle- 1,00,000
Employee Provident Fund- 50,000
Section 80CCD:
Contribution to NPS- 50,000
Section 80CCG:
RGESS- 50,000 (50% ie 25,000 is eligible for dedn.)
Section 80D:
Medical insurance premium- 55,000

23. Investments
Section 10:
TA=1600*12=19,200
HRA=5000*12=60,000
Section 24:
Housing loan interest- 2,00,000
(principle- 40lakh @9.55%pa for 20 years)
Section 80TTA:
Savings account- 1,90,800
Dedn. Of interest 9,540 (@5% pa)
Taxable income (after deductions)- 1,90,800
Tax- 38,160

24. Thank You