CFP - Module 1_IIFP_Students

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MODULE POSITIONINGMODULE OS ON NG

Foundation Module for your programme• Foundation Module for your programme

• Understand the process of financial planning

• Preview into the world of a financial planner

S k i f h h i li bj i h • Sneak view of the other specialist subjects in the course

• Obtain the beginner level understanding of specialist bj tsubjects

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OUR STRATEGYOU S EGY

Understand the subject• Understand the subject

• Concentrate on TVM sums

• Understand basics of specialist subjects

U d d li i f h b i k l d• Understand application of the basic knowledge

• Be equipped with Code of Ethics

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FINANCIAL FINANCIAL FINANCIAL FINANCIAL FIN N I L FIN N I L PLANNINGPLANNINGFIN N I L FIN N I L PLANNINGPLANNING

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FINANCIAL PLANNING -F N N L L NN NG DEFINITION

• Systematic, scientific and disciplined process to help people achieve their financial goals

• Relationship focused process• Relationship focused process

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PROFESSIONAL PROFESSIONAL PROFESSIONAL PROFESSIONAL PROFESSIONAL PROFESSIONAL WORLD OF A WORLD OF A

PROFESSIONAL PROFESSIONAL WORLD OF A WORLD OF A WORLD OF WORLD OF

FINANCIAL PLANNERFINANCIAL PLANNERWORLD OF WORLD OF

FINANCIAL PLANNERFINANCIAL PLANNER

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Work of Financial Planner• Financial planner helps people achieve their financial

goals by:

Work of Financial Planner

goals by:– Making informed decisions about their money and

how it can be used to best advantage– Develop a sound financial plan covering all aspects

of their financial well being (from wealth creation to wealth protection)(from wealth creation to wealth protection)

– Choose products that meet their specific needs; and

h f l l – Review their financial situation on regular basisand revise their financial plan as necessary

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Work of Financial PlannerW f FFinancial planner is similar to the medical general practitionersgeneral practitioners

Caring for the financial health of the clientCaring for the financial health of the client

Establishing long term, trusting relationship with the clients,

A N b f f i l ibiliti d A Number of professional responsibilities and obligations are conferred

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Regulatory FrameworkRegulatory Framework• The financial planning business is regulated by a number of

laws principally laws, principally – the Securities (Contracts) Regulation Act, 1956– the SEBI Act, 1992 for securities trading,– the Insurance Act, 1938– the Insurance Regulatory and Development Authority

Act, 1999 for life and general insurance– the Consumer Protection Act, 1986 for protecting

consumers against misconduct, misrepresentation, and unfair trade practices.

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Regulatory Framework– Business will also be regulated by the various codes of

practice

mainly the FPSB’s code of practice and the life and general insurance codes of practice.

Scope of Servicesp• The comprehensive or holistic approach to financial planning

- initial analysis of the client’s total financial well-being –b th d i f tboth now and in future

• In addition to investments, other areas covered are estate planning, insurance risk management, income and expenditure, retirement benefits, wealth accumulation and taxation

• Consumer may request for a limited service

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f Scope of ServicesTh l t l l t bli h t th t f • The planner must clearly establish at the commencement of dealing with the client that a limited service is being provided

• If the client has requested a limited service,the financial planner should obtain such a request in writing from the client.

• Independent advisory services p y

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Remuneration ModelsRemuneration ModelsService Fees :

Clients pays a fixed fee for the provision of advice and ongoing reviews as agreed between the two parties.

Commissions :

Commission payments represent a process of ‘selling’ investments; that is, a process designed to convince the client that he/she should invest in particular investment

d products.

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Categories of Potential ClientsCategories of Potential Clients

B d C t A GBroad Category Age GroupYoung Adult 18-25Young Family 25-35g yMature Family 35-45Empty Nesters 45-55S lf E l d /B i Self Employed /Business ownerHigh- Income earnerPre-retiree/ retiree 55-65+

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Relationship with other Relationship with other professionals

Chartered Accountants;

Attorneys;

Lawyers;

Insurance Agents;

Investment Agents;g

Brokers, etc..

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Professionalism in Financial PlanningProfessionalism in Financial Planning• Features that characterize the membership of a profession:

– A confidential relationship between the professional advisor and his/her client that is recognized and protected in law;protected in law;

– A relationship of special trust between the professional advisor and his/her client;advisor and his/her client;

– A high level of expertise in the professional advisor i d h h i l d f d i d acquired through an involved process of education and

apprenticeship.

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Professionalism in Financial PlanningProfessionalism in Financial Planning

St i t t d d d l ti f d i i t – Strict standards and regulations for admission to practice of the profession;

– Strict standards concerning educational qualifications to qualify for professional practice; and

– The more recent requirement for continuing professional education linked to a person’s continuing qualification to practice

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Professionalism in Financial PlanningProfessionalism in Financial Planning

P f i li i li • Professionalism implies:

– Pride in work

– Commitment to quality

– Dedication to the interests of the client, and

A i d i t h l– A sincere desire to help

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Professional language of a rofess onal language of a financial plan

A fi i l l i th bl i t f th li t t • A financial plan is the blueprint for the client to proceed from their current financial position to a more desirable position in the future.p

• Professionalism in financial planning includes the l d f l i hi h h l i style and tone of language in which the plan is

written.

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Successful Financial Planner -Successful Financial Planner Qualities

T h i l kill • Technical skills:

There is an achievement of technical competencies through a course such as Certified Financial Planner Professional Education Programme.

In addition, commitment to ongoing education and professional development as a means of maintaining and improving technical competencies.

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Successful Financial Planner -Qualities

• People Skills :

Qualities

Strong interpersonal skills

‘P l kill ’ i li i l h i f i • ‘People skills’ - capacity to listen intently to the information which is being conveyed by the client.

• Empathise with clients at certain times as the client explains difficulties, problems and fears

• High standard of business ethics

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SIX STEP PROCESS

• Establishing client planner relationship• Establishing client planner relationship

• Gathering client data and determining goals and objectives

• Identification of financial problems

• Preparation of written alternatives and recommendationsp

• Implementation of agreed recommendations

• Review and revision of plan

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THE SIX STEPSTHE SIX STEPSTHE SIX STEPSTHE SIX STEPS

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Establishing Client-Planner Establ sh ng l ent lanner relationship

• Important step in the process

• Developing trust

• Preparing for the meetingp g g

• Explaining your role in the context of the client

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Establishing Client-Planner Establ sh ng l ent lanner relationship (contd..)

• Define the scope of the engagement:

Id tif th i t b id d– Identify the services to be provided

– Disclose the compensation arrangements

– Determining the clients and planners responsibilities

– Establish the duration of the engagement

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Establishing Client-Planner Establ sh ng l ent lanner relationship (contd..)

– Provide additional information necessary to define or limit the scope.

– Complaint handling mechanisms – making the client aware of the same

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Gathering client dataGather ng cl ent data

• Important to collect all relevant data required for the • Important to collect all relevant data required for the process

• Qualitative and Quantitative data collected

• Data collection forms used:– Personal details– Income and expenditure details

A t d li biliti d t il– Assets and liabilities details– Insurance details

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Goal SettingGoal Sett ng

• Help the client in setting milestones

• Prioritizing the client’s goals

• Distinguishing between needs and wants of the client

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Goal Setting (contd..)Goal Sett ng (contd..)

• Important to factor in the following:

Cli t’ ttit d l d t ti– Client’s attitudes, values and expectations

– Risk tolerance

– Time horizon

• Collection of supporting documents and records

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Analysis of Datanalys s of Data

Understand the collected information• Understand the collected information

A l th bl b th d i li d• Analyze the problems – both express and implied

S d i h i il bl• Support advice, where no expertise available

• Contact client, where information collected is not sufficient

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Developing StrategiesDevelop ng Strateg es

• Develop alternativesDevelop alternatives

U h i d d i d l i i• Use research, own or independent, in developing strategies

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Presenting financial planresent ng f nanc al plan

• Discuss the draft plan with the client

• Support the presentation with diagrams and charts, wherever necessaryy

• Presentation to make the client understand the plan• Presentation to make the client understand the plan

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Implementing the financial p gplan

• Devise an action plan to proceed

• Help the client in selection of the products

• Co-ordinate with other professionals such as accountants, attorneys, investment advisors, wherever necessary

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Monitoring the financial Mon tor ng the f nanc al plan

• A continuous process

R i th f th l• Review the progress of the plan

• Any changes in the clients circumstances to be reviewed and incorporatedincorporated

• Recommendations to accommodate any changes or new goals

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GENERAL PRINCIPLESGENERAL PRINCIPLESGENERAL PRINCIPLESGENERAL PRINCIPLES

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REGULATORY REQUIREMENTSREGULATORY REQUIREMENTS

Public confidence essential even for trust• Public confidence – essential even for trust

• RBI, SEBI & IRDA – three main apex bodies acting as regulatorsregulators

• No direct regulation for CFPs

• Governed by the FPSB

H t bid b th d f thi f f i l • Have to abide by the code of ethics for professional conduct

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CODE OF ETHICSCODE OF ETHICSCODE OF ETHICSCODE OF ETHICS

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ETHIC OF INTEGRITYE H OF N EG Y

• Misleading advertising, promotional activities and representation of authoritiesrepresentation of authorities

Responsibilities regarding funds and properties of clients• Responsibilities regarding funds and properties of clients

N t t t t b d i ti th i• No statements to be made misrepresenting the services

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ETHIC OF OBJECTIVITYE H OF OBJE V Y

• Exercise reasonable and prudent professional judgement

• Adequate disclosures

• Adequate care to be exercised for conflict of interests

• Annual disclosure requirements

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ETHIC OF COMPETENCEE H OF OM E EN E

• Be informed of the developments in financial planning

• Offer advice in areas of competence

• Reasonable standards for appointment of representatives

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ETHIC OF FAIRNESSE H OF F NESS

P ti li t i f d b t th • Prospective clients informed about the company

• Compensation shall be fair and reasonable

• Rules to be followed by members in industry too

• Disclosure requirements to be maintained with employers

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ETHIC OF E H OF CONFIDENTIALITY

• Clients details to be kept confidential, some exceptions provided

• Members doing business owes responsibility to act in good faith to their employersfaith to their employers

• Member liable to hand over to the client documents of the • Member liable to hand over to the client, documents of the client, when asked for

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ETHIC OF E H OF PROFESSIONALISM

• Respect for other financial planning professionals

• Maintain professional indemnity insurance

• Members should not misstate their authority to represent the FPSBthe FPSB

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ETHIC OF DILIGENCEE H OF D L GEN E

• Services to be provided on a timely basis• Services to be provided on a timely basis

• Sufficient information to be collected

• Suitable strategies to be developed

• All significant recommendations to be made in writingg g

• Implementation to be ensured on a timely manner

• Establish and maintain written policies and procedures for effective control and conduct of its business

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ETHIC OF COMPLIANCEE H F L E

All services to be performed services in accordance with • All services to be performed services in accordance with applicable laws, rules and regulations

• Co operate with the FPSB in respect of any investigations• Co-operate with the FPSB in respect of any investigations

• All applicable post certification requirements to be compliedcomplied

• Effective system of supervision of all representative activities performance and trainingactivities, performance and training

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LECTURE 2LECTURE 2LECTURE 2LECTURE 2

TIME VALUE OF MONEYTIME VALUE OF MONEYTIME VALUE OF MONEYTIME VALUE OF MONEYTIME VALUE OF MONEYTIME VALUE OF MONEYTIME VALUE OF MONEYTIME VALUE OF MONEY

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L f h i f f th f t f • Loss of purchasing power of money: one of the factors for the interest compensation

• Interest types – Simple and Compound

• Simple Interest – Interest paid as per the period nominated p p p pfor the instrument

• Compounding – takes into account growth on growth – the Compounding takes into account growth on growth the multiplier effect

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• Simple Interest:• Simple Interest:

Ram invests Rs. 10,000 in a bank FD which pays him 8% interest on a simple interest basis for 3 years.p y

Ram would receive Rs. 800 per year towards interest on the fixed deposit, even if Ram does not withdraw the interest on the deposit at maturity Ram would receive a total on the deposit, at maturity Ram would receive a total amount of:

Rs. 12,400 – Principal: Rs. 10,000 , p ,Interest: Rs. 2,400 (800 * 3 years)

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• Compound Interest:• Compound Interest:

In the above example, if the bank offered 8% p.a. on a compounded basis, if Ram chooses to receive the total p ,interest on maturity, then the bank would pay Ram Rs. 12,597 – Principal: Rs. 10,000

Interest: Rs. 2,597

The additional amount of Rs. 197 (2,597 – 2,400) is on account of the compounding over the three years.

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• Time Value of Money:

– Singular Cash Flows

– Regular Cash Flows

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Si l C h Fl• Singular Cash Flows:

– Future Value

– Present Value

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• Future Value:

– Calculation of Future ValueCalculation of Future Value• FV = PV *[(1+i)^n]

Where:Where:FV = Future ValuePV = Present valueI = Interest RateI = Interest RateN = No. of periods

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E l 1• Example 1:

Abhay deposits Rs. 5,000 in a bank, which pays 8% interest compounded annually How much will the deposit grow after 6 compounded annually. How much will the deposit grow after 6 years?

• Solution:– PV = Rs. 5,000,– Interest = 8%– Period = 6 years– FV = ?FV ?Calculate using the formula or using the financial calculator

FV = 6,298.56A

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• Example 2:• Example 2:

If Ajay borrows Rs. 20,000 @ 10% p.a. compounded half yearly, how much amount will Ajay have to pay back after 4 years?

Solution:

- PV = Rs. 20,000- Interest = 10% p.a. or 5% per half year- Period = 4 years or 8 half years- FV = ?FV = 29 549FV = 29,549

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I t t i t t b• Important points to remember:

– All the four parameters should be in equal terms

– Convert the period or the rate of interest, wherever necessary

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OTHER PROBLEMSOTHER PROBLEMS

R h l i st d Rs 28000/ i d sit f 5 • Rahul invested Rs. 28000/-in a deposit for 5 years. Rate of interest offered to him is 12% per annum, compounding monthly for 1st 3 years and

di t l f t 2 Wh t compounding quarterly for next 2 years. What maturity amount will he get?

• Ans : FV = 50748 73• Ans : FV = 50748.73

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• Mr Gupta aged 57 years has recently booked profit by • Mr. Gupta, aged 57 years, has recently booked profit by selling some shares that he purchased long time back and got Rs. 283000/-. A Financial Planner suggested him to put the money in a bank FD’s at this age so that the corpus doesn’t erode because of stock market volatility The doesn t erode because of stock market volatility. The present ROI in bank FD of 3 years 6 months is 9.75%p.a. compounded quarterly. Please calculate how much he will get on maturity?

• Ans : FV = Solve=396471.54

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• Sanjay has won a lottery of Rs 10 lakhs and a Bank • Sanjay has won a lottery of Rs. 10 lakhs and a Bank approached him to get this deposit from him in the form of a Bank FD. The Bank offered him 2 options, i) to deposit the money for 5 years at 9% p.a. compounded quarterly and ii) to deposit the money for 5 years at 10%p a compounded to deposit the money for 5 years at 10%p.a. compounded half yearly. Sanjay could not make out which option is best.

Ans. : FV = 15,60,509.20 @ 9%FV = 16,28,894,.62 @ 10%

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Ram invests Rs 10 000/ for 3 years in a fixed term deposit • Ram invests Rs. 10,000/-for 3 years in a fixed term deposit offering interest @ 6% p.a. compounding Half yearly. After the end of 3 years Ram invests whole maturity amount of this term deposit into another term deposit for further 2 p pyears @ 8 % p.a. compounded quarterly. How much will be the maturity amount Ram will get?

• Ans : FV = solve = 13,990.22

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PRESENT VALUE

• Present Value:• Present Value:

– Calculation of Present Value• PV = FV / [(1+i)^n]PV = FV / [(1+i) n]

Where:FV = Future ValuePV = Present valueI = Interest RateN = No. of periods

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• Example 1:• Example 1:

Ashok wishes to get Rs. 100,000 after 5 years from now. He expects to get an annual return of 9% compounding annually, what amount should he invest today?amount should he invest today?Solution:- FV = Rs. 100,000- Period = 5 years- Interest = 9%- PV = ??

Calculate using the formula or the financial calculatorCalculate using the formula or the financial calculator

PV = Rs. 64,993

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• Example 2:• Example 2:

Ram has taken a loan from Lakshman. Ram gives Lakshman 2 options of giving back the money. He asks Ram to take Rs. 50,000 today or Rs 70 000 in 6 years time Assuming that Rs 50 000 can today or Rs. 70,000 in 6 years time. Assuming that Rs. 50,000 can be invested for 6 years @ 6% p.a. compounded annually. Evaluate which option is better for Ram?

Solution:Solution:

There are two ways to solve this problem, either by using a PV approach or by using FV approach.

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• PV approach:• PV approach:

Parameters:- FV = Rs 70 000FV = Rs. 70,000- Interest = 6% - Period = 6 years- PV = ??

PV = Rs. 49,347

Compare this PV with Rs. 50,000 – whichever is higher is a better option for Ram – here, option A

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• FV approach:• FV approach:Parameters:- PV = Rs. 50,000- Interest = 6% Interest = 6% - Period = 6 years- FV = ??FV = Rs. 70,926,

Compare this FV with Rs. 70,000 – whichever is higher is a better option for Ram – here, option A

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• Complex Example:• Complex Example:

Mr. Shah has booked a new flat in an under construction project. As per the payment schedule, he has to pay a fee p j p p y , p yof Rs. 100,000 today. Then Rs. 1.75 lacs after 1 year, Rs. 2.5 lacs after 2 years and Rs. 3.25 lacs after 3 years. He is interested in setting the required amount today itself in the form of a bank FD. You are required to advise how much qshould he invest if the returns are 8% for 1 year, 8.5% for 2 years and 9% for 3 years, on a quarterly compounding basis?

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• Solution:• Solution:

Problem to be broken down into 3 parts:

Part 1:

FV = 175,000Interest = 2% (8% p a )Interest = 2% (8% p.a.)Period = 4 periods (1 year)PV = ??Calculate PV for Part I

PV = 161,673

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Part 2:Part 2:

FV = 250,000Interest = 2 125% (8 5% p a )Interest = 2.125% (8.5% p.a.)Period = 8 periods (2 years)PV = ??

Calculate PV for Part II

PV = 2,11,292.19

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Part 3:Part 3:FV = 325,000Interest = 2.25% (9% p.a.)Period = 12 periods (3 years)PV = ??Calculate PV for Part III

PV = 248 841 92PV = 248,841.92

Total PV = Part I + Part II + Part III = Rs. 721,807.05

T l b i d i Fi d D i d R 721 807 05Total amount to be invested in Fixed Deposit today = Rs. 721,807.05

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OTHER PROBLEMSO HE OBLEMS

Rahul wants to save for his foreign trip which he plans to • Rahul wants to save for his foreign trip which he plans to take after 2 years from now. He expects this trip will cost him Rs.3,50,000/-at that time. How much should he set aside for this trip now, if ROI is 10% p.a. compounded p , p pyearly?

Ans : PV = 289256.19

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S il is ff d Rs 80000/ ft 7 s Wh t • Sunil is offered Rs 80000/- after 7 years. What amount shall he accept today in “lieu” of this amount if available ROI is 10% compounded Half Y l d i t d t i th h t Yearly and is expected to remain same throughout this period of 7years?

Ans : PV 40 405 436• Ans : PV = 40,405.436

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• Mr Sharma has got his son admitted to a college today where he • Mr. Sharma has got his son admitted to a college today, where he has to pay a fee of Rs. 1 lakh today i.e. at the time of admission. Then Rs 1.75 lakhs after 1 year, Rs. 2.5 lakhs after 2 years and Rs.3.25 lakhs after 3 years. He wants to set aside the amount required today itself in the form of Bank FDR So how much he required today itself in the form of Bank FDR. So how much he needs to put aside today if ROI is 8% for 1 year, 8.5% for 2 years and 9% for 3 years, all compounded quarterly?

Ans : PV = 161672.94 @ 8%PV = 2,11,292.19@ 9 % PV = 2,48,841.92@ 9%

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• The Management of a Company knows that they will have to • The Management of a Company knows that they will have to pay Gratuity of approx Rs.20 Lakhs 5 years from now, to their employees retiring at the time and approx. Rs 14 lakhs 7 years from now, for employees retiring in that year. The company presently having surplus cash flows wants to The company, presently having surplus cash flows, wants to put aside money today for that liability which is sure to arise. If the rate of interest available in market is 10% compounded quarterly, how much money should be put aside today to meet these liabilities?today to meet these liabilities?

• Ans : PV = 12 20 541 88Ans : PV 12,20,541.88PV = 7,01,228.89

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TIME PERIODS

Example 1:Example 1:Sachin has been offered by his friend that Vinod that if he invests Rs. 150,000 with him, he would provide him with interest @ 10% p.a. compounded annually for the time Sachin wants to keep the funds invested Sachin is interested in knowing how much time the funds invested. Sachin is interested in knowing how much time it will take this amount to grow to Rs. 10 lacs?

Solution:FV = Rs 10 00 000- FV = Rs. 10,00,000

- PV = Rs. 150,000- Interest = 10%- Period = ??Solve for n = 20 years

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• Example 2:

Sridhar wants to know how fast can he double his money at a rate of interest of 9% p.a., if he wishes to invest Rs. 150,000 now?

Solution:

PV = 150,000PV 150,000FV = 300,000 (doubling his money)I = 9%n = ??

Solve: n = approx. 8 years

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V s h s i l t Aj L t s • Vyas has given a loan to Ajay. Loan amount was Rs. 10,000/- and Vyas got back Rs 20,471/- from Ajay. If rate of interest charged by Vyas was 12% d d M thl i h 12% per annum compounded Monthly, in how many years has Vyas got back his money from Ajay?

Ans : N 6 sAns : N = 6 years

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• Manish got Rs 44 423 34 as maturity amount of • Manish got Rs 44,423.34 as maturity amount of his deposit from ABC Chit Funds Ltd Manish has given this company a deposit of Rs 27,000/- at an Annual Nominal Rate of interest of 10% Annual Nominal Rate of interest of 10% compounded monthly. How much would have been the tenure of this deposit in Years, Half years, Quarters and Months?

• Ans : N = 60 months

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RATE OF RETURNE OF E U NExample 1:

Amar had invested Rs. 12,000, which has grown to Rs. 20,000 in 5 years. At what rate has his investment grown?

S l iSolution:

PV = 12,000FV = 20,000FV 20,000N = 5 I = ?

S l : I 11%Solve: I = 11%

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• Example 2:

XYZ Bank advertises that a deposit of Rs 25 000 with them would XYZ Bank advertises that a deposit of Rs. 25,000 with them would become Rs. 40,000 in four years. What is the interest rate implicit in the offer?

Solution:Solution:

PV = 25,000FV = 40,000 4 n = 4 years

I = ?

Solve for I = 12%f

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Deepak deposited Rs 60 000/ in a bank • Deepak deposited Rs 60,000/- in a bank deposit and got Rs. 98,317/- on maturity after 5years. If compounding was done

t l h t th l N i l quarterly, what was the annual Nominal rate of this deposit?

• Ans : I = 2.50%

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Aj ’ d i f R 1 00 000/ • Ajay’s deposit of Rs. 1,00,000/- earns an interest of Rs. 32,827/- in 3 years. What is the Nominal and Effective Rate of is the Nominal and Effective Rate of interest if compounding was done Monthly?

• Ans : I = 9 48%• Ans : I = 9.48%

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M hit ds Rs 2 00 000/ f f i t i • Mohit needs Rs 2,00,000/- for a foreign trip one year from now. His investment advisor tells him about a scheme in which he can accumulate this

t i b ki thl t f amount in a year, by making a monthly payment of Rs. 15360/- only per month for 12 months. Please calculate for Mohit, much Nominal and effective

t f I t t i b i ff d i thi h ?rate of Interest is being offered in this scheme?

• Ans : I = 15%

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LECTURE 3LECTURE 3LECTURE 3LECTURE 3

R l C h Fl• Regular Cash Flows:

AnnuityAnnuity

Meaning: A series of payments, paid at M an ng s r s of paym nts, pa at successive intervals of time over a specified period of time

Examples: Salary, EMIs, PF contributions

• Types of Annuities:yp

Ordinary AnnuityAnnuity DuePerpetual AnnuityG i A itGrowing AnnuityImmediate AnnuityDeferred AnnuityDeferred Annuity

Ordinary AnnuityOrdinary Annuity

– Conceptp

Cash flows occuring at the end of the periods. F S l h i d t th d f For eg: Salary when received at the end of a month is referred to as an ordinary annuity

• Example 1:• A 10 year ordinary annuity has a future value of

Rs 84 000 If rate of interest is 9% then what Rs. 84,000. If rate of interest is 9%, then what would be the amount of each annuity payment?

Solution:n = 10i= 9%i= 9%FVA = 84,000PMT = ?Solve for PMT = Rs. 5,528.89

• Example 2:

Ajay wants to purchase a car 5 years from now. His investments are presently worth Rs. 48,000. H k ps this inv stm nt in fix d d p sit t He keeps this investment in a fixed deposit at a ROI of 10% p.a. and he is ready to contribute Rs. 5,000 from the end of this month, every month for 5 years in a RD What would be his accumulat-for 5 years in a RD. What would be his accumulated savings in these accounts at the end of 5 yrs?Solution: PV = 48000

PMT = 5000PMT = 5000n = 5 * 12 = 60i= 10/12 = 0.833%FV ??FV = ??

Solve for FV = 466,160.18

• Annuity DueAnnuity Due– Concept

Cash flows occuring at the beginning of the periods.

For eg: Salary when received at the beginning of a month is referred to as an ordinary of a month is referred to as an ordinary annuity

• Example 1:

A 10 year annuity due has a future value of Rs. 84,000. If rate of interest is 9%, then what

uld b th m unt f ch nnuit p m nt?would be the amount of each annuity payment?

Solution:n = 10i= 9.35%FVA = 84 000FVA 84,000PMT = ?

Solve for PMT = Rs 5 072 37Solve for PMT = Rs. 5,072.37

• Example 2:

Ramesh wants to start a recurring deposit, by making equal contributions` at the beginning of every month for 5 years He wants to accumulate every month for 5 years. He wants to accumulate Rs. 500,000 in this period. How much should be his monthly contribution if the rate of interest offered by the bank is 9% p.a.?ff y pSolution:

n = 5*12 = 60n = 5 12 = 60i= 9/12 = 0.75%FV = 500,000PMT ?PMT = ?Solve PMT = 6,580

• Complex Example:

Amar has deposited Rs. 50,000 in a company FD, which pays interest at the rate of 10% p.a. How much m unt c n b ithd n t th b innin much amount can be withdrawn at the beginning of each year for 5 years if first withdrawal is 6 years from now?

Solution:

Problem has to be divided into 2 parts:

• Part 1:

Calculating the FV of the sum deposited now

PV = 50000n = 6 yearsn = 6 yearsi= 10%FV = ?FV ?

Solve FV = 88,578

• Part 2:

Calculating the amount to be withdrawn at the beginning of the next 5 years?beginning of the next 5 years?

PV = 88578n = 5i= 10%PMT = ?PMT = ?

Solve in the begin mode for PMT = 21,242.42g ,

h / h d f • Ajay has to pay Vyas Rs. 2800/- at the end of every month for 2 years. If the rate of interest is 11% p.a., then how much amount can be accepted by Vyas to settle the loan today?

Ans. PV = 60,075.73

• Ajay is depositing Rs 50 000/- in an account Ajay is depositing Rs. 50,000/ in an account today an he plans to contribute Rs. 2,500/- per month in this account after getting his salary. If h is ttin ROI f 9% p mp nd d he is getting a ROI of 9% p.a., compounded monthly, then how much will be the accumulated balance in that account after 4 years?

Ans. FV = 2,15,372.04

• Ajay has deposited Rs. 5,00,000/- in a bank today @ 9.5% p.a. He wants to know if he withdraws this money in monthly installments at the end of this money in monthly installments, at the end of month, for 5 years, then how much will be each installment?

Ans PMT = 10 500 93Ans. PMT = 10,500.93

• Vyas deposited Rs 3 00 000/ in a bank and • Vyas deposited Rs. 3,00,000/- in a bank and banker told him that from the end of the month he could withdraw Rs. 6,374/- every month for 5

k h h h years. Vyas wants to know how much ROI he is being offered, please help him?

• Ans. I = 0.833%

• Rohan has won a lottery in which he will get Rs. 3 20 000/ f t 20 Th 3,20,000/- every year for next 20 years. The lottery organizer gave him another offer, the offered him to take Rs. 30,00,000/- in lieu of the above mentioned periodic payments If Rate the above mentioned periodic payments. If Rate of Interest available is 8% p.a. Please advise Rohan, which offer, is better for him?

• Ans. PV = -31,41,807.17 (reject the offer)

• Vyas wants to retire from work on his 60th

birthday. He wants to put some amount of funds aside each year, so that he is able to withdraw Rs 50 000/- per year for 20 withdraw Rs. 50,000/ per year for 20 years once he retires, with first withdrawal on his 61st birthday. Vyas is 20

ld t t H h h ld h year old at present. How much should he set aside each year for his retirement goal if he can get ROI of 10%?if he can get ROI of 10%?

• Ans. PV = 4,25,678.186n . V , 5,67 . 6

• Manish is taking a housing loan of Rs. 7,00,000/-Manish is taking a housing loan of Rs. 7,00,000/and is paying a monthly installment of Rs. 8,310/-on this loan. If bank is charging ROI at 7.5% p.a. on monthly rests, then in how much time can this on monthly rests, then in how much time can this loan be repaid?

• Ans. N = 10 years (120 months)

• What amount needs to be invested today at y10%p.a., so that it pays Rs. 1 Lakh p.a., for 5 years from the 6th to 10th year? First payment starts at the beginning of 6th yearat the beginning of 6 year.

• Ans. PV = 3,79,078.68

Deepak is 35 years of age today and wants to Deepak is 35 years of age today and wants to know that if he needs to earn an annual income of Rs. 1,00,000/- from the age of 60 to 75 years, in h f h h h h the beginning of each year, then how much

amount he needs to invest today? The rate of interest is 10%..

Ans. PV = Rs. 8,36,668.74

• Manish joins BIFM Ltd. with a salary package • of Rs. 5,00,000/- p.a. His present age is 33

years. He wants to start accumulating funds for buying a flat in Delhi 5 years from now. He feels h n ds t h p s f Rs 25 00 000/ f he needs to have a corpus of Rs. 25,00,000/- for this dream. He wants to contribute 50% of this target from his own savings. His financial planner advised him to save Rs 12 800/- p m starting advised him to save Rs 12,800/ p.m., starting from today, for 5 years in a scheme to reach is goal . Please calculate what is the rate of return being projected by his Financial Planner in the g p j yoffered scheme.

• Ans. I = 1.50%Ans. I 1.50%

• Vyas has got Rs 5 93 170 54 as maturity proceeds Vyas has got Rs. 5,93,170.54 as maturity proceeds of his Life Insurance Policy. His annual premium was Rs.15000/- p.a. and he paid his premium for 16 s Pl s l l t th t f t n th t 16 years. Please calculate the rate of return that he got on this policy?

• Ans. I = 10%

LECTURE 4LECTURE 4LECTURE 4LECTURE 4

TEST QUESTIONSTEST QUESTIONSTEST QUESTIONSTEST QUESTIONS

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• At the time of retirement, Mrs. Shyamala is given , y ga choice between two alternatives:

l f 10 000 l h – an annual pension of Rs. 10,000 as long as she lives; and

– a lump sum amount of Rs. 50,000 .

If Mrs. Shyamala expects to live for 15 years and the interest rate is 15%, which option appears more attractive? more attractive?

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• A 12-payment annuity of Rs. 10,000 will begin 8

years hence (the first payment occurs at the end

f 8 ) Wh i h l f hi of 8 years). What is the present value of this

annuity if the discount rate is 14%? annuity if the discount rate is 14%?

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• Fifteen annual payments of Rs. 5,000/- are made p y ,

into a deposit account that pays 14% interest per

year. What is the future value of this annuity at

the end of 15 years?the end of 5 years?

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• As per the latest advertisement, IDBI Bank p ,

states that it will pay a lumpsum of Rs. 44,650/-

at the end of 5 years to the investors who deposit

annually Rs. 6,000/- per year. What is the

interest rate implicit in the offer?

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• Shahrukh Khan wants to go on a world tour which g

will cost him Rs. 1 million. He is able to save Rs.

80,000/- annually to fulfill his desire. How long

will he have to wait if his saving are able to fetch

him a return of 14%p.a.

• Michael Schumacher received an amount of Rs.

20,00,000/- on retirement from the Ferrari’s. He

deposit it in his bank account which pays him 12%

interest. If he withdraws annually Rs. 2,00,000/-

how long he can continue to do so.

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GROWING GROWING GROWING GROWING GROWING GROWING ANNUITIESANNUITIESGROWING GROWING

ANNUITIESANNUITIES

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• Type 1: The formula for calculating FV of a Type 1: The formula for calculating FV of a growing annuity where contribution increases by a Fixed Percent age every year is:F f G FV of Growing Annuity =

PMT x [{(1+R)N – (1+G)N}/{(1+R)-(1+G)}]Here PMT = First installmentHere, PMT = First installment

N = No. of PeriodsR = Rate of InterestR Rate of InterestG = Growth Rate of Periodic

DREAMZ INFINITE FINANCIAL PLANNERS

• Type 2: The formula for calculating FV of a growing annuity where contribution increases by a every year is:where contribution increases by a every year is:FV of Growing Annuity =

A x SN + [D x (SN –N)/I]N [ ( N ) ]

Here, A = First installmentSN = Future Value of Ordinary Annuity of Re.1

f “N” i d t “I” I t st for “N” period at “I” Interest N = Period of DepositI = Rate of InterestD = Amount Growing per periodic installmentD = Amount Growing per periodic installment

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• Rahul is 30 years of age and is currently earning a l l f R 3 00 000/ H h t t d annual salary of Rs 3,00,000/-p.a. He has started

saving 10% of his salary at the end of each year. What accumulated amount he would be having in gthis scheme at his retirement age of 60?

• Ans. FV = 1,63,29,000/-

• Deepak is 40 years of age and he is getting a l f R 38 000/ th H i h t salary of Rs. 38,000/- per month. He wishes to

save 20% of his every Quarterly Salary every year at the end of the year. If his salary y y yincreases by 10% every year and ROI is 11% p.a. then what will be his accumulated saving at the age of 58?age of 58?

• Ans. FV = 89,70,432

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• Debashish opened a monthsly recurring deposit p y g paccount with an initial deposit of Rs. 5,000/-. If he increases his investment by a fixed amount of Rs 100/- every month then what would be the Rs. 100/- every month, then what would be the amount in his account after 3 years, assuming that rate of interest remains constant at 9% p.a.

• Ans. NFV = 2,74,416.42

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P l • Perpetual Annuity

– Concept: • Fixed amount being received till perpetuity,

where n (no. of periods) is unknown• Formula:

PV of perpetual annuity – PV of perpetual annuity = Annuity required/ Rate of interest

DREAMZ INFINITE FINANCIAL PLANNERS

• Example 1:

Amar wants to initiate an endowment prize in his school in memory of his son He wants an amount of Rs 1 500 being memory of his son. He wants an amount of Rs. 1,500 being passed on to the student who scores the first rank every year in Standard 8. How much amount should the school take from Amar, if it expects an interest rate of 6%?

Solution:

PV of perpetuity = Annuity/ Expected rate of interestPV of perpetuity = Annuity/ Expected rate of interest

= 1500/0.06

= 25,000

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• Rahul wants to invest some amount of money Rahul wants to invest some amount of money today so that, if rate of interest remains constant, he gets a month interest of Rs. 7500/-

m nth If th R t f Int s is 9% th n every month. If the Rate of Interes is 9%, then how much amount Rahul should invest today?

• Ans. PV of Annuity in Perpetuity = Rs.10,00,000.

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• Vyas opened a SIP in a Mutual Fund scheme. He Vyas opened a SIP in a Mutual Fund scheme. He contributed Rs. 2,500/- per month in that scheme and his total unit holding after 4 years was worth Rs. 1,76,522/- after 4 years. He encashed it and Rs. 1,76,522/ after 4 years. He encashed it and got the units redeemed. He wants to know how much was his realized return on this investment. Please tell him both Nominal Yield on the Please tell him both Nominal Yield on the investment.

A I 1 5%• Ans. I = 1.5%

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EFFECTIVE RATE OF NTERE TINTEREST

• Effective Rate of Interest:– Concept

– Calculation:EROI = (1+i)^m-1

where, i= rate of interest for the period ofcompounding

m= periods of compoundingm periods of compounding

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• Example 1:• Example 1:

If rate of interest is 11% p.a. compounded quarterly, what is the effective rate?

Solution:

i= 11/4 = 2.75m= 4

S l f EROI 11 46%Solve for EROI = 11.46%

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• Example 2:• Example 2:

Calculate the effective rate of interest offered by NSC, which pays interest @ 8% p.a. compounded semi-annually?p y p p y

Solution:

i= 4m= 2

S l f EROI 8 16%Solve for EROI = 8.16%

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REAL RATE OF RETURNREAL RATE OF RETURN

R l R t f t• Real Rate of return

– Concept

– Also called as the inflation adjusted rate of return

– Calculation:

RROI [(1 )/(1 i)] 1RROI = [(1+r)/(1+i)]-1

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• Example 1:

Amrish is getting a return of 11% on his investments. If the current inflation is at 7%, calculate the real rate of returns?

Solution:Solution:

n= 11%i= 7%

Solve for RROI = 3 7%Solve for RROI = 3.7%

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• Net Present Value

– Concept • A discounted cash flow method used to

evaluate the projects or investments• Useful for decision making• Useful for decision making• Two ways to solve:

– Present Value for each cash flowPresent Value for each cash flow– Using the Cash function in the financial

calculator

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• Mr. Ashar invested Rs. 200,000 in an investment th t i R 40 000 f th fi t 4 d R that gives Rs. 40,000 for the first 4 years and Rs. 60,000 for the next 3 years. If the discount rate is 12%, you are requested to calculate the NPV of the cash flows?the cash flows?

Solution:

Method 1 – Financial calculatorUse the Cash function – input i=12%pNext, input the cash flow per year in the order they occurSolve for NPVSolve for NPV

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• Method 2:• Method 2:

Can be solved using the concept of PVA alsog p

Part I:P t C h tfl 200 000 ( t 0)Present Cash outflow = -200,000 (at year 0)

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Part II:

PMT = 40000 4 n = 4 years

i= 12%PVA = ?PVA = ?

Solve for PVA = 121 494 (at year 0)Solve for PVA 121,494 (at year 0)

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Part III - a:

PMT = 60000n = 3 yearsi= 12%PVA ?PVA = ?

Solve for PVA = 144 110Solve for PVA = 144,110

This PVA would be at the end of the 4th year, Th s PVA would be at the end of the 4 year, which has to converted to year 0.

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Part III - b:

FV = 60000n 4 yearsn = 4 yearsi= 12%PV = ?PV = ?

Solve for PV = 91,584

NPV = (Part II + Part IIIb) – Part I= 13,078.40

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V s is j ti i st idi Rs • Vyas is projecting an income stream providing Rs. 2,000/- for first 3 months, Rs.3,200/- for the next 2 months, Rs. 3,700/- for next 6 months and R 800 f 2 th th ft Pl l l t Rs. 800 for 2 months thereafter. Please calculate the Present Value of this cash stream if rate of interest is 9%?

• Ans NPV = 24 513 72• Ans. NPV = 24,513.72

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Aj is b in ff d 2 in stm nts hich h • Ajay is being offered 2 investments, which have periodic cash flows. Please advise him which one is better if rate of interest is 12% p.a.?

• Scheme 1:– Initial Outflow = 1 00 000Initial Outflow = 1,00,000– Cash Inflows = 20,000

30,00015,000 35,0001 15 000 1,15,000

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• Scheme 2:I iti l O tfl 1 00 000– Initial Outflow = 1,00,000

– Cash Inflows: NIL60,00018,00036,0001 20 0001,20,000

A NPV 39 946 88Ans. NPV = 39,946.88NPV = 51,613.55

Recommend Scheme 2

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• Internal Rate of Return:

Concept:

Rate at which the present value of outflows equals the present value of inflowsequals the present value of inflows

Can be used to compare the returns of 2 pinvestments for their evaluation

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• Calculation:Calculation:

– Trial and Error method

– Using financial calculator (Sums solved herein are based on the use of financial calculator)financial calculator)

DREAMZ INFINITE FINANCIAL PLANNERS

• Example 1:

In the previous sum, find the IRR?

Solution:Steps to solve the problem using the calculator is th s m s f NPVthe same as for NPV.

Difference – the rate (i) will not be input, the ff ( ) p ,cash flows will be entered in the same order and then solve for IRR

Answer = 14%

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• Manish invested in a Limited Payment yEndownment Policy of sum assure of Rs. 3,00,000/- in which policy term was of 15

b t i bl l f 5 years but premium was payable only for 5 years. He paid an annual premium of Rs. 24 863/ and got Rs 5 30 000/ on 24,863/- and got Rs. 5,30,000/- on maturity after 15 years. Please calculate the Rate of Return he got?f u g

• Ans IRR = 11 69%Ans. IRR 11.69%

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LECTURE 5LECTURE 5LECTURE 5LECTURE 5

Payback period :

- Traditional method of evaluation of projects- does not use the discounted cash flow methods- does not use the discounted cash flow methods- takes into account the speed at which the cost of the project is recovered

• Calculation: h h h h l – PBP is that period in which the original

investment is recovered in periodic cash flows:

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• Example 1:

Dinesh invested Rs. 100,000 in a scheme that pays back Rs. 28,000 per year for 5 years. Calculate the Payback period?the Payback period?

Solution:

Initial outflow = Rs. 100,000Yearly inflows = Rs. 28,000y ,

PBP will be [28000 + 28000 + 28000 + (16000/28000)]( 6000/ 8000)]

= 3.57 years

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• Example 2:

Consider the problem used for the NPV method

the PBP would be worked out as:

=[40000+40000+40000+40000+(40000/60000)]

= 4 67 years= 4.67 years

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• Ram made some investment in which initial cash • Ram made some investment in which initial cash outflow was Rs. 40,000/- and its yield cash inflows for next 5 years. Please calculate the Pay

k d h h fl f Back period. The cash inflows of 5 years were as follows:

• Year 1: Rs 12 000/-Year 1: Rs. 12,000/• Year 2: Rs. 10,000/-• Year 3: Rs. 14,000/-,• Year 4: Rs. 8,000/-• Year 1: Rs. 10,000/-• Ans. PBP = 3.5 years

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INVESTMENT INVESTMENT INVESTMENT INVESTMENT INVES MEN INVES MEN CONCEPTSCONCEPTS

INVES MEN INVES MEN CONCEPTSCONCEPTS

• Holding Period Return– Concept– Calculation of HPR– Calculation of HPR

HPR = (Current Yield + Price Change)/ Initial InvestmentInvestment

Current Yield = Dividends, Interest income dearned

Price change = Capital Appreciationg p pp

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E l 1• Example 1:

Ajay bought some shares for Rs. 75,000. After 1 year he t a dividend f Rs 1500 One year after receivin he got a dividend of Rs. 1500. One year after receiving the dividends, he sold these shares for Rs. 90,000. You are requested to calculate the HPR for Ajay.

Solution:

Dividends = 1 500Dividends = 1,500Price Change = (90,000 – 75,000) = 15,000

HPR = (1 500 + 15 000)/75 000 = 22%HPR = (1,500 + 15,000)/75,000 = 22%

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• Example 2:p

Mahesh invested Rs. 20,000 in shares of Infosys Ltd. He got a dividend of Rs. 1,200 after one year. In 2nd

h t di id d f R 1 400 d th ld year, he got a dividend of Rs. 1,400 and then sold these shares for Rs. 25,000 after receiving the dividends. Calculate the HPR.

Solution:

Dividends = 1 200 + 1 400 = 2 600Dividends = 1,200 + 1,400 = 2,600Price Change = (25000 – 20000) = 5,000

HPR = (2600 + 5000)/ 20000 = 38%HPR = (2600 + 5000)/ 20000 = 38%

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• C.A.G.R– Concept– Concept– Calculation of CAGR

CAGR = [{(1 + HPR)^1/n} – 1] * 100

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• Example 1:

Ajay bought some shares for Rs. 75,000. After 1 year he got a dividend of Rs. 1500. One year after receiving the dividends, he sold these shares for Rs. 90,000. You are , ,requested to calculate the HPR for Ajay.

Solution:

HPR = (1,500 + 15,000)/75,000 = 22%(as worked out in the previous slides)

CAGR = [{(1+0.22)^1/2}-1]*100

= 10 45% 10.45%

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• Example 2:p

Mahesh invested Rs. 20,000 in shares of Infosys Ltd. He got a dividend of Rs. 1,200 after one year. Ltd. He got a dividend of Rs. 1,200 after one year. In 2nd year, he got a dividend of Rs. 1,400 and then sold these shares for Rs. 25,000 after receiving the dividends. Calculate the HPR.

Solution:

HPR = (2600 + 5000)/ 20000 = 38% or 0.38

CAGR [{(1+0 38)^1/2} 1]*100CAGR = [{(1+0.38) 1/2}-1]*100

= 17.47%DREAMZ INFINITE FINANCIAL PLANNERS

CALCULATING CALCULATING CALCULATING CALCULATING CALCULATING CALCULATING REQUIRED RATE OF REQUIRED RATE OF

CALCULATING CALCULATING REQUIRED RATE OF REQUIRED RATE OF

INTERESTINTERESTINTERESTINTEREST

• What rate of interest is required to maintain an investment if the inflation is 6% and tax rate is 10%?

Ans. ROI = 6.67%n . 6.67

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• What rate of interest is required to maintain an i t t if th i fl ti i 4 90% d t t investment if the inflation is 4.90% and tax rate is 10%?

• Ans. ROI = 5.44%

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• Risk and return concepts:St d d D i ti– Standard Deviation• Deviation from the expected returns

– Variance• Derived as the square of standard deviation q f

of a security

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• Example:• Example:Following are the returns of a stock during the last five years:

Year Return1 6%2 4%

%3 5%4 -7%5 8%

Compute the following:

a Standard Deviation of the stocka. Standard Deviation of the stockb. Variance of the stock

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Period Returns R E (R) [R E (R )2]Period Returns R - E (R) [R - E (R )2]

1 6 2.8 7.842 4 0 8 0 642 4 0.8 0.643 5 1.8 3.244 -7 -10.2 104.045 8 4.8 23.04

E(R ) = 3.2

sum of [R - E (R )2] = 138.8

Variance = 27.76S.D. = 5.27

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– Beta• Measure of volatility of a security or a

portfolio in comparison to the market as a whole – sensitivity of a stock with respect to the marketto the market

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• Performance Measures for Portfolio returns:• Performance Measures for Portfolio returns:– Treynor Measure:

= (Rp – Rf)/b (Rp Rf)/b

Where, Rp = return on portfoliop pRf = risk free returnb = beta of portfolio

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• Example:

Fund Alpha’s expected return = 12%Beta of the fund = 0.4Ri k f t 8%Risk free rate = 8%Solve for Treynor’s Index?

T. Index = (12-8)/0.4 = 10

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– Sharpe Measure:= (Rp – Rf)/S D= (Rp – Rf)/S.D.

Where, Rp = return on portfolioWhere, Rp return on portfolioRf = risk free returnS.D. = Standard Deviation of portfolio

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• Example:Pioneer Mutual Fund has delivered an average return of 10% over the last year and has a ystandard deviation of 0.15. Calculate the sharpe measure for Pioneer, if the risk free return is 5%.

Solution:

Rp = 10%Rp = 10%Rf = 5%S.D.= 0.15

Sharpe measure = (10-5)/0.15 = 33.33

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• Jensen’s Measure:

= Rp – [Rf + b(Rm-Rf)]

Where, Rp = return on portfolioRf i k f tRf = risk free returnb = Beta of the portfolioRm = return on market portfolioRm = return on market portfolio

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• Example:

Pioneer Mutual Fund has delivered an average return of 10% over the last year and has a beta of 0.95. During the same time, the market index delivered returns of 12%. Calculate the Jensen’s measure for Pioneer if the risk free return is the Jensen s measure for Pioneer, if the risk free return is 5%.Solution:

Rp = 10%Rf = 5%Rm = 12%b 0 95b = 0.95

Jensen’s Measure = 10 – [5 + 0.95(12-5)] = 4.335

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BOND PROBLEMSBOND PROBLEMSBOND PROBLEMSBOND PROBLEMS

B d P bl• Bond Problems:

2 types of problems:2 types of problems:

One: Finding out the current price/ value of the On F n ng out th curr nt pr c / a u of th bond

Two: Finding out the YTM

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• Current Price of the Bond:• Current Price of the Bond:

- Concept: used to find out the right price of the p g pbond, where the expected rate is different than the coupon rate.

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• Example:ExampleWhat will be the value of the bond with a par value of Rs. 1,000 that yields 8% return and will mature after 5 years? The market rate in the mature after 5 years? The market rate in the bonds market is 6%Solution: FV = 1,000

PMT = 80n = 5i= 6%i= 6%PV = ?

PV = 1,084.24

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• Example:Example

A bond (face value of 1,000) with a yield of 12%, pays interest semi-annually. The bond has a term to maturity of 4 rs Th xp ct d i ld is 14% find its curr nt pric ?4 years. The expected yield is 14%, find its current price?

Solution:

FV = 1,000PMT = 60 (semiannually)n = 8 (semiannually)n 8 (semiannually)i= 7%

Solve for PV = ?

Ans = 940.28

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• Yield to Maturity of the Bond:– Concept:Concept:

• It is the internal rate of return of the bond that equates the present value of the bond’s

fl h l f floutflows to the present value of its inflows• In case the market rate of interest is

different than the coupon rate YTM of the different than the coupon rate, YTM of the bond will be different than the coupon rate

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• Example:R h h d R 1 000 f l b d f R Ramesh purchased a Rs. 1,000 face value bond for Rs. 1032.40. The bond has a 10% coupon rate and four years to maturity, it makes annual payments.

Solution:Using the calculator

FV = 1,000PV = 1032.40PMT 100PMT = 100n = 4i=?S l f i hi h i th YTM 9%Solve for i, which is the YTM = 9%

DREAMZ INFINITE FINANCIAL PLANNERS

AMORTISATION AMORTISATION AMORTISATION AMORTISATION MOR IS ION MOR IS ION SCHEDULESSCHEDULES

MOR IS ION MOR IS ION SCHEDULESSCHEDULES

• Amortization Schedule:– Concept

• Schedule depicting the payment of the loan instalments Also depicts the break up of the loan • Also depicts the break-up of the loan instalment into the principal and interest repayment

• Most commonly used method is the EMI schedule

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• Example:

Amrish has taken a loan amounting to Rs. 500,000. XYZ Bank has offered him an interest rate of 9% XYZ Bank has offered him an interest rate of 9% p.a. for a tenure of 20 years. Amrish is interested to know how much of EMI will he have to pay for the same and also the repayment schedule for the the same and also the repayment schedule for the first 2 years.

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• Solution:Solution

First step: To find out the EMI or the monthly repayment figure using the PVA/ FVA formula:

PV = 500,000n = 240 monthsi 9/12 0 75%i= 9/12 = 0.75%PMT = ?

Solve for PMT = 4 499 or approx 4 500Solve for PMT = 4,499 or approx 4,500

Next Step would be to draw the amortization schedule for 2 years!y

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Months EMI Interest Principal O/s Principal

1 4,500 3,750 750 499,2501 4,500 3,750 750 499,2502 4,500 3,744 756 498,4943 4,500 3,739 761 497,7334 4,500 3,733 767 496,9665 4,500 3,727 773 496,1936 4,500 3,721 779 495,4157 4,500 3,716 784 494,6308 4,500 3,710 790 493,8409 4,500 3,704 796 493,04410 4,500 3,698 802 492,24211 4,500 3,692 808 491,43412 4,500 3,686 814 490,61913 4,500 3,680 820 489,79914 4 500 3 673 827 488 97214 4,500 3,673 827 488,97215 4,500 3,667 833 488,14016 4,500 3,661 839 487,30117 4 500 3 655 845 486 456

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MEAN MEAN –– ARTHEMATIC ARTHEMATIC MEAN MEAN –– ARTHEMATIC ARTHEMATIC ME N ME N R HEM I R HEM I MEANMEAN

ME N ME N R HEM I R HEM I MEANMEAN

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GEOMETRIC MEANGEOMETRIC MEANGEOMETRIC MEANGEOMETRIC MEAN

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• Compute Geometric Mean return for an investment with the following per period return investment with the following per period return 8.9% , 10%, 7.7%, 13%?

Ans. GM = 9.88%

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• Four Portfolios have an annual return of 5%, 8%, 12% and 19% Assuming Rs 50 000/- is invested in 12% and 19%. Assuming Rs 50,000/ is invested in each portfolio. Calculate the average rate of return on the portfolio?

• Ans. ROR = 11%

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• Sathi owns the following portfolio.Sathi owns the following portfolio.

Shar Weight

Beta Exp. R te t Return

1. 0.30 1.20 202 0 25 0 75 152. 0.25 0.75 153. 0.45 1.0 22

• What is the expected rate of return on the portfolio?

• Ans. Expected rate = 19.65

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• Sathi owns the following portfolio

Share Weight Beta Exp. Return

1 0 30 1 20 201. 0.30 1.20 20

2. 0.25 0.75 153 0 45 1 0 22

• What is the Portfolio Beta?

3. 0.45 1.0 22

• Ans. Portfolio Beta = 0.9975

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• Following are the information of three mutual funds • Following are the information of three mutual funds, Reliance, TATA, SBI and the market.

Mean Standard BetaReturn % Deviation%

Reliance 14 17 1.2

TATA 10 15 0.95

SBI 13 19 1.35

M k t 12 18 1Market Index

12 18 1.

The risk free return rate is 5%. Calculate the Treynor The risk free return rate is 5%. Calculate the Treynor Measure of Reliance Fund.Soln = 7.5

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• The market price of a bond is Rs 1600/- and the face value of Rs 2000/- The bond will pay face value of Rs. 2000/ . The bond will pay interest @ 5%p.a. for 3 years and redeemed at par. Compute YTM?

• Ans YTM = 13 54• Ans. YTM = 13.54

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• A Rs.10,000/- face value zero coupon bond with a 10 years term to maturity. Currently sells as to y y yproduce on 8% YTM. What is the bond’s price? Calculate the bond’s price if its yield rises to 10% its yield falls to 5%?10%., its yield falls to 5%?

• Soln. = 4632,3855,6139, ,

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• Rajiv recently purchased bond with a Rs. 1,000/-face value, a 10% coupon rate, and four years to maturity The bond makes annual interest maturity. The bond makes annual interest payments the first to be received in one year from today. Rajiv paid Rs. 1032.40 for the bond.I What is the bond’s yield to maturity?I. What is the bond s yield to maturity?II. If the bond can be called two years from now

at a price Rs. 1100, what is its yield to call?

• Soln. 9%,12.76%

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LECTURE 6LECTURE 6LECTURE 6LECTURE 6

EMPLOYEE BENEFITS

D fi d B fit l• Defined Benefit plans

• Defined Contribution plans

• Hybrid plans

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DEFINED BENEFIT DEFINED BENEFI PLANS

s ifi s th b fits h l i s t • specifies the benefits each employee receives at the time of retirement

• employee may or may not contribute for the same

• benefit payable is not dependent on the contributions made by the employee

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DEFINED CONTRIBUTION PLANS

• benefit payable herein is based upon the contributions made by the employee and/ or by contributions made by the employee and/ or by the employer during the work life of the employee

• growth rate of the funds – important factor

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HYBRID PLANS

• Combination of both plans

• Rate of contribution is fixed and the benefits payable is also fixed

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EMPLOYEE’S PERSPECTIVE –EM LOYEE S E S E VE DEFINED BENEFIT PLANS

• Advantages:

– Assured of getting a retirement benefit, which can be ascertained even during work life

Int st t isk t nsf d t mpl -Interest rate risk transferred to employer

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• Disadvantages:

sti i d b f th l b s – vesting period before the employee becomes eligible for the benefits

– Benefits to employees may not be given immediately before retirement

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EMPLOYEE’S PERSPECTIVE PERSPECTIVE –

DEFINED DEFINED CONTRIBUTION PLANS• Advantages:

– No vesting period for the benefitsNo vesting period for the benefits– No fear of employer tactics to affect the

benefit available at the time of retirement

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Di d t• Disadvantages:

– Benefit dependent on the employee’s – Benefit dependent on the employee s contributions during work-life

– Interest rate risk is borne by the employee

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EMPLOYER’S PERSPECTIVE –

DEFINED BENEFIT DEFINED BENEFIT PLANS

• Advantages:– benefit payable to the employee is fixed

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• Disadvantages:

– Difficult to ascertain the exact cost of the retirement benefits for the employerretirement benefits for the employer

– Employer has to bear the brunt of the interest t m m ntsrate movements

– Need for regulatory approvalsf g y pp

– Individual employee’s share difficult to be demarcateddemarcated

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EMPLOYER’S PERSPECTIVE –DEFINED CONTRIBUTION DEFINED CONTRIBUTION

PLANSAdvantages:• Advantages:– Employer’s liability towards the employee’s retirement

benefits is well defined – Changes or movements in interest rates do not affect – Changes or movements in interest rates do not affect

the employer’s liability– No need for actuarial valuations and certifications from

regulatory authoritiesregulatory author t es– Share of each employee can be easily ascertained – Informed decisions in relation to the promotion and pay

revisions for the employees can be undertaken. p y

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GRATUITY

St t d f t it t t l • Started of as a gratuitous payment to employees in the past

• lesser benefits paid or denial of benefits to some employees

• Governed by Payment of Gratuity Act, 1972

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• Applicability:

– to every factory, mine, oilfield, plantation, port and railway company;y p y

– every shop or establishment within the meaning of any law for the time being in force in relation to the shop & establishment Act in a St t i hi h 10 State in which 10 or more persons are employed, or were employed, on any day of the preceeding twelve months

h th t bli h t l f – such other establishments or class of establishments, in which ten or more employees are employed, or were employed, on any day of the preceeding 12 months as the CG my by the preceeding 12 months, as the CG my by notification specify in this behalf.

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• Liability to pay gratuity under the Act:– Mandatory to pay gratuity in case of

superannuation retirement resignation death superannuation, retirement, resignation, death or disablement.

– In case of superannuation and retirement, pemployee should have put in a minimum of 5 years of continuous service for the liability

– But in case of employee leaving due to death or – But in case of employee leaving due to death or disablement, minimum service period criteria does not exist.

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• Taxability under I T Act:Taxability under I.T. Act:

Employees divided into three categories:` a Government employeesa. Government employees

b. Employees covered under P.O.G.AE l th th & bc. Employees other than a. & b.

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LEAVE ENCASHMENT• Encashment can be done at retirement or

during period of serviceg p f

• Employees divided into 2 categories –Government & Non-government

• Encashment during service, taxable in both g ,cases

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• At retirement, whether on superannuation or otherwise:– Govt. employees – amount recd is exempt

Other employees (whichever is less):– Other employees (whichever is less):• Amount actually received• Notified amount – Rs 300 000Notified amount Rs. 300,000• 10 months average salary (10 months

immediately preceeding the date of retirement)

• Cash equivalent of earned leave (Leave on the basis of 30 days leave for every the basis of 30 days leave for every completed year of service.)

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RETRENCHMENT COMPENSATIONCOMPENSATION

• Compensation received by a workman under the Industrial Disputes Act Industrial Disputes Act

• Amount exempt under this clause shall not exceed-

t l l t d i d ith th – an amount calculated in accordance with the provisions of clause (b) of section 25F of the Industrial Disputes Act, 1947; or

– such amount, not being less than five lakh rupees, as the Central Government may, specify in this behalf, p y ,• whichever is less:

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VOLUNTARY RETIREMENT

COMPENSATIONCOMPENSATION• The employer has to have a separate scheme • The employer has to have a separate scheme

known as the Voluntary Retirement Scheme

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• Exemption under I.T:– a public sector company; or– (ii) any other company; or– (ii) any other company; or– (iii) an authority established under a Central,

State or Provincial Act; or(iv) a local authority; or– (iv) a local authority; or

– (v) a co-operative society; or – (vi) a University established or incorporated by

d C t l St t P i i l A t d or under a Central, State or Provincial Act and an institution declared to be a University under section 3 of the University Grants Commission Act 1956 (3 of 1956); or Act, 1956 (3 of 1956); or

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( ii) I di I tit t f T h l ithi – (vii) an Indian Institute of Technology within the meaning of clause (g) of section 3 of the Institutes of Technology Act, 1961 (59 of gy (1961); or

– (viia) any State Goverment; or( iii) h i i f h – (viii) such institute of management as the Central Government may, by notification in the Official Gazette, specify in this behalf , p y

Upto an amount of Rs. 500,000

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PROVIDENT FUNDSDE F D• Statutory Provident Fund

– maintained by Government and semi-govt maintained by Government and semi govt organizations, local authorities, railways, universities and recognized educational institutions institutions

– Eligibility:• Temporary govt servants after continous Temporary govt servants after continous

service of one year, re-employed pensioners and permanent govt servants

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• Contribution

Sum to be fixed by the employees, subject to a min of 6% of emoluments and not more than the employee’s total emoluments.

Emoluments include pay, leave salary and any remuneration of the nature of pay recd on foreign remuneration of the nature of pay recd on foreign service. DA excluded.

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R i d P id t F d• Recognised Provident Funds:– Applicability:

• (a) to every establishment which is a factory • (a) to every establishment which is a factory engaged in any industry specified in Schedule I and in which twenty or more

l d dpersons are employed and

(b) to any other establishment employing ( ) y p y gtwenty or more persons or class of such establishments which the Central Government may by notification in the Government may by notification in the Official Gazette specify in this behalf

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• Contributions:• Contributions:– 12 per cent of the basic wages dearness

allowances and retaining allowance (if any) g ( y)– Reduced contribution (10%) in case of:

• In case of sick companies or • where the accumulated losses of the

company exceeds its entire net worth at the end of any financial yearend of any financial year

• any establishment engaged in manufacturing of jute, bread, coir or gum industries

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• Employees Pension Fundp y

– Carved out of the PF scheme – an eg. Of the h b d h l d b hybrid scheme – employee does not contribute, but employer does.

– Contribution: • 8.33% of employer contribution to PF + p y

1.16% by Central Government

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• Employees Deposit Linked Insurance:p y p

– to provide life insurance benefit to employees covered under PF covered under PF

– all employees who are members of EPF scheme Eget auto membership of EDLI

– Contribution @ 0 50% of employees salary is Contribution @ 0.50% of employees salary is paid (max limit of Rs. 6500) and @ 0.01% as admin charges

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• No maturity benefit. Life ins cover available only No maturity benefit. Life ins cover available only as long as member of EPF.

In th nt f d th f n mpl d in • In the event of death of an employee during employment, nominee is paid an amount equal to the average balance in the PF account during the

st 12 ths d i th i d f past 12 months or during the period of membership, whichever is less.

• If average balance exceeds Rs. 35,000 then amount will be 35000 plus 25% in excess, subject to max of 60,000to max of 60,000

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PUBLIC PROVIDENT FUND• Governed under the PPF Act, 1968

• Saving avenue for self employed professionals & employed people too

• Account can be opened:– SBI branches and its subsidiariesSBI branches and its subsidiaries– Head Post Office– Sub-post offices– Any of the nationalised banks

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TAX TREATMENT

• Statutory Provident Fund:• Statutory Provident Fund:

– Employer’s contribution – exempt from tax

– Employee’s contribution – deduction u/s 80-C

– Interest on PF balance – exempt from tax

Lumpsum payment at the time of retirement – Lumpsum payment at the time of retirement –exempt from tax

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• Recognised Provident Fund:Recognised Provident Fund:

– Employer’s contribution – exempt upto limitsp y p p

– Employee’s contribution – deduction available

– Interest on contribution – exempt upto limits

– Lumpsum payment at the time of retirement –exempt in case of certain conditionsexempt in case of certain conditions

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• Unrecognised Provident Fund:g

– Employer’s contribution – taxability deferred

– Employee’s contribution – no deduction available

– Interest on contribution – exemption based on limits

– Lumpsum payment at the time of retirement –taxability as laid down

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SUPER ANNUATION

Ch t i ti DB DC t b d t i d b • Characteristic – DB or DC – to be determined by the employers and employees

• No statutory superannuation benefit available for employees

• Benefit provided by employer through approved life insurance companieslife insurance companies

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F di • Funding arrangements:

– Payment by employer

– Payment through Trust

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PAYMENT BY EMPLOYERYMEN BY EM LOYE

• One case: No scheme, payment for annuity restricted to only few employees at retirement –restricted to only few employees at retirement out of current revenue

• Second case: Scheme framed, benefits paid by the employer without any fundthe employer without any fund.

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• Disadvantages:

– In absence of scheme, not everyone covered, y

– Else, payment of pension dependent on the financial situation of the employer → No profits, no pensionsituation of the employer No profits, no pension

– AS 15 by ICAI lays down that the retirement benefits has to be provided on an accrual basishas to be provided on an accrual basis.

– Can also arrange with Life Insurance Companies

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PAYMENT BY TRUSTS

• Second method to administer super-annuation benefits

• Separate Trust to be created, which is irrevocable and distinct from the employerp y

• Employer has to transfer the contributions to the ti b fitsuperannuation benefit

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APPROVED APPROVED SUPERANNUATION FUNDH l s l j t b fits i l ti • Helps an employer enjoy tax benefits in relation to the payments made for the fund

• Defined in I.T. Act: “Approved Superannuation Fund means a superannuation fund or any part of a superannuation fund which has been and continues superannuation fund which has been and continues to be approved by the Chief Commissioner or Commissioner in accordance with the rules contained in Part B of the Fourth Schedule.”contained in Part B of the Fourth Schedule.

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PENSION PLANS –ENS ON L NS INSURANCE COMPANIES

LIFE INSURANCE CORPORATION OF INDIA• LIFE INSURANCE CORPORATION OF INDIA

– Both Immediate & Deferred Pension PlansBoth Immed ate & Deferred ens on lans

– Jeevan Akshay V:di i Pl• Immediate Annuity Plan

• Purchased through single payment or regular payment toop y

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JEEVAN AKSHAY –TYPES OF ANNUITIESRegular annuity for life Regular annuity for life .

• Annuity payable for 5 , 10 , 15 or 20 years certain and thereafter as long as the annuitant is aliveAnnuity for life with return of purchase price on Annuity for life with return of purchase price on death of the annuitant .Annuity increasing at simple rate of 3% p.a. Annuity for life with a provision of 50% of the Annuity for life with a provision of 50% of the annuity to spouse for life on death of the annuitant Annuity for life with a provision of 100% of the

it t f lif d th f th annuity to spouse for life on death of the annuitant

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• Jeevan Suraksha• Jeevan Dhara• Jeevan Dhara

These are Deferred Annuity plans that f y pallow the policyholder to make provision for regular income after the selected termterm

Tax relief under Section 80 CCC is available on premiums paid under New available on premiums paid under New Jeevan Suraksha 1.

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ICICI PRUDENTIAL

• Life Time Super Pension– 5 Annuity options– 5 Annuity options– 4 Investment funds – flexibility of ULIP plans– Tax benefitsTax benefits– Life cover - optional

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Lif Li k S P i• Life Link Super Pension

– Single premium payment– Single premium payment

– Option to pre determine your retirement ageOpt on to pr t rm n your r t r m nt ag

– Also offers tax benefits

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F f• Forever Life

– Regular premium payment termsRegular premium payment terms

– Riders available with policy

– 5 options of annuity payouts

– Guaranteed additions

– Life cover available

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OTHER COMPANIESHDFC STANDARD Lif• HDFC STANDARD LifeProvide both unit linked as well as traditional policiesp

Kotak Mahindra Life Insurance Company• Kotak Mahindra Life Insurance Company– Unit linked retirement plan

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PENSION PRODUCTS –MUTUAL FUNDS

UTI M t l F d UTI R ti t B fit • UTI Mutual Fund → UTI Retirement Benefit Plan

• Templeton Mutual Fund → Templeton India Pension Plan

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UTI Retirement Benefit U et rement Benef t Plan

Obj ti• Objective:– To provide pension to investors at the age of

58 yearsy• Functioning:

– Similar to mutual fundsAny resident/non resident individual in the age – Any resident/non-resident individual in the age group of 18 to 52 years can join the plan, which matures at age 58.

ld b l – Investments could be lump sum or systematic

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• The minimum investment - Rs. 10,000 (in a lump sum or in instalments of a minimum of Rs 500 (a maximum of four instalments a year) up to the age f 52 of 52.

• There is no limit on the maximum amount you can i

yinvest.

• A minimum of Rs 10,000 can be invested in a lumpsum or periodically up to the age of 52 years to set up a retirement kitty. p y

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• After the age of 58, investments can be encashed at the NAV-based repurchase price.

• If staying invested a monthly pension from the • If staying invested, a monthly pension from the age of 58 for the rest of your life.

• Premature repurchase before the age of 58 is allowed at a discount of 10 per cent to the NAV allowed at a discount of 10 per cent to the NAV.

• After the age of 52, pension begins five years from the date of investment from the date of investment.

• Repurchase allowed at the NAV-related repurchase price five years from the date of investment investment.

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PROBLEMSC t• Concepts:– Present Value of payments– Future Value of payments– Future Value of payments– Present value of annuities

• PMT * [(1+i)^n-1]/iPMT [(1 i) n 1]/i– Future value of annuities

• PMT * [1-{1/(1+i)^n}]/i

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• Problem1:• Problem1:

Calculate the present value of an immediate Calculate the present value of an immediate annual annuity payable for 10 years certain at the rate of Rs. 10,000 p.a., the first instalment being pdue at the end of one year. Assume rate of interest as 7% p.a.

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• Solution:• Solution:– Variables:

• Annuity - 10,000Annuity 10,000• No. of years (n) - 10• Rate of interest (i) - 7%• Present Value - Find (?)

• Use present value of an annuity formula to find out the present value of the income streamstream

• Answer – Rs. 70,236DREAMZ INFINITE FINANCIAL PLANNERS

P bl m 2: • Problem 2:

What would be the present value at a rate of p finterest of 6% p.a. of a deferred annuity payable for ten years certain, the first payment falling due at the end of 6 years from now The annuity due at the end of 6 years from now. The annuity is payable at the rate of Rs. 100,000 p.a. for the first 5 years and Rs. 200,000 p.a. for the next 5 yearsyears.

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• Solution outline:Solution outline– Annuity starts from year 6 (end) to year 15

(end) for a total period of 10 yearsT find t th p s nt l n i t 0 – To find out the present value now, i.e. at year 0 – payment to begin at the end of 6 years from now

– Two stage model:• First – find out the present value of the

annuity for 10 yearsannu ty for years» This can be broken down into 2 parts

as the annuity payments differ over the period of 10 yearsthe period of 10 years.

• Second – find out the present value as on today of the amount as arrived above

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• Part I:

S t A ( s 6 t 10)– Segment A (years 6 to 10)• Annuity (A) – 100,000• No of years (n) – 5No. of years (n) 5• Interest rate (i) - 5%• Present value at year 5 – Find (?)y ( )

– PV of annuity formula – Rs. 432,947.67

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– Segment B (years 11 to 15)• Annuity (A) – 200,000• No. of years (n) – 5• Interest rate (i) - 5%Interest rate (i) 5%• Present value at year 10 – Find (?)

– PV of annuity formula – Rs. 865,895.33Convert this PV of annuity to present – Convert this PV of annuity to present value as on year 5

– Future value (FV) - Rs. 865,895.33N f i d ( ) 5– No. of periods (n) - 5

– Interest rate (i) - 5%– Present Value (PV) - Find (?)

» Answer – Rs. 678, 451.65

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• Total present value at year 5 – Rs.11,11,399.32• Convert this amount to present value at year 0

– FV – 11,11,399.32– n - 5

i 5%– i - 5%– PV - ?

• Answer 870 810 45• Answer – 870,810.45

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• Problem 3:– Varun, aged 45 years saves at 8% p.a. Rs.

200 000 in the beginning of a year for the 200,000 in the beginning of a year for the first 8 years and then stops saving. On retirement at the age of 65 years, he intends

k id f R 10 00 000 f h to keep aside a sum of Rs. 10,00,000 out of the accumulated amount of the above savings as liquid money for emergencies and to invest the q y gbalance amount at 6 % p.a. providing withdrawal of a fixed amount at the end of every year for 15 years Find the amount of annual withdrawal15 years. Find the amount of annual withdrawal.

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• Solution outline:

Retirement after 20 years– Retirement after 20 years

– Contribution period – first 8 years (in the p y (beginning)

Amount to be set aside for contingencies– Amount to be set aside for contingencies

– To find out the amount of annual withdrawal from the balance accumulated funds.

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• Find future value at the end of 8 years for the contribution made during this period

– A - Rs. 200,000

– n- 8

– i - 9%

– FV - 24,04,207.29

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F d f l f h l d • Find future value of the accumulated amount at the end of the balance 12 years

– PV - 24,04,207.29

12– n- 12

– i - 9%i 9%

– FV - ? (Find)• Answer – Rs. 67,62,229.17

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• Derive amount available for withdrawals and find out the annual withdrawal amount:

A t R 500 000– Amount as reserve – Rs. 500,000– Balance amount available – 67,62,229.17 –

500,000 = 62,62,229.17500,000 6 ,6 , 9. 7– PV - 62,62,229.17– n - 20– i - 6%– A - ?

• Answer: Rs. 545,970

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S l ti tli• Solution outline:

To arrive at the amount required to maintain herTo arrive at the amount required to maintain herstandard of living at her retirement age byInflating her per annum expenditure at thenf at ng h r p r annum p n tur at thinflation rate.

90% of the same would be the requiredexpenditure during retirement

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• PV - 250,000• n - 25 (55-30)n 25 (55 30)• i - 5% p.a.• FV - ?

– Use simple PV and FV formula to solve– Answer – Rs. 846,589

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P bl 5• Problem 5:

Sharib aged 25 plans to retire at age 55 His life Sharib, aged 25 plans to retire at age 55. His life expectancy is 75. His current annual expenditure is Rs. 250,000. He estimates no reduction in his

i If i i expenses post-retirement. If interest rate is expected to be 8.5% and inflation is 5% p.a., how much will he save to per annum in order to achieve phis targeted income, if he does not want to leave an estate.

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• Solution outline:– Problem to be divided into 3 parts:

• First, find the value of the annual d expenditure at age 55

• Second, find out the present value of the amount needed to fund the retirement amount needed to fund the retirement standard of living (retirement corpus)

• Third, find out the amount to be saved per annum during working life for the retirement corpus.

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• First step: Value of annual expenditure at age 55PV - 250,000

30n -30i - 5%FV - ?FV ?

– Use the FV formula

• Answer: Rs. 10,80,486

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S c nd st p: P s nt lu f ti m nt c pus• Second step: Present value of retirement corpus

– A - 10,80,486, ,

– n- 20 (75-55)

– i - 3.33% (real return, adjusted for inflation) [(1+r)/(1+i)]-1inflation) [(1+r)/(1+i)] 1

– PV - ? (find)

• Answer – Rs. 1,55,90,483

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• Third step: Amount to be saved per annum

FV Rs 1 55 90 483– FV - Rs. 1,55,90,483

– N - 30

– I - 8.5%

– A - ? (find)

Answer – Rs. 125,512

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• Problem 6:Problem 6

Rahul, aged 42 years has got a contractual ssi nm nt in D b i f p i d f 15 s H assignment in Dubai for a period of 15 years. He

has been on this assignment for the past 6 years and has already saved Rs. 5 lakh every year. He

l s t s Rs 15 l kh f his b l now plans to save Rs. 15 lakh for his balance period, then come back to India for a retired life. If his savings earn an interest @ 7% p.a. during th l ti t h h ill h the accumulation stage, how much money will he accumulate when he returns to India?

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• Solution outline:Step 1: Find the accumulated balance of the

annual savings done over the last 6 yearsannual savings done over the last 6 years.

Step 2: Find out the future value of the Step F nd out the future value of the accumulated value as arrived in Step 1.

Step 3: Find out the accumulated value of the annual savings over the next 9 years

Step 4: Add step 2 + step 3

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• Step 1:

– PMT - 500,000– N - 6

I 7%– I - 7%– FV - ? (find)

• Answer - Rs. 35,76,645.37

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• Step 2:

PV 35 76 645 37PV - 35,76,645.37n - 9I - 7%I 7%FV - ? (find)

Answer: 65,75,516.63

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• Step 3:

PMT - 15,00,000N - 9I 7%I - 7%FV - ? (find)

Answer: 1,79,66,983.12

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• Step 4:

St 2 St 3Step 2 + Step 3

65 75 516 63 + 1 79 66 983 12 = 65,75,516.63 + 1,79,66,983.12 = 2,45,42,499.75

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• Problem 7:

I th b bl if his lif t is 85 In the above problem, if his life expectancy is 85

years and the accumulated savings earn a return years, and the accumulated savings earn a return

of 8% p.a., how much money can he spend p.a. p , y p p

during his retired life?

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• Solution outline:

We have derived the accumulated value as at the

i f i i h d i time of retirement, using the same, we can derive

the spending per annum that can be madethe spending per annum that can be made.

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• PV - 2,45,42,499.75• N - 8%• I - 34

PMT (fi d)• PMT - ? (find)

• Answer: Rs. 21,18,118.60

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• Problem 8:

M h l d 33 l 12% f hi l Mehul, aged 33, plans to save 12% of his salary at the end of every year until his retirement at the age of 58 years. He is currently getting an annual g y y g gsalary of Rs. 360,000 which is expected to increase 8% every year. If his savings earn 7.5% interest p.a., how much accumulated money will he p , yhave on his retirement?

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• Solution outline:Solution outline:Problem based on increasing annuity

• Formula to be used:A*[{(1+r)^n-(1+g)^n}/(r-g)]

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A - 43,200 (12% of 360,000)n - 25 (58 years – 33 years)I - 7.5%g 8% (growth rate of annuity)g - 8% (growth rate of annuity)

FV - ? (find)( )

Answer: Rs. 64,81,171.44

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