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Identified total Value of Current Liabilities 
Posted by: admin  05162016, 10:20 PM  Forum: Numericals
 No Replies


From the following heads, Arrive the total Value of Current Liabilities:
BANK OVERDRAFT 10
BILLS PAYABLE 15
PROVISION FOR EXPENDITURE 25
OUTSTANDING EXPENDITURE 20
PREPAID EXPENSES 15
SUNDRY CREDITORS 20
BOOK DEBTS 15
a. 120 b. 90 c. 105 d. 75 e. 85



GDP CONCEPTS 
Posted by: pradeep_iob  07192015, 05:32 PM  Forum: CAIIB Advanced Bank Management
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1) Gross Domestic Product (GDP): It is the total market value of all the final goods and services
produced within the territorial boundary of a country, using domestic resources, during a
given period of time, usually 1 year.
2) Gross national Income at Market Price =
GDP at Market Price + Taxes less subsidies on production and imports (net receivable from
abroad + Compensation of Employees (Net Receivables from abroad) + Property income (Net
receivables from abroad)
3) Gross National Product (GNP) = GDP + Total Capital gains from overseas investment ()
income earned by foreign nationals domestically
4) According to the National Income Accounting, there are three ways to complete GDP:
i. Expenditure wise
ii. Income wise
iii. Product wise
5) Expenditure Method:
GDP= Consumption + Gross Investment + Government Spending + (Exports Imports)
GDP = C+I+G+(XM)
a. Consumption : This included personal expenditures pertaining to food, households,
medical expenses, rent, etc
b. Gross Investment : Business Investment as capital which includes construction of a
new mine, purchase of machinery and equipments for a factory, purchase of
software, expenditure on new houses, buying goods and services but investments on
financial products is not included as it falls under savings.
c. Government spending: It is the sum of government expenditures on final goods and
services.
d. Exports: This includes all goods and services produced for overseas consumptions.
e. Imports: This includes any goods or services imported for consumption and it should
be deducted to prevent from calculating foreign supply as domestic supply.
6) Income Approach : GDP from the income is the sum of the following major components:
i. Compensation of employees
7
ii. Property income
iii. Production taxes and depreciation on capital
7) Compensation of Employees: It represents wages, salaries and other employee supplements
8) Property Income: It constitutes corporate profits, proprietor’s income, interests and rents
9) GDP at market price measures the value of output at market prices after adjusting for the
effect of indirect taxes and subsidies on the prices.
10) Market price is the economic price for which a good or service is offered in the market
place.
11) GDP at factor cost measures the value of output in terms of the price of factors used in its
production.
12) GDP at factor cost = GDP at Market Price – (Indirect taxes – Subsidies)
13) Product Approach
In India we have getting GDP product wise belongs to 8 sectors.
14) Real GDP or GDP at constant price: It means the value of today’s output at yesterday price.
Real GDP is calculated by tracking the volume or quantity of production after removing the
influence of changing prices or inflation.
15) Normal GDP or GDP at Current prices: It represents the total money value of final goods and
services produced in a given year, where the values are expressed in terms of the market
prices of each year.
16) Factors of production are : Land, Labour, Capital and Entrepreneur



LIBERALIZED REMITTANCES SCHEME (LRS) 
Posted by: anupma  06252015, 09:07 PM  Forum: CAIIB Bank Financial Management
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LIBERALIZED REMITTANCES SCHEME (LRS)
Resident Indian individuals are permitted to freely remit up to USD 125,000 per financial year for any current or
capital account transactions or a combination of both. (For example to acquire and hold immovable property or
shares or any other asset outside India) without prior approval of RBI. Individuals will also be able to open,
maintain and hold foreign currency accounts with a bank outside India for making remittances under this scheme.
The foreign currency account may be used for putting through all transactions connected with or arising from
remittances eligible under this scheme.
LRS facility is in addition to the Remittances allowed as above except in the case of Gifts / Donations.
Gifts/Donations are subsumed under LRS. No sublimit within the overall limit of USD 125,000. Should have been
a Customer of the bank for a minimum of one year. PAN number is mandatory. For this facility, applicants should
designate one branch of one bank.
Remittances can be consolidated in respect of family members subject to the individual family members
complying with the terms & conditions of the Scheme. The LRS for Resident Individuals is available to all resident
individuals including minors. In case the remitter is a minor, the LRS declaration form should be countersigned by
the minor's natural guardian. Facility is available only for Resident individuals and is not to corporates,
partnership firms, HUFs, trusts, etc. Facility is not available for the following:
Prohibited purposes such as purchase of Lottery tickets, Sweepstakes, Proscribed (prohibited) magazines etc.
Remittances either directly or indirectly to Nepal, Bhutan, Pakistan or Mauritius or Countries identified by Financial
Action task force. Remittances directly or indirectly to Individuals /entities identified by RBI as posing significant
risk of terrorism.
FX FOCILMES TO RESIDENTS OTHER THAN INDIVIDUALS
ADs have been permitted to make remittances on account of donations by Corporates for some specified purposes
subject to a limit of one per cent of the foreign exchange earnings during the previous three financial years or
USD 5 million, whichever is less. Other residents like partnership firms, trusts etc., are free to remit up to USD
5,000 per annum per donor / remitter each as gift and donation. Remittances exceeding the limit will require prior
permission from the Reserve Bank



BUDGET TERMS 
Posted by: seema_bob  06242015, 08:09 PM  Forum: CAIIB Advanced Bank Management
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BUDGET TERMS
BUDGET: It is the Annual Financial Statement by the Finance Ministry inaccordance with provisions of Article 112 of the Indian Constitution,giving details of proposed govt expenditure and how money will be raised.
CENTRAL PLAN: It consists of the Government’s budget support to the Plan and the internal and extra budgetary resources raised by public enterprises.
PlanExpenditure: It includes both revenue and capital expenditure of the government on the Central Plan,Central assistance to States and Union Territory plans.
NonPlanExpenditure: It includes bothrevenueandcapitalexpenditureoninterestpayments, theentiredefenceexpenditure(bothrevenueandcapitalexpenditure),subsidies,postaldeficit,policy,pensions,
economic services, loans topublic enterprises andloans aswellasgrants toStateGovt.,UTandforeignGovt.
BUDGET IS DIVIDED IN TO TWO PARTS: CAPITAL AND REVENUE:
CAPITALBUDGET: Itconsistsofcapital receiptsandpayments. Italsoincorporates transactions inthePublicAccount. Ithas twocomponents:CapitalReceiptandCapitalExpenditure.
Capital Receipt: Include loans raised by the government frompublicwhich are calledmarket loans, borrowings fromthe RBI and other parties through sale of Treasury Bills, loans received fromforeign
governments, recoveries of loans grantedbyCentretoState andUTgovernments and otherparties.
CapitalExpenditureayments foracquisitionofassets likeland,buildings,machinery,equipment,as alsoinvestments inshares etc,andloansby theCentretoStates,Govt.companies,corporations and
otherparties.*REVENUEBUDGET:Revenuereceipts of thegovernment (tax revenuesplus other revenues)andtheexpendituremet fromtheserevenues. Ithas twocomponents:RevenueReceiptand
RevenueExpenditure.RevenueReceipt: It includes proceeds of taxes andotherduties leviedby theCentre, interestanddividendoninvestmentsmadeby theGovt. feesandother receipts forservices
renderedby thegovernment.
Revenue Expenditure: It ismeant for the normal running of government departments and various services, interest charges on debt incurred by the government and subsidies. Broadly speaking, expenditure
which does not result in creation of assets is treated as revenue expenditure. All grants given to StateGovt. and other parties are also treated as revenue expenditure even though some of the grantsmay be for
creationofassets.
*STEPS IN BUDGET PRESENTATION:
BudgetSpeech: It is thefirststepinpresentationofbudget.TheSpeechis presentedevery yearby theFinanceMinister intheLokSabha,usuallyonlastworkingdayofFebruary.
ExpenditureBudget:Containsexpenditureestimatesmadeforaschemeorprogrammeunderbothrevenueandcapitalheads.
FinanceBill:This contains thegovernment’sproposals for levyofnewtaxes,modificationof theexistingtaxstructureorcontinuanceof theexistingtaxstructurebeyondtheperiodapprovedbyParliament.
DemandsforGrants: It is astatement ofestimates ofexpenditurefromtheConsolidatedFundandis required tobe voted by theLokSabha.Generally, oneDemand forGrant is presented by each
Ministry.AppropriationBill: It is presented toParliament for its approval, so that the government canwithdrawfromtheConsolidatedFund the amounts required formeeting theexpenditurechargedon
theConsolidatedFund.No amount canbewithdrawn fromtheConsolidatedFundtill theAppropriationBill is voted and enacted.
*TYPES OF DEFICIT: Excess of Expenditure over Receipts is known as Deficit.
BudgetaryDeficit: It is the excess of total expenditure over total receipts.
CapitalDeficit: It refers to the excess of capital expenditure over capital receipts.
RevenueDeficit: It refers to the excess of revenue expenditure over revenue receipts.
Fiscal Deficit: It is the difference between the revenue receipts plus certain nondebt capital receipts and the total expenditure including loans (net of repayments). This indicates the total borrowing
requirementsof thegovernment fromall sources.
PrimaryDeficit: It is the difference between fiscal deficit and interest payments.
MonetisedDeficit: It indicates the level of support extended by theRBI to theGovt’s borrowing programme.
VARIOUS GOVT ACCOUNTS:
Consolidated Fund: It ismadeupofall revenues receivedby thegovernment, loans raisedby it,andalsoits receipts fromrecoveriesof loans grantedby it.Allexpenditureof thegovernment is incurredfromthe
ConsolidatedFundandnoamountcanbewithdrawnfromtheFundwithoutauthorisationfromParliament.
Public Account: It is an account inwhichmoney received through transactions not relating to theConsolidated Fund is kept.Besides the normal receipts and expenditure of the government relating to the
Consolidated Fund, certain other transactions enter government accounts in respect of which the government actsmore as a banker, for example, transactions relating to provident funds, small savings
collections, otherdeposits etc.Suchmoney is kept inthePublicAccount andtheconnecteddisbursements.
Contingency Fund: It is an imprest placed at the disposal of thePresident and is used by the government to incur all its urgent and unforeseen expenditure. Parliamentary approval for such expenditure and for
withdrawalofanequivalentamountfromtheConsolidatedFundissubsequentlyobtainedandtheamountspent fromtheContingencyFundisrecoupedtotheFund.



Time Value of Money 
Posted by: sarita  06222015, 07:25 PM  Forum: CAIIB Advanced Bank Management
 No Replies


Time Value of Money
When cash flows take place at different time intervals, their value is different for a no. of reasons such as interest factor, inflation,
uncertainty ettz. In order to ascertain their value, these flows are required to be compared. The comparison is possible by using a time
line that shows the value and timing of cash flows.
Terms associated with cash flow:
When cash flows take place at different time intervals, their value is different for a no. of reasons such as interest factor, inflation,
uncertainty ettz. In order to ascertain their value, these flows are required to be compared. The comparison is possible by using a time
line that shows the value and timing of cash flows.
Terms associated with cash flow:
Positive cash flow : When a firm receives cash which is called inflow, it is a positive cash flow. Negative cash flow: When a firm makes
payments, this is outflow of cash and is called negative cash flow.Future cash flow & present cash flow : Future cash flows are worth less than the present cash flow. Rs.ioo available with a person presently and Rs..100 to be received after a year, carry higher present value. It is becausethe people prefer present consumption rather than in future and to put off their consumption for future, more value requires to be offered.Similarly due to inflation, there is erosion in money value.Further there is uncertainty about receipt of money in
future.Discounting: It is a process by which the future cash inflows are adjusted/discounted according the their present value. (say
Rs.ioo received at the end of a year, if discounted at say io%, will give a value around Rs.9o). For this purpose, the rate that used is
called discount rate.
Compounding : It is a process by which the present value is converted into future value by using a given rate of interest.
Tradeoff: When present consumption is putoff, for some future time period in return for some monetary return such as interest, this is
called exchange or Trade Off.
Effect of Inflation and Risk on the discount rate.
The inflation reduces the purchasing power of future cash flows and it reduces the value of future cash flows. Hence, if the inflation is higher, the discount rate will be higher to calculate the present value.Risk is due to uncertainty. If risk is higher, the discount rate would be higher.
Importance of discounting of the cash flows.The comparison becomes easier for cash inflows of different periods.The user becomes
indifferent for present and future cash inflows and can take more rationale decisions.
Other kinds of cash flows: The cash flows can be simple cash flows, annuities, growing annuities, perpetuities and growing perpetuities.
Simple cash flow: It is single cash flow to occur at a specified future time. Say Rs.i000 to be received at the end of one year. Its
present value can be worked out by discounting back by using an appropriate discount rate.
CALCULATION OF PRESENT AND FUTURE VALUES OF CASH FLOWS Calculation of present value of a future (simple) cash
flow: The present value can be calculated by using the formula
PV = Discount Factor x CI OR PV = 1 / (1+r) x C1 (where CI is the expected cash flow at the end of period .1)
Example : A person wants to get Rs.10 lac after one year. With prevailing interest rate of 9%, how much he should invest.
= 10,00,000 / 1.09 = 917531.19
Calculation of net present value
It can be calculatdd as NPV= PV of future cash flow required investment OR it can be calculated as
= [(Ci / (t+r) + (Ci / (i+r) + (Ci / (i+r) + (Cn (i+r)]  Co Co = Cash flow at time o i.e. today.
r' means rate of discount.
Ci = Present value of cash flow at end of period one.
You proposes to invest Rs.8 lac in a house and expect that it will fetch Rs.io lac at the end of the year. At 9% interest rate,
what is the net present value. Use the data in the above problem.
NPV= PVrequired investment
= 917531.19  800000 = 117531.19
Example2 : X paid Rs.l00000 to Y on Jan 01, 2009. Y returned Rs.65000 after one year, Its.g0000 at end of 2nd year.
What is the present value of amount paid by Y to X and what is net present value of the cash flows for X at 10% discount rate ? Present value of amount paid by X = 100000
Present value of amount paid by after one year = 6500o / 1.1 = 59090 Present value of amount paid by Y after 2 years = 90000 / 1.1 x 1.1 = 74380 Present value of total amount paid by Y = 59090 + 74380 = 133470
Net present value of cash flows = 133470  100000 = Rs. 33470
Effect of Inflation and Risk on the present value.
The inflation reduces the purchasing power of future cash flows and it reduces the present value of future cash flows.
Risk is due to uncertainty. If risk is higher, the discount rate would be higher and present value of future cash flows would be lower.
Rule to take decision on making an investment:
If net present value at an acceptable discount rate is zero or positive, the investment can be made.
If internal rate of return (i.e. acceptable discount rate at which net present value is zero) is greater than the opportunity cost of capital, the investment can be made.
Ibbotson and Sinquefield's Study:
Ibbotson and Sinquefield conducted a study of returns on investment in bonds and stock between the period 1926  1992. It was found
that average return on stocks was 12.4%, on treasury bonds 5.2%, on treasury bills 3.6%. If investment is made in these 3 instruments at above rates of return, with a time horizon of 40 years, the future value of investment at 12.4% in stock will be 12 times more than
investment in treasury bonds at 5.2%
at 12.4% in stock will be 25 times more than investment in treasury bills at 3.6% This snows that if the time horizon is longer, the gap between the return will be greater.
Conversion of nominal cash flows of future period, to real cash flows. Real cash flow = (Nominal cash flow) / (1+ inflation rate) If the inflation rate is 10% per annum and an investor expects Rs.io lac, what will be his real cash flow. Real cash flow = (Nominal cash flow) / (1+ inflation rate) 10,00,000 / 1+10% = 10 lac / 1.10 = Rs. 909091
Calculation of future value of a present (simple) cash flow: This can be done by way of compounding by using the formula
CF o (1+0 where (1 = at the end of period 0 (CF o = present cash flow) and ( r = rate of discount)
Example : X deposited Rs.i0000 with bank at 10% rate of interest for 2 years. What is the future value (maturity value) of this amount: =
10000 (1+10)2 = 10000 x 1.10 x 1.10 = 12100
Rule of 72
By using this method, we can find out as to, in how much period (appx), an amount will become double at a particular interest rate. If 72 is divided by the interest rate, the resultant product, is the time period during which the amount will be doubled. For example if the
interest rate is 8%, the amount will double in 9 years.
Concept of effective rate of interest
It is the actual rate of interest that takes into account the compounding effect of interim interest payment, if any. At more frequent
compounding, the effective rate of interest would be more.
Determination of effective rate of interest It can be done by using the following formula:
(1+ given annual RoI /N )n  1 (where N = no. of compounding periods. Say42= months).
Where the annual interest rate is 20%, what will be effective rate, where the compounding is on halfyearly (semiannual) basis.
(1+ 'given annual Rol /N )n  1
(1.10 2  1) = 1.21 — 1.00 = 21%
Effective rates for various compounding frequencies for 10% RoI:
Where compounding frequency is annual Effective Rol = 0.10 = 10% Where the compounding frequency is semi annual: Effective Rol = (1 + 10/2) 2  1) = 10.25% Where the compounding frequency is monthly : Effective RoI = (1 + 10/12) 12 1) = 10.47% Where the
compounding frequency is daily : Effective Rol = (i + 10/365)3°5  1) = 10.5156% Where the compounding frequency is on continuous
basis: Effective Rol = e,1°  1) = 10.5171% Continuous compounding & calculation of effectiveinterest rate :It can be computed as = exp r  1 (where 'exp' means exponential number and 'r' means given interest rate).
Impact of frequency of compounding on effective rate of interest:
Effective rate increases and present value of future cash flows decreases if compounding is more frequent. ANNUITYIt is a constant cash
flow, accruing at regular intervals of time, for a prefixed period.It can occur at the beginning of each period (called annuity due) or at the
end of each period (called ordinary annuity)
Present value of amendofthe period annuity (Ordinary ann ty):
= PV (A,r,n) = A fi(1/ (1+r) n) r
(Alternative formulae : PV = A / r [{(1+r)n 1} / (1+r)n j
(A = annuity r=discount rate n=no. of years.
Example1: Calculate the PV of Rs.9000 each year for 5 year/5 where R41$12%.
= PV (A,r,n) = A {1(1/ (i+r) n r \ C) ‘'k
= 9000 {141/ (1+12)s) / 0.12 = 32442.98
Example2 : X deposits Rs.i000 at end of each year for 4 y ars at io rate of Hite t. is the present value of the amount, +.1D be deposited:
= A + A/r [11/(i+r) ni /(i+r) = moo+ 1000 / 0.1 [11/(1+0.10)41] / (Li) = 1000+ moo / 0.1 [11/(1.331)] (1.1) = woo+ moo / 0.1 [10.7513)] (1.1) = 1000+ 10000 [0.2487] (1.1) = woo + 2487 = 3487 (Li) = 317
Future value of an endofthe period annuity (Ordinary annuity):
= FV (A,r,n) = A {(i+r)n 1} r
(Alternative formulae : FV = A / r {(1+1)n 1} (A = annuity r=discount rate n=uo. of years.
Example  Z deposits Rs.i0000 annually for next 5 years. At 10% rate of interest, what will he be getting?
= A [ (1 +r) n  1] / r = 10000 [ (1 +0.10) 5 / 0.10]
= 10000 [1.610511/ 0.10] = 10000 [0.61051 / 0.10] = Rs.61051
P r e s e n t v a l u e o f b e g i n n i n g  o f  a  p e r i o d a n n u i t y ( A n n u i t y d u e ) o v e r n y e a r s : = A + A / r { [ 1  1 ( i + r ) n 
i ] (A = c a s h f l o w p e r p e r i o d o r a n n u i t y , r = r a t e o f i n t e r e s t , n = n o . o f p a yme n t s )
Example : X deposits Rs.i000 at beginning of each year for 4 years at 10% rate of interest. What is the present value of the amount, to be
deposited:
= A + A/r [11/(t+r) n1] = 1000+ 1000 / 0.1 [11/(1+0.10)41]
= 1000+ 1000 / 0.1 [11/(1.331) = 1000+ 1000 / 0.1 [10.7513)]
= 1000+ 10000 [0.2487] = 1000 + 2487 = 3487
Future value of beginningofaperiod annuity (Annuity due):
= C {[(i+r) n 1] r } x (i+r) OR A / r [(i+r) {(1+r)n1)11
Example  Z wants to deposit Rs.10000 in a recurring deposit account for 3 years in the
beginning of the year. At io% p.a., how much will he be getting? =A/r{(1+r)[(i+r)ni]}
10000/0.10 +0.0 [(1 +0.1) 3  = 10000 / 0.10 [(1 +0.1) (1.331)  1]
= 10000 / 0.10 [1.1 x .331] = 10000 / 0.10 x 0.3641 = Rs.36410
C a l c u l a t i o n o f A n n u i t y g i v e n f u t u r e v a l u e : = A ( F V , r , n ) = F V { r / ( i + r ) n  1 } Z w a n t s t o
r e c e i v e R s . 6 1 0 5 1 a n d w a n t s t o d e p o s i t a n e q u a l a m o u n t f o r 5 y e a r s a t 1 0 % p . a . . H o w
much should deposit regularly?
= 61051{0.10 / (i+0.10)5 1}
= 61051{0.10 / (1.61051) 1}
Compiled by Mr. Sanjay Kumar Trivedy, Sr. Mgr., RSTC, mumbai
26
= 61051{0.10 / 0.61051 = Rs.i0000
Baloon repayment loan
it is a loan in which repayment of interest only is made during life period of the loan. The amount o loan is repaid in one instalment
at the end of repayment period, such as debenturesand bond's. The companies raising bonds or debentures set aside funds in a
sinking fundsmaturing with maturity period of the loan, so that do not face any problem at the time ofrepayment.
Sinking fund It is fund created by companies for meeting special repayment obligations in which regularcontributions are made on
annual or other basis.
Growing annuity It a cash flow which grows at a constant rate for a specified period of time.If A is the current cash flow and g is the
expected growth rate, the value can be calculated asunder:
Present value of a growing annuity : =A [(i+g) / (r — g)] {(1(1+g) n / (i+r) " ) (g stands for expected growth rate)The present value
can be estimated in cases except when the growth rate is equal to discountrate, the present value is equal to the nominal sums of
annuities over the period, without the
growth effect.
Present value of a growing annuity for n years be calculated when r = g It is = nA
PERPETUITY
It is a constant cash flow paid or received at regular time intervals forever, such as a life time pension or rentals received from use of land.
Calculation of present value of perpetuity : It can be calculated by use of the formula : A / rWhen the coupon rate is equal to interest
rate, the value will be equal to face value.
Growing perpetuity It is a cash flow which forever, is expected to grow at a constant rate. The present value of a growing perpetuity can
be written as.. Ci / (rg)
Console Bond It is a bond which does not have maturity. On such bond fixed coupon or RoI is paid.An investor has a console bond of
Rs.i0000 with 8% fixed coupon. If the interest rate is 10%,the current value of the bond would be: When a firm receives cash which is called inflow, it is a positive cash flow. Negative cash flow: When a firm makes
payments, this is outflow of cash and is called negative cash flow.Future cash flow & present cash flow : Future cash flows are worth less than
the present cash flow. Rs.ioo available with a person presently and Rs..100 to be received after a year, carry higher present value. It is
becausethe people prefer present consumption rather than in future and to put off their consumption for future, more value requires to be
offered.Similarly due to inflation, there is erosion in money value.Further there is uncertainty about receipt of money in
future.Discounting: It is a process by which the future cash inflows are adjusted/discounted according the their present value. (say
Rs.ioo received at the end of a year, if discounted at say io%, will give a value around Rs.9o). For this purpose, the rate that used is
called discount rate.
Compounding : It is a process by which the present value is converted into future value by using a given rate of interest.
Tradeoff: When present consumption is putoff, for some future time period in return for some monetary return such as interest, this is
called exchange or Trade Off.
Effect of Inflation and Risk on the discount rate.
The inflation reduces the purchasing power of future cash flows and it reduces the value of future cash flows. Hence, if the inflation is higher,
the discount rate will be higher to calculate the present value.Risk is due to uncertainty. If risk is higher, the discount rate would be higher.
Importance of discounting of the cash flows.The comparison becomes easier for cash inflows of different periods.The user becomes
indifferent for present and future cash inflows and can take more rationale decisions.
Other kinds of cash flows: The cash flows can be simple cash flows, annuities, growing annuities, perpetuities and growing perpetuities.
Simple cash flow: It is single cash flow to occur at a specified future time. Say Rs.i000 to be received at the end of one year. Its
present value can be worked out by discounting back by using an appropriate discount rate.
CALCULATION OF PRESENT AND FUTURE VALUES OF CASH FLOWS Calculation of present value of a future (simple) cash
flow: The present value can be calculated by using the formula
PV = Discount Factor x CI OR PV = 1 / (1+r) x C1 (where CI is the expected cash flow at the end of period .1)
Example : A person wants to get Rs.10 lac after one year. With prevailing interest rate of 9%, how much he should invest.
= 10,00,000 / 1.09 = 917531.19
Calculation of net present value
It can be calculatdd as NPV= PV of future cash flow required investment OR it can be calculated as
= [(Ci / (t+r) + (Ci / (i+r) + (Ci / (i+r) + (Cn (i+r)]  Co Co = Cash flow at time o i.e. today.
r' means rate of discount.
Ci = Present value of cash flow at end of period one.
Examplei : You proposes to invest Rs.8 lac in a house and expect that it will fetch Rs.io lac at the end of the year. At 9% interest rate,
what is the net present value. Use the data in the above problem.
NPV= PVrequired investment
= 917531.19  800000 = 117531.19
Example2 : X paid Rs.l00000 to Y on Jan 01, 2009. Y returned Rs.65000 after one year, Its.g0000 at end of 2nd year.
What is the present value of amount paid by Y to X and what is net present value of the cash flows for X at 10% discount rate ? Present value
of amount paid by X = 100000
Present value of amount paid by after one year = 6500o / 1.1 = 59090 Present value of amount paid by Y after 2 years = 90000 / 1.1 x 1.1 =
74380 Present value of total amount paid by Y = 59090 + 74380 = 133470
Net present value of cash flows = 133470  100000 = Rs. 33470
Effect of Inflation and Risk on the present value.
The inflation reduces the purchasing power of future cash flows and it reduces the present value of future cash flows.
Risk is due to uncertainty. If risk is higher, the discount rate would be higher and present value of future cash flows would be lower.
Rule to take decision on making an investment:
If net present value at an acceptable discount rate is zero or positive, the investment can be made.
Compiled by Mr. Sanjay Kumar Trivedy, Sr. Mgr., RSTC, mumbai
25
If internal rate of return (i.e. acceptable discount rate at which net present value is zero) is greater than the opportunity cost of capital, the
investment can be made.
Ibbotson and Sinquefield's Study:
Ibbotson and Sinquefield conducted a study of returns on investment in bonds and stock between the period 1926  1992. It was found
that average return on stocks was 12.4%, on treasury bonds 5.2%, on treasury bills 3.6%. If investment is made in these 3 instruments at
above rates of return, with a time horizon of 40 years, the future value of investment at 12.4% in stock will be 12 times more than
investment in treasury bonds at 5.2%
at 12.4% in stock will be 25 times more than investment in treasury bills at 3.6% This snows that if the time horizon is longer, the gap between
the return will be greater.
Conversion of nominal cash flows of future period, to real cash flows. Real cash flow = (Nominal cash flow) / (1+ inflation rate) If the inflation
rate is lo% per annum and an investor expects Rs.io lac, what will be his real cash flow. Real cash flow = (Nominal cash flow) / (1+ inflation
rate) io,00,000 / 1+1o% = 10 lac / 1.10 = Rs. 909091
Calculation of future value of a present (simple) cash flow: This can be done by way of compounding by using the formula
CF o (1+0 where (1 = at the end of period 0 (CF o = present cash flow) and ( r = rate of discount)
Example : X deposited Rs.i0000 with bank at 10% rate of interest for 2 years. What is the future value (maturity value) of this amount: =
10000 (1+10)2 = 10000 x 1.10 x 1.10 = 12100
Rule of 72
By using this method, we can find out as to, in how much period (appx), an amount will become double at a particular interest rate. If 72 is
divided by the interest rate, the resultant product, is the time period during which the amount will be doubled. For example if the
interest rate is 8%, the amount will double in 9 years.
Concept of effective rate of interest
It is the actual rate of interest that takes into account the compounding effect of interim interest payment, if any. At more frequent
compounding, the effective rate of interest would be more.
Determination of effective rate of interest It can be done by using the following formula:
(1+ given annual RoI /N )n  1 (where N = no. of compounding periods. Say42= months).
Where the annual interest rate is 20%, what will be effective rate, where the compounding is on halfyearly (semiannual) basis.
(1+ 'given annual Rol /N )n  1
(1.10 2  1) = 1.21 — 1.00 = 21%
Effective rates for various compounding frequencies for 10% RoI:
Where compounding frequency is annual Effective Rol = 0.10 = 10% Where the compounding frequency is semi annual: Effective Rol = (1
+ 10/2) 2  1) = 10.25% Where the compounding frequency is monthly : Effective RoI = (1 + 10/12) 12 1) = 10.47% Where the
compounding frequency is daily : Effective Rol = (i + 10/365)3°5  1) = 10.5156% Where the compounding frequency is on continuous
basis: Effective Rol = e,1°  1) = 10.5171% Continuous compounding & calculation of effectiveinterest rate :It can be computed as = exp r
 1 (where 'exp' means exponential number and 'r' means given interest rate).
Impact of frequency of compounding on effective rate of interest:
Effective rate increases and present value of future cash flows decreases if compounding is more frequent. ANNUITYIt is a constant cash
flow, accruing at regular intervals of time, for a prefixed period.It can occur at the beginning of each period (called annuity due) or at the
end of each period (called ordinary annuity)
Present value of amendofthe period annuity (Ordinary ann ty):
= PV (A,r,n) = A fi(1/ (1+r) n) r
(Alternative formulae : PV = A / r [{(1+r)n 1} / (1+r)n j
(A = annuity r=discount rate n=no. of years.
Example1: Calculate the PV of Rs.9000 each year for 5 year/5 where R41$12%.
= PV (A,r,n) = A {1(1/ (i+r) n r \ C) ‘'k
= 9000 {141/ (1+12)s) / 0.12 = 32442.98
Example2 : X deposits Rs.i000 at end of each year for 4 y ars at io rate of Hite t. is the present value of the amount, +.1D be deposited:
= A + A/r [11/(i+r) ni /(i+r) = moo+ 1000 / 0.1 [11/(1+0.10)41] / (Li) = 1000+ moo / 0.1 [11/(1.331)] (1.1) = woo+ moo / 0.1 [10.7513)]
(1.1) = 1000+ 10000 [0.2487] (1.1) = woo + 2487 = 3487 (Li) = 317
Future value of an endofthe period annuity (Ordinary annuity):
= FV (A,r,n) = A {(i+r)n 1} r
(Alternative formulae : FV = A / r {(1+1)n 1} (A = annuity r=discount rate n=uo. of years.
Example  Z deposits Rs.i0000 annually for next 5 years. At 10% rate of interest, what will he be getting?
= A [ (1 +r) n  1] / r = 10000 [ (1 +0.10) 5 / 0.10]
= 10000 [1.610511/ 0.10] = 10000 [0.61051 / 0.10] = Rs.61051
P r e s e n t v a l u e o f b e g i n n i n g  o f  a  p e r i o d a n n u i t y ( A n n u i t y d u e ) o v e r n y e a r s : = A + A / r { [ 1  1 ( i + r ) n 
i ] (A = c a s h f l o w p e r p e r i o d o r a n n u i t y , r = r a t e o f i n t e r e s t , n = n o . o f p a yme n t s )
Example : X deposits Rs.i000 at beginning of each year for 4 years at 10% rate of interest. What is the present value of the amount, to be
deposited:
= A + A/r [11/(t+r) n1] = 1000+ 1000 / 0.1 [11/(1+0.10)41]
= 1000+ 1000 / 0.1 [11/(1.331) = 1000+ 1000 / 0.1 [10.7513)]
= 1000+ 10000 [0.2487] = 1000 + 2487 = 3487
Future value of beginningofaperiod annuity (Annuity due):
= C {[(i+r) n 1] r } x (i+r) OR A / r [(i+r) {(1+r)n1)11
Example  Z wants to deposit Rs.10000 in a recurring deposit account for 3 years in the
beginning of the year. At io% p.a., how much will he be getting? =A/r{(1+r)[(i+r)ni]}
10000/0.10 +0.0 [(1 +0.1) 3  = 10000 / 0.10 [(1 +0.1) (1.331)  1]
= 10000 / 0.10 [1.1 x .331] = 10000 / 0.10 x 0.3641 = Rs.36410



