Download MOD A - SBH SC/ST WELFARE

JAIIB/DBF
Accounting & Finance for
Bankers
MODULE-A
Basics of BUSINESS MATHEMATICS
Why Mathematics in Banking
• To calculate interest on deposits and advances
• To calculate yield on bonds in which banks have
to invest substantial amount.
• To calculate depreciation
• To decide on buying/selling rates of foreign
currencies
• To calculate minimum capital required by the
bank
• To appraise loan proposals
What level of maths is required
• In banking, very high level of maths is not
needed
• We should know the following basic
mathematical operations
• Addition,e.g. 24+33+9+56=122
• Subtraction,e.g.138-41-72=25
• Multiplication,e.g. 1.1*1.1=(1.1)2 =1.21
• Division,e.g.1/12=0.0833
• (1+r)n is often used. It simply means that 1+r is
multiplied by 1+r , n times. E.g. if r=0.1 and
n=3,this is equal to 1.1*1.1*1.1 =1.331
Weightage of maths in JAIIB/DBF
Exam
• Constitutes one of the four modules of the
paper of Accounting & Finance.Therefore,
the weightage in this paper is about 25%
• It is possible to get good score in
questions related to this module, as only
simple mathematics is involved and use of
calculator is allowed
Can we cover entire syllabus in this
class
• We can have conceptual clarity of the
entire syllabus on business maths.
• You need to read the book (Accounting &
Finance for Bankers Second edition 2008 )
thoroughly, and solve problems from the
work book.
• You may get in touch with me whenever
you need any clarification
• My mail id is [email protected]
Simple interest
• Important symbols ; P=amount deposited
initially, called Principal
• r=rate of interest. 12% per annum means that if
you deposit Rs 100 for one year,you will get
interest of Rs 12 at the end of the year.In our
calculations,we will take r=12/100=0.12 p.a.
• T=number of years for which P is deposited
• I=total interest receivable. I=P*r*T
• A=amount receivable.A=P+I=P+(P*r*T)=P(1+rT)
Compound interest
• If you deposit Rs 100 @12%p.a.,it becomes Rs 112 at
the end of one year.For next year,you should get interest
on Rs112,which is 112*12/100=13.44.This is called
compounding.In case of simple interest, you would have
received interest of Rs 12 only for the 2nd year also.
• Compounding can be yearly,as shown above, or can be
monthly,quarterly,half yearly etc.More frequent
compounding means more interest for you.
• In yearly compounding, A=P(1+r) after 1year, P(1+r)2
after 2years,and so on.After T years, A=P(1+r)T
• If compounding is n times in a year, A=P(1+r/n)nT
• Rule of 72 is used to find the period in which our money
doubles.
Other important terms associated
with interest
• Fixed and Floating interest rate; When the interest rate is fixed for
the entire tenure of the loan or deposit, it is called fixed rate .When it
is linked to some benchmark,and may change depending upon the
market conditions, it is called floating rate.
• Front ended and back ended interest rate;When loan is disbursed
after deducting the amount of interest for a future period, like in bills
discounting,it is called front ended. When the entire loan amount is
disbursed and interest is charged after a period of time, it is back
ended.
• Flat rate of interest is different from interest on reducing balance.
Example: interest on Rs 1000 @10%p.a. for 3years will be Rs 300
with flat rate of interest even though the loan is being repaid every
month. Banks normally charge interest on reducing balance but
NBFCs normally charge interest on flat basis.
Discount factor
• We have seen that P becomes P(1+r)T in T
years.Therefore,if somebody promises to give you Rs
P(1+r)T after T years,you should know that it is worth
only Rs P today.
• Amount receivable in future is to be multiplied by a
number(always less than one) to arrive at the present
worth of that amount.
• In above example,P(1+r)T is to be multiplied by 1/(1+r)T
to arrive at present worth P. So ,the discount factor is
1/(1+r)T.
• E.g.,if rate of intt is 10%p.a., r=0.10. Therefore, discount
factor is 1/1.10 for 1 year, 1/1.21for 2 years and so on.
Present value of money
• PV= Future amount* Discount Factor(DF)
• DF = 1/(1+r)T
• E.g.,if rate of intt is 10%p.a., r=0.10. Therefore,
discount factor is 1/1.10 for 1 year, 1/(1.10)2
=1/1.21 for 2 years and so on.
• In above example,PV of Rs 100 ,to be received
after 2 years will be, 100*1/(1.10)2 =100/1.21=Rs
82.64.Similarly,PV of Rs 100,to be received after
5 years, will be100*1/(1.10)5
Future value of money
• Depending on the rate of interest, the amount you
receive in future(A), will be more than the amount(P)
available now.
• A=P(1+r)T ,when the compounding is yearly.
• Therefore,FV=Present Amount*(1+r)T . We call (1+r)T
compounding factor.
• E.g.,if rate of intt is 10%p.a., r=0.10. Therefore,
compounding factor is 1.10 for 1 year, (1.10)2 =1.21 for 2
years and so on.
• In above example,FV of Rs 100 , after 2 years will be,
100*(1.10)2 =100*1.21=Rs 121.Similarly,FV of Rs 100,
after 5 years, will be100*(1.10)5
Annuities
• A series of fixed payments/receipts at a
specified frequency, over a fixed period.
• E.g. Payment of Rs 1000 every year by
LIC for next 20 years . Also, a Recurring
deposit with bank for Rs 100 for 5 years.
• 2 types of Annuities. Ordinary Annuity;
payment is at the end of the period.
Annuity Due; payment is at the beginning
of each period.
Present and Future value of
Annuity
• For calculating PV of Annuity, PV of each
payment is calculated and added.E.g. if Rs 100
is paid at the end of each year for 10 years, we
calculate pv of each of these 10 payments of Rs
100 separately and add these 10 values.
• Similarly, for calculating FV of Annuity, FV of
each payment is calculated and added.E.g. if Rs
100 is paid at the end of each year for 10 years,
we calculate fv of each of these 10 payments of
Rs 100 separately and add these 10 values.
Precaution while calculating PV
and FV
• In the formulae, given in the books,we
have to correctly arrive at r, i.e.the interest
rate.E.g.the given intt rate is 12%p.a.If the
payment is received yearly, r will be equal
to 12/100=0.12.But if payment is received
monthly, it will be 12/100*12=0.01.For
quarterly payment, it will be 0.03 and for
half yearly payment, it will be 0.06
Sinking fund
• Concept same as that of Annuity
• Suppose, you need a fixed amount(A)
after,say, 5 years.You deposit an
amount(C)every year with a bank.This
becomes A after 5 years and can be used
for repaying a debt or any other
purpose.As the rate of intt and the FV is
known, we can calculate C.
Understanding Formula for
EMI,Annuities(1)
• Let us take case of a home loan of Rs 1lac at 12%p.a.
,repayable in 180 instalments (here p=1,00,000and
r=12/100*12=.01)
• In the 1st month, bank will charge interest equal to
p*r=Rs 1000 and so, the outstanding amount will
become Rs 1,01,000.
• What happens if the EMI is fixed at p*r, which is Rs
1000?This EMI will meet only the interest applied and so
the principal will remain unchanged at Rs 1,00,000.This
process will continue and the loan will remain
outstanding for ever. Therefore, EMI has to be slightly
more than p*r so that some amount can go towards
reducing the principal amount
Understanding Formula for
EMI,Annuities(2)
If EMI has to be more than p*r, we should multiply
p*r by a fig which is more than 1.
This fig is (1+r)n / (1+r)n -1.You will observe that
denominator in less than numerator by 1 only.
E.g., if numerator is 4.3210, the denominator will
be 3.3210 .So, this fig is always more than 1.
As you know, (1+r)n is an important fig in business
maths, and if the above concept is clear, you will
never have difficulty in remembering EMI
formula
Understanding Formula for
EMI,Annuities(3)
• Once you are comfortable with EMI formula, you can
derive yourself the formula for PV and FV of Annuities.
• Home loan is like an ordinary annuity in which payment
takes place at the end of each month for an amount
equal to EMI,and p is like the present value of
annuity.Therefore, in a question, if periodic payment ,n
and r are given, you can calculate PV. FV is calculated
by multiplying PV by (1+r)n.
• In case of annuity due,the payments are at the beginning
of the period and not at the end as is the case with
ordinary annuity. Therefore, both PV and FV will be more
than what is arrived in case of ordinary annuity. The
multiplying factor is (1+r)
Bonds
• A Bond is a form of debt raised by the issuer of
the bond.
• Issuer of the bonds pays interest to the
purchaser for using his money.
• Terms associated with bonds: Face value,
Coupon rate, Maturity, Redemption value,
Market value.
• Face value and redemption value may be
different but these are fixed and known.
• Market value of the bond may be different form
the face value and keeps changing.
Valuation of bonds
• The purchaser of the bonds gets regular interest
payments as also the redemption amount on maturity.
• The interest on bond( also called coupon rate) is fixed at
the time of its issue. But interest rate in the market keeps
changing, and,therefore,market price of bond also
changes.
• The market price or intrinsic value of a bond is different
from the face value if the coupon rate is different from
the market interest rate at that particular time.
• Market value is equal to PV of all the coupon receipts
and redemption value discounted at the prevailing
market rate.
Yield on bonds
• Current yield =coupon interest/current
market price.
• E.g. if face value of a bond is Rs 50,
coupon rate is 8% pa, and market price is
Rs 40, then the current yield=4/40=0.1 or
10%
• Yield to Maturity(YTM) is that discount rate
at which all future cash flows equal the
present market value.
Theorems for bond valuation
•
•
•
•
Effect of change in market interest rate
Effect of maturity period
Bond price is inversely related to YTM
Interest rate elasticity= %age change in
price/%age change in YTM .This is always
negative as both move in opposite
direction.
Capital budgeting
• Used to choose between various projects.
• A capital project involves capital outflow( investment)
and capital inflows(net profit) over the life of the project.
• PV of all cash inflows will be +ve and PV of all cash
outflows will be negative.PV will depend on the discount
rate( cost of capital)
• Summation of all the PVs of cash inflows and outflows is
called Net Present Value(NPV)
• IRR is that discount rate at which NPV of a project is
zero.
• Other method used for capital budgeting is pay back
period method.
Depreciation
• Concept of depreciation
• Straight line method;(cost-residual value)/
estiamted usful life
• Written Down Value method or declining balance
mehtod : %age is fixed
• Sum of years’ digits method; Example, if an
asset is to be depreciated over five years, add
digits 5,4,3,2,1 .The total is 15.For the 1st year
depreciation is 5/15,for 2nd year,4/15 , and so on
• AS-6 deals with Depreciation Accounting
Forex Arithmatics
• Earlier RBI used to fix buying and selling rates of
Forex.Now market forces decide the exchange
rate.
• Direct and indirect quotations.From 2-8-93 only
direct quotations are being used.
• Cross rate/chain rule; e.g. if 1US$=Rs 48 and
1Euro=US$1.25, then 1Euro=Rs1.25*48
• Value date: Cash/ready,TOM, Spot, Forward
• Premium and discount.
• Factors affecting premium/discount
Capital adequacy
•
•
•
•
Need for capital in banks.
How much capital?
Basel II norms
RBI norms
Sample questions
•
1.What is the Present Value of Rs. 115,000 to be received after 1
year at 10%?
–
–
–
–
•
121,000
100,500
110,000
104,545
2.At 10% p.a. 2 year discount factor is
–
–
–
–
•
0.826
1.00
0.909
0.814
3.If 1 year discount is 0.8333, what is the discount rate?
–
–
–
–
10%
20%
30%
15%
Sample questions
•
4.Present Value is defined as
–
–
–
–
•
Future cash flows discounted to the present at an appropriate
discount rate
Inverse of future cash flows
Present cash flows compounded into the future
Discounting of compounded future cash flows
5.Annuity is defined as
–
–
–
–
Equal cash flows at equal intervals forever
Equal cash flows at equal intervals for a specified period
Unequal cash flows at equal intervals for specified period
Unequal cash flows at equal intervals forever
Sample questions
•
•
6.What is the N P V of the following at 15%
t=0
t=1
t=2
-120,000 -100,000
300,000
19,887
80,000
26,300
40,000
7.A bond holder of a company has one of the following
relationship with
It .Identify
•
•
•
•
•
•
–
–
–
–
•
shareholder
depositor
creditor
employee
Sample questions
•
8.The yield to maturity is a rate of return which
a. gives the current yield
b .Is the discount rate at which the present value, of the coupons
and the final payment at face value, equals
the current price
c .gives the return at maturity on the bond for the original holder
d. b) and c)
•
9.The relationship between the bond prices and
interest rates is one of the
Following
•
–
–
–
–
direct & linear
inverse & linear
direct and curvilinear
no relationship
Sample questions
•
10) What does the rate of return equal to if interest rates do
not change during the pendency of the bond ?
–
yield to maturity
–
coupon rate
–
compounded rate
–
current yield
11.A Bond of face value Rs.5000 carries a coupon interest rate of
12%. It is quoted in the market at Rs.4500. What is the current
yield of the bond?
–
12%
–
10%
–
13.3%
–
14.2%
Sample questions
• 12.Which of the following investment rules
does not use the time value of the money
concept?
• A.The payback period
• B.Internal rate of return
• C.Net present value
• D.All of the above use the time value
concept
Sample questions
•
13.A capital equipment costing Rs200,000 today has Rs 50,000
salvage value at the end of 5 years. If the straight line depreciation
method is used, what is the book value of the equipment at the
end of 2 years?
•
Rs200,000
•
Rs170,000
•
Rs140,000
•
Rs50,000
14.Cost of Car is Rs. 300,000, Depn. Rate is 10% on WDV. What is the
book value of car after 3 years.
•
210,000
•
220,00
•
214,300
•
218,700
Sample questions
•
•
•
15.If P=principal, r = rate of interest , n=
number of instalments
Then formula for equated monthly
instalment (EMI) is
(p*r)(1+r)n
(1+r)n – 1
Sample questions
•
•
•
•
•
16.If the rates in Mumbai are US
$1=Rs.42.850 .In London market are US
$ 1=Euros 0.7580 Therefore for one Euro
we will get
a) Rs.56.45
b Rs.56.53
c) Rs.56.38
d) Rs.56.50
Sample questions
• 17.The purchase price of an asset is Rs 45,000 and is to be
depreciated over next 5 years using sum of years’ digits .What will
be book value after one year?
• A) Rs 30,000
• B) Rs 25,000
• C) Rs 27,500
• D) Rs 35,000
• 18. If the sales income is Rs 10 lacs, Fixed costs are Rs 5 lacs,
variable costs are Rs 3 lacs, depreciation is Rs 1 lacs, and tax rate
is 20%, what is cash profit after tax?
• A Rs 1 lac
• B Rs2 lacs
• C Rs 1.80 lacs
• C Rs 1.60 lacs
Sample questions
• 19. A home loan with a floating rate of interest is
repayable in 120 EMIs of Rs 5000 each. If the rate of
interest increases, which of the following will be done by
the bank, in the normal course:
• The amount of EMI will become more than Rs 5000
• The amount of EMI will remain Rs 5000 but the number
will be more than 120
• Both amount and number of EMIs will increase
• Both amount and number of EMIs will remain same and
bank will charge a one time additional amount
Sample questions
• 20. Basel Committee on Banking Supervision (BCBC) was set up
by—
•
a)United Nations
•
b)RBI and Central Banks of some other countries
•
c)G-10 countries
•
d)None of the above
• 21. Which of the following correctly states the 3 main pillars of Basel
II accord;
•
a)Credit Risk, Operational Risk,Market Risk
•
b)Minimum capital Requirement,Supervisory Review
Process,Market Descipline
•
c)Standard Approach, Internal rating Based
approach,Securitisation Framework
•
d)Income Recognition,Asset Classification,Provisioning
Sample questions
• 22. Capital Adequacy is defined as—
•
a)Capital as a percentage of all risk weighted
assets including non fund based and non performing
assets
•
b) Capital as a percentage of risk weighted assets
excluding non performing assets
•
c) Capital as a percentage of risk weighted assets
excluding non fund based and non performing assets
•
d) Capital as a percentage of risk weighted assets
excluding non fund based assets
Sample questions
•
•
•
•
•
•
•
•
•
•
•
•
23.Which of the following is a Direct Quote:
In India : 1US $ = Rs 43.2350
In U S A : 1Euro = US $ 1.9200
In Germany : 1 DM = US $ 1.2450
All the above
24. Market quotes are: US $ 1 = Rs 42.8450/545
Euro 1 = US $ 1.9720/40
By selling Euro 1,00,000 , you will get ;
a) Rs 84,59,478
b )Rs 84,50,907
c) Rs 84,49,034
d) None of the above
Sample questions
• 25. Market quote is ; 1Euro =US $ 1.5780/90, 3 month forward: 110105. If you have to buy Euro, the rate of 1 Euro will be—
•
a) US $ 1.5890
•
b) US $ 1.5895
•
c) US $ 1.5680
•
d) None of the above
• 26. If the Spot rate is Euro 1 = US $ 1.500 and the interest rate in
Europe is higher by3% p.a. than that in USA, what will, theoretically ,
be Euro’s 90 days Forward rate, assuming 360 days in a year?
•
a)1.51125
•
b)1.48875
•
c)1.50750
•
d)1.49250