Download Module A - Basics of Business Mathematics - Presentation

JAIIB/Diploma in Banking &
Finance
Accounting & Finance for
Bankers
S.C.Bansal
MODULE-A
BUSINESS MATHEMATICS –
Presentation & MCQs
Why Mathematics in Banking
• To calculate interest on deposits and advances
• To calculated 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
Weightage of maths in JAIIB/DBF
Exam
• Constitutes one of the four modules of the
paper of Accounting & Finance( total 3
papers)
• Therefore, the weightage in the total exam
is about 10%
• 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 thoroughly and
solve problems
• 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.
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.
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 proportional to
YTM
• Interest rate elasticity= %age change in
price/%age change in YTM
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
Forex Arithmatics
• Earlier RBI used to fix buying and selling rates of
Forex.Now LERMS( liberalised exchange rate
management system) is used.
• 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
–
–
•
gives the current yield
Is the discount rate at which the present value, of the coupons
and the final payment at face value,
equals the current price
–
–
•
gives the return at maturity on the bond for the original holder
b) or 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
•
13) 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
14.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
• 15.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
•
16.A capital equipment costing Rs200,000 today hasRs 50,000
slavage 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
17.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
•
•
•
18.If P=principal, r = rate of interest , n=
number of instalments
Then formula for equated monthly
instalment (EMI) is
(p*r)(i+r)n
(1+r)n – 1
Sample questions
•
•
•
•
•
19.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