Interest Rate Theory

Presented by:
Mohammad Maksudul Huq Chowdhury
Head of Branch
Exim Bank, Islampur Branch,
Dhaka, Bangladesh
1

 The Theory of Interest Rate
 Loan-able Funds Theory
 Liquidity Preference Theory
 Forces that affect Interest Rates
 Interest Rate Fundamentals
 Structure of Interest Rates
 Time Value of Money and Interest Rates
2

An interest rate is the price paid by a borrower (or debtor) to
a lender (or creditor) for the use of resources during some
time interval. The amount of the loan is the principal, and
the price paid is typically expressed as a percentage of the
principal per unit of time (generally a year).
Interest rates are among the most closely watched variables
in the economy. Thus, participants in financial markets
attempt to anticipate interest rate movements when
restructuring their positions so that they can capitalize on
favorable movements or reduce their institution’s exposure to
unfavorable movements.
3

There are two theories of the determination of the interest rate
A. Loanable funds theory and
B. Liquidity preference theory.
4

 Theory of how the general level of interest
rates are determined
 Explains how economic and other factors
influence interest rate changes
 Interest rates determined by demand and
supply for loanable funds
5

This theory proposes that the general level of
interest rates is determined by the complex
interaction of two forces.
 The first is the total demand for funds by firms,
governments, and households (or individuals),
which carry out a variety of economic activities
with those funds. This demand is negatively
related to the interest rate (except for the
government’s demand, which may frequently not
depend on the level of the interest rate).
6

 The second force affecting the level of the
interest rate is the total supply of funds by firms,
governments, banks and individuals. Supply is
positively related to the level of interest rates, if
all other economic factors remain the same. With
rising rates, firms and individuals save and lend
more, and banks are more eager to extend more
loans. (A rising interest rate probably does not
significantly affect the government’s supply of
savings).
7

 Equilibrium in the Market
The equilibrium interest rate is the rate that equates
the aggregate demand for loanable funds with
aggregate supply of loanable funds.
The aggregate demand for funds (DA) can be written as:
DA = Dh + Db + Dg + Df
where Dh = household demand for loanable funds
Db = business demand for loanable funds
Dg = government demand for loanable funds
Df = foreign demand for loanable funds
8

The aggregate supply for funds (SA) can be written as:
SA = Sh + Sb + Sg + Sf
where Sh = household supply for loanable funds
Sb = business supply for loanable funds
Sg = government supply for loanable funds
Sf = foreign supply for loanable funds
9

The Results of a Shift in the Demand for Savings
If aggregate demand for loanable funds increases without aggregate
increase in aggregate supply, there will be a shortage of loanable
funds and interest rate will rise until an additional supply of
loanable funds is available to accommodate excess demand.
11

The Results of a Shift in the Supply of Savings:
Conversely, an increase in aggregate supply of loanable funds without a
corresponding increase in aggregate demand will result in a surplus of
loanable funds. In this case interest rate will fall until the quantity of
funds supplied no longer exceeds the quantity of funds demanded.
12

In many cases, both supply and demand for
loanable funds are changing over time.
Given an initial equilibrium situation, the
equilibrium interest rate should rise when
DA > SA and fall when DA < SA
13

 The Liquidity Preference theory, originally
developed by John Maynard Keynes, analyzes
the equilibrium level of the interest rate
through the interaction of the supply of money
and the public’s aggregate demand for holding
money. Keynes assumed that most people hold
wealth in only two forms: “money” and
“bonds”.
14

 For Keynes, money is equivalent to currency
and demand deposits, which pay little or no
interest but are liquid and may be used for
intermediate transactions. Bonds represent a
broad Keynesian category and include long-
term, interest-paying financial assets that are
not liquid and that pose some risk because
their prices vary inversely with the interest
rate level. Bonds may be liabilities of
governments or firms.
15

Demand, Supply and Equilibrium:
16

 The real rate is the growth in the power to consume
over the life of a loan. The nominal rate of interest, by
contrast, is the number of monetary units to be paid
per unit borrowed and is, in fact, the observable
market rate on a loan. In the absence of inflation, the
nominal rate equals the real rate. The relationship
between inflation (Inflation is a state of disequilibrium
at which aggregate demand exceeds aggregate supply
at the existing prices causing a rise in general price
level) and interest rates is the well-known Fisher’s Law,
which can be expressed this way:
17

(1+ i) = (1+ r) X (1+ p)
Where, i = the nominal rate,
r = the real rate,
p= the expected percentage change in the price
level of goods and services over the loan’s life.
The above equation is approximately close enough:
i = r+ p
When the real interest rate is low, there are
greater incentives to borrow and fewer incentives
to lend.
18

 Interest rate movements affect the values of virtually
all securities
They have a direct influence on debt instruments
- Bonds, Securities
They have an indirect influence on stocks and
exchange rates
Interest rates changes impact the value of financial
institutions
Managers of financial institutions closely monitor
rates
Interest rate risk is a major risk impacting financial
institutions
Changes in interest rates impact the real economy
19

 Economic Growth
 Inflation
 Money Supply
 Budget Deficit
 Foreign Flows of Funds
20

Economic Growth:
 Expected impact is an outward shift in the
demand schedule without obvious shift in supply
 Result is an increase in the equilibrium interest
rate
21

Inflation
If inflation is expected to increase
 Households may reduce their savings to make
purchases before prices rise
 Supply shifts to the left, raising the equilibrium rate
 Also, households and businesses may borrow more to
purchase goods before prices increase
 Demand shifts outward, raising the equilibrium rate
22

Money Supply
 When the central bank increases the money
supply, it increases supply of loanable funds
 Places downward pressure on interest rates
23

Budget Deficit
 Increase in deficit increases the quantity of
loanable funds demanded
 Demand schedule shifts outward, raising rates
 Government is willing to pay whatever is
necessary to borrow funds, “crowding out” the
private sector
24

Foreign Flows
 In recent years there has been massive flows between
countries
 Driven by large institutional investors seeking high returns
 They invest where interest rates are high and currencies are
not expected to weaken
 These flows affect the supply of funds available in each
country
 Investors seek the highest real after-tax, exchange rate
adjusted rate of return around the world
25

Change in the money supply has three different
effects upon the level of the interest rate
 the liquidity effect,
 the income effect, and
 the price expectations effect.
26

i. Liquidity Effect: This effect represents the initial reaction of
the interest rate to a change in the money supply. With an
increase in the money supply, the initial reaction should be a
fall in the rate. The reason for the fall is that a rise in the
money supply represents a shift in the supply curve.
Figure: The Liquidity Effect of an Increase in the Money Supply
27

 ii. Income Effect: A decline in the supply would tend to cause
a contraction. An increase in the money is economically
expansionary; more loans are available and extended, more
people are hired or work longer, and consumers and
producers purchase more goods and services. Thus, money
supply changes can cause income in the system to vary.
Figure: The Income Effect of a Change in the Money Supply
28

iii. Price Expectations Effect:
 Although an increase in the money supply is an economically
expansionary policy, the resultant increase in income depends
substantially on the amount of slack in the economy at the
time of the Central Bank’s action.
-If the economy is operating at less than full strength, an
increase in the money supply can stimulate production,
employment, and output;
-if the economy is producing all or almost all of the goods and
services it can (given the size of the population and the
amount of capital goods), then an increase in the money
supply will largely stimulate expectations of a rising level of
prices for goods and services.
Thus, the price expectations effect usually occurs only if the
money supply grows in a time of high output.
29

1. Features of a Bond:
 Maturity
 Principal Value
 Coupon Rate
30

2. Yield on a Bond:
 The yield on a bond investment should reflect
the coupon interest that will be earned plus
either (1) any capital gain that will be realized
from holding the bond to maturity, or (2) any
capital loss that will be realized from holding
the bond to maturity.
31

The yield to maturity is a formal, widely accepted
measure of the rate of return on a bond. The yield
to maturity of a bond takes into account the
coupon interest and any capital gain or loss, if the
bond were to be held to maturity. The yield to
maturity is defined as the interest rate that makes
the present value of the cash flow of a bond equal
to the bond’s market price. In mathematical
notation, the yield to maturity, y, is found by
solving the following equation for y.
32

Where, P = market price of bond
C = coupon interest
n = time to maturity
)1(
.........
)1()1()1( y
c
Y
c
y
c
Y
c
p








33

The yield to maturity is determined by a trial-error process. The
steps in that process are as follows:
Step-1: Select an interest rate.
Step-2: Compute the present value of each cash flow using the
interest rate selected in step-1.
Step-3: Total the present value of the cash flows found in step-2.
Step-4: Compare the total present value found in step-3 with the
market price of the bond and, if the total present value of the
cash flows found in step-3 is:
34

 Equal to the market price, then the interest rate
used in step-1 is the yield to maturity;
 Greater than the market price, then the interest rate
is not the yield to maturity. Therefore, go back to
step-1 and use a higher interest rate.
 Less than the market price, the interest rate is not
the yield to maturity. Therefore, go back to step-1
and use a lower interest rate.
35

3. The Base Interest Rate:
 The securities issued by the government of the
country, popularly referred to as Treasury Securities
or simply Treasuries, are backed by the full faith and
credit of the government. Consequently, market
participants throughout the world view them as
having no credit risk. As a result, historically the
interest rates on Treasury Securities have served as
the benchmark, interest rates throughout the
domestic economy, as well as in international capital
markets.
36

4. The Risk Premium:
 Market participants’ talk of interest rates on non-
Treasury securities as “trading at a spread” to a
particular on-the- run Treasury security (or a spread
to any particular benchmark interest rate selected).
37

 We can express the interest rate offered on a non-Treasury
security as: For example, if the yield on a 10-year non-Treasury
security is 7% and the yield on a 10-year Treasury security is 6%,
the spread is 100 basis points. This spread reflects the
additional risks the investor faces by acquiring a security that is
not issued by the government and, therefore
 Base interest rate + Spread Or, equivalently,
 Base interest rate + Risk Premium
 One of the factors affecting interest rate is the expected rate
of inflation. That is, the base interest rate can be expressed as:
 Base interest rate = Real rate of interest + Expected rate of
inflation
38

 5. Types of Issues
 6. Perceived Creditworthiness of Issuer
39

7. Term to Maturity
The volatility of a bond’s price is dependent on its
maturity. More specifically, with all other factors
constant , the longer the maturity of a bond, the
greater the price volatility resulting from a change in
market yields. The spread between any two maturity
sectors of the market is called a maturity spread or
yield curve spread. The relationship between the
yields on comparable securities but different maturities
is called the term structure of interest rates.
40

8. Inclusion of Options:
An option that is included in a bond issue is
referred to as an option.
 call provision
 put provision
 convertible bond
41

9. Taxability of Interest:
 The yield on a taxable bond issue after income taxes are paid
is equal to:
After-tax yield = Pretax yield (1- Marginal Tax Rate)
 Alternatively, we can determine the yield that must be
offered on a taxable bond issue to give the same after-tax
yield as a tax-exempt issue. This yield is called the
equivalent taxable yield and is determined as follows:
ratetaxmarginal-1
yieldexempt-Tax
YieldTaxableEquivalent 
42

Time Value of Money (TVM) means changes of value
of time over time. Over the time, value of the
money changes and so, same amount of money at
current time and in some future time is not
considered as equally worthy – this is called the
theory of time preference.
43

 TVM is determined by a number of factors such as:
 Consumption preference – people prefer current consumption
to future consumption of same level of satisfaction.
 Uncertainty – Future is always uncertain. People would like to
be compensated for that uncertain future cash flow against
certain current cash flow.
 Inflation – The purchasing power of money is always depleting,
as inflation is a common factor for any economy. Therefore,
more cash flow is required to purchase same consumption worth
as some current level of cash flow can do.
 Investment Opportunity – capital itself has its return. In a
capital market, one is expected to get some return at market
rate called “pure interest rate”. Therefore, whatever may be
the cash flow now; the future cash flow should be more than
this.
44

Congratulations!!! You have won a cash prize! You
have two payment options: A - Receive $10,000 now
or B - Receive $10,000 in three years. Which option
would you choose?
45

If you're like most people, you would choose to
receive the $10,000 now. After all, three years is
a long time to wait. Why would any rational
person defer payment into the future when he or
she could have the same amount of money now?
For most of us, taking the money in the present
is just plain instinctive. So at the most basic
level, the time value of money demonstrates
that, all things being equal, it is better to have
money now rather than later.
46

 But why is this? A $100 bill has the same value as a
$100 bill one year from now, doesn't it? Actually,
although the bill is the same, you can do much more
with the money if you have it now because over time
you can earn more interest on your money.
 Back to our example: by receiving $10,000 today, you
are poised to increase the future value of your money
by investing and gaining interest over a period of
time. For Option B, you don't have time on your side,
and the payment received in three years would be
your future value. To illustrate, we have provided a
timeline:
47

If you are choosing Option A, your future value will
be $10,000 plus any interest acquired over the three
years. The future value for Option B, on the other
hand, would only be $10,000. So how can you
calculate exactly how much more Option A is worth,
compared to Option B? Let's take a look.
48

If you choose Option A and invest the total amount at
a simple annual rate of 4.5%, the future value of your
investment at the end of the first year is $10,450,
which of course is calculated by multiplying the
principal amount of $10,000 by the interest rate of
4.5% and then adding the interest gained to the
principal amount:
Future value of investment at end of first year:
=($10,000x0.045)+$10,000
= $10,450
49

You can also calculate the total amount of a one-year
investment with a simple manipulation of the above
equation:
 Original equation: ($10,000 x 0.045) + $10,000 = $10,450
 Manipulation: $10,000 x [(1 x 0.045) + 1] = $10,450
 Final equation: $10,000 x (0.045 + 1) = $10,450
50

The manipulated equation above is simply a removal of
the like-variable $10,000 (the principal amount) by
dividing the entire original equation by $10,000.
If the $10,450 left in your investment account at the end
of the first year is left untouched and you invested it at
4.5% for another year, how much would you have? To
calculate this, you would take the $10,450 and multiply
it again by 1.045 (0.045 +1). At the end of two years, you
would have $10,920:
Future value of investment at end of second year:
=$10,450x(1+0.045)
= $10,920.25
51

The above calculation, then, is equivalent to the following
equation:
Future Value = $10,000 x (1+0.045) x (1+0.045)
Think back to math class and the rule of exponents, which
states that the multiplication of like terms is equivalent to
adding their exponents. In the above equation, the two like
terms are (1+0.045), and the exponent on each is equal to
1. Therefore, the equation can be represented as the
following:
52

We can see that the exponent is equal to the number of
years for which the money is earning interest in an
investment. So, the equation for calculating the three-year
future value of the investment would look like this:
53

This calculation shows us that we don't need to calculate
the future value after the first year, then the second year,
then the third year, and so on. If you know how many years
you would like to hold a present amount of money in an
investment, the future value of that amount is calculated by
the following equation:
54

If you received $10,000 today, the present value would of
course be $10,000 because present value is what your
investment gives you now if you were to spend it today. If
$10,000 were to be received in a year, the present value of
the amount would not be $10,000 because you do not have
it in your hand now, in the present. To find the present
value of the $10,000 you will receive in the future, you
need to pretend that the $10,000 is the total future value of
an amount that you invested today. In other words, to find
the present value of the future $10,000, we need to find out
how much we would have to invest today in order to receive
that $10,000 in the future.
55

To calculate present value, or the amount that we would
have to invest today, you must subtract the (hypothetical)
accumulated interest from the $10,000. To achieve this, we
can discount the future payment amount ($10,000) by the
interest rate for the period. In essence, all you are doing is
rearranging the future value equation above so that you may
solve for P. The above future value equation can be rewritten
by replacing the P variable with present value (PV) and
manipulated as follows:
56

Let's walk backwards from the $10,000 offered in Option B.
Remember, the $10,000 to be received in three years is
really the same as the future value of an investment. If
today we were at the two-year mark, we would discount the
payment back one year. At the two-year mark, the present
value of the $10,000 to be received in one year is
represented as the following:
Present value of future payment of $10,000 at end of year
two:
57

Note that if today we were at the one-year mark, the above
$9,569.38 would be considered the future value of our
investment one year from now.
Continuing on, at the end of the first year we would be
expecting to receive the payment of $10,000 in two years. At
an interest rate of 4.5%, the calculation for the present
value of a $10,000 payment expected in two years would be
the following:
Present value of $10,000 in one year:
58

Of course, because of the rule of exponents, we don't have
to calculate the future value of the investment every year
counting back from the $10,000 investment at the third year.
We could put the equation more concisely and use the
$10,000 as FV. So, here is how you can calculate today's
present value of the $10,000 expected from a three-year
investment earning 4.5%:
59

So the present value of a future payment of $10,000 is
worth $8,762.97 today if interest rates are 4.5% per
year. In other words, choosing Option B is like taking
$8,762.97 now and then investing it for three years.
The equations above illustrate that Option A is better
not only because it offers you money right now but
because it offers you $1,237.03 ($10,000 - $8,762.97)
more in cash! Furthermore, if you invest the $10,000
that you receive from Option A, your choice gives you a
future value that is $1,411.66 ($11,411.66 - $10,000)
greater than the future value of Option B.
60

Let's add a little spice to our investment knowledge.
What if the payment in three years is more than the
amount you'd receive today? Say you could receive either
$15,000 today or $18,000 in four years. Which would you
choose? The decision is now more difficult. If you choose
to receive $15,000 today and invest the entire amount,
you may actually end up with an amount of cash in four
years that is less than $18,000. You could find the future
value of $15,000, but since we are always living in the
present, let's find the present value of $18,000 if interest
rates are currently 4%. Remember that the equation for
present value is the following:
61

In the equation above, all we are doing is discounting
the future value of an investment. Using the numbers
above, the present value of an $18,000 payment in four
years would be calculated as the following:
Present Value
From the above calculation we now know our choice is
between receiving $15,000 or $15,386.48 today. Of
course we should choose to postpone payment for four
years!
62

These calculations demonstrate that time literally is
money - the value of the money you have now is not
the same as it will be in the future and vice versa. So,
it is important to know how to calculate the time value
of money so that you can distinguish between the
worth of investments that offer you returns at different
times.
63

Interest Rate Theory

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