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Fin 221: Chapter 4
The level of interest rates
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What are Interest Rates?
• Interest rates are:
• The price of borrowing money for the use of its
purchasing power (it is the rental price of money).
• To a borrower, they are penalty for consuming
income before it is earned.
• To a lender , they are reward for postponing
current consumption until the maturity of the
loan.
• Interest rates serve an Allocative Function in the
economy. They allocate funds between SSUs
and DSUs and among financial markets.
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The Real Rate of Interest
• The interest rate paid on savings basically depends on:
1. The rate of return on investment (The rate of return
producers can expect to earn on investment capital.)
2. Savers’ time preference for current versus future
consumption : Most people prefer to consume goods
today rather than tomorrow. This is known as positive
time preference.
• The expected return on investment projects sets an upper
limit on the interest rate producers can pay to savers,
whereas consumer time preference for consumption
establishes how much consumption consumers are willing
to forgo (save) at the different levels of interest rates
offered by producers.
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The Real Rate of Interest…………..cont.
• Investment is negatively related to interest rate. Other
things remaining the same, the higher the interest rate,
the lower the desired investment (desired investment
demand curve slopes downwards).
• Desired saving is positively related to interest rate. The
higher the interest rate ,the higher the desired savings are
(desired saving supply curve slopes upwards)..
• The market equilibrium interest rate for the
economy is determined by the interaction of supply
and demand for funds (see diagram)
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Determinants of the Real Rate of Interest
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The Real Rate of Interest………..cont.
• The market equilibrium rate of interest (r*) is
achieved when desired savings of savers ( S*) equals
desired investments( I*) by producers across all
economic units. ( see diagram)
• The equilibrium rate of interest is called the Real Rate
of Interest ( this is because it is determined by the real
output of the economy).
• The real rate of interest is the fundamental long-run
rate of interest in the economy ( it is the base interest
rate for the economy).
• Changing economic forces cause interest rates to
change ( by causing a shift in the savings or
investment curves)…( refer to diagram).
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Loanable funds theory of interest
• The loanable funds ( LFs) is a framework used
to determine interest rate in the short-run.
• In the short–run interest rates depend on the
supply of and the demand for LFs, which in
turn depend on productivity and thrift.
• The need to sell financial claims issued by
DSUs constitutes the demand for LFs.
• The SSUs supply LFs to the market ( SSUs
purchase financial claims offered by DSUs to
earn interest on their excess funds).
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Loanable funds theory………….cont.
Sources of supply and demand for LFs :
Supply of LFs (SSUs):
- Consumer savings.
- Business savings( depreciation and retained earnings)
- Government budget surpluses.
- C.B actions (increases the money supply).
Demand for LFs (DSUs) :
- Consumer credit purchases.
- Business investment.
- Government budget deficits.
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Loanable funds theory……………..cont
• In general, higher interest rates stimulate more savings and
more LFs. The supply curve of LFs slopes upward.
• The demand for LFs decreases as the interest rate increases.
The demand curve for LFS slopes downward.
• The intersection of LFs supply and demand curves, determine
the equilibrium interest rate and the equilibrium quantity of
LFs savings and demanded
• If the interest rate is below the equilibrium rate, there will be
shortage of LFs which will force the interest rate up. On the
other hand, if the interest rate is above the equilibrium rate, a
surplus of LFs will exist forcing the rate downward restoring
the equilibrium.
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Loanable Funds Theory
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Loanable funds theory…….cont.
• Changes in interest rate (other things
remaining constant) brings changes in
quantity of LFs demanded and supplied, and
thus movements along the SL and DL curves.
• Changes in factors other than the interest rate
will change the supply and demand for LFs.
There will be a shift in the supply and
demand curves, and as a result a new
equilibrium occurs.
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Factors affecting supply of LFs
1.
Changes in the quantity of money:
If quantity of money increases, supply of LFs increases.The SL
curve shifts to the right, resulting in a new equilibrium with
lower interest rate and higher equilibrium quantity.
2.Changes in the income tax : a decrease in income tax increases
saving ,Thus the supply of LFs increases and the SL shifts to the
right (Tax is government revenue).
3. Changes in government budget from deficit to surplus position:
This will also lead to a shift in SL curve to the right.
4.Changes in business saving ( depreciation and retained earnings).
An increase in business savings will increase supply of LFs and
cause the SL curve to shift to the right.
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Factors affecting demand for LFs
1.Changes in future expected profits of business activities : If
businesses are expected to generate higher profits in the future,
the demand for investment funds will increase and so the
demand for LFs.The DL curve shifts to the right resulting in a
new equilibrium with higher interest rate and higher
equilibrium quantity.
2. Changes in tax level : an decrease in taxes, will increase
government deficit, therefore increasing the demand for LFs,
hence the DL curve will shift to right.
3.Changes in government budget from surplus to deficit position:
this occurs due to increase in government expenditure (the
government must borrow to cover the deficit). The demand for
LFs will therefore increase and this will cause the DL curve to
shift to the right .
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Price expectations and interest rate
• Changes in price level affect both the realized
return that lenders receive on their loans and
the cost that borrowers must pay for them.
• Unanticipated inflation benefits borrowers at
expense of lenders.
• Lenders charge added interest to offset
anticipated decreases in purchasing power.
• Expected inflation is to be embodied in nominal
interest rates.
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Price expectations and interest rate
How to protect against price changes??
Protection against changes in purchasing power (PP)
can be incorporated in the interest rate on a loan
contract.
Example :
An SSU and a DSU plan to exchange money and
financial claims for a period of one year. Both agreed
that a fair rental price for the money is 5% and both
anticipate an 8% inflation rate during the year. What
would be the contract rate on the loan ?To answer this
question we need to discuss the Fisher Effect.
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Price expectations and interest rate……..cont
The Fisher Effect :
The Fisher Effect Theory states that the nominal interest rate
(contract rate) includes real interest rate and expected annual
inflation rate.
The Fisher Equation is expressed as:
(1+ i ) = (1+r) ( 1+ ΔPe )
i
Where : = the observed nominal rate of interest.
r = real rate of interest in the absence of price level
changes( interest rate where no inflation exists).
ΔPe = expected annual change in commodity prices
(expected annual rate of inflation).
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Price expectations and interest rate……..cont
- Solving the Fisher Equation for ( i) we obtain the following equation:
i = r + ΔPe + (r ΔPe)
- The equation shows the relationship between nominal (contract)
rates and rates of expected inflation. The inflation component of the
equation is commonly referred to as the Fisher Effect.
- Based on the equation, the contract rate between the above
mentioned SSU and DSU is:
i = 0.05 +0.07 + ( 0.05 x 0.07 ) = 0,1235=12.35%
- On a loan of $1000 the lender will get :
Total compensation = 1000 + (1000X5% )+ (1000X 7% )+ (1000
X5%X7%) = 1123.5
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Price expectations and interest rate……..cont
The Fisher Equation…Cont;
4.The final term of the Fisher equation (r ΔPe )is
approximately equal to zero. So, in many situations it
is dropped from the equation without creating a
critical error.
The equation without the final term is referred to as the
Approximate Fisher Equation and is stated as :
i = r + ΔPe
Therefore, approximately i = 5%+7% =12%
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The Realized Real rate
The Fisher equation is based on expected inflation rate. The actual
rate of inflation may be different from the anticipated rate. For
the real interest rate and the nominal interest rates to be equal,
the expected rate of inflation must be zero (ΔPe = 0).
• The actual inflation rate, more than likely will not equal to
what was expected.
• This may lead to the realized rate of return on a loan to be
different from the nominal interest rate agreed at the time of
the loan contract.
• The realized (actual) real rate is calculated as :
r = i - ΔPa,
Where; r = is the realized real rate of return.
i = the nominal interest rate.
ΔPa = is the actual rate of inflation.
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Inflation and loanable Funds Model
• Te higher the expected inflation rate ,the higher
is the demand for LFs ( consumption
increases). The DL will shift upwards (to the
right ). by the amount (ΔPe) .The shift from DLo
to DL1(see diagram) implies that borrowers are
willing to pay the inflation premium ΔPe.
• Similarly, the higher the expected inflation rate the
lower is supply for LFs ( savings decrease), so SL
curve will shift upwards ( to the left) by the amount
ΔPe .The shift from SL0 to SL1 will be such that
lenders are given a higher nominal yield to
compensate for their loss of purchasing power.
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Inflation and loanable Funds Model
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Inflation and loanable Funds Model
• The net effect of inflation is that the market
rate of interest will rise from ( r0) to (i1) ,
where the difference between ( i1 ) and ( r0) is
the expected inflation rate (ΔPe) or :
i1 = r0 + ΔPe
• Even though the real rate (r0 ) remains
unchanged, the nominal rate of interest (i1 )
has adjusted fully for the anticipated rate of
inflation (ΔPe ) and the quantity of LFs in the
market has remained the same at Q0
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Interest Rate Movements and Inflation.. Cont’d
• Historically, interest rates tend to change
with changes in the rate of inflation,
substantiating the Fisher equation.
• Short-term rates are more responsive to
changes in inflation than long-term rates.
• That is Short-term interest rates change
more than long-term interest rates for a
given change in inflation.
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