Transcript Time Value of Money

CHAPTER 4
THE BEHAVIOR OF INTEREST
RATES
What are Interest Rates?
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Rental price for money.
The time value of consumption.
Opportunity cost.
Expressed in terms of annual rates.
As with any price, interest rates serve to
allocate funds to alternative uses.
The Real Rate of Interest
• There is a preference for "real"
applications for savings such as
consumption or real investment.
– Real interest rate compensates for delayed
consumption.
– The higher the desire for consumption, the
higher the real rate of interest.
The Real Rate of Interest
(concluded)
• The real rate of interest is determined by the
demand and supply for savings at a given point
in time.
– The real rate is the price needed to delay
consumption of funds demanded for real
investment.
– Upward shifts to the right (increases) in demand for
desired real investment cause the real rate of
interest to increase.
– If the supply of desired savings shifts upward
(increases) to the right, the real rate of interest
declines.
Determinants of the
Real Rate of Interest
Loanable Funds Theory of
Interest
• The level of interest rates is determined by the
supply and demand for loanable funds.
– The real rate of interest is the long-term base rate of
interest.
– Short-run supply/demand factors and financial
market risks affect nominal interest rates.
– The quantity demanded of loanable funds, DL, is
inversely related to the level of interest rates; the
quantity supplied is directly related to interest rates.
Loanable Funds Theory of
Interest (concluded)
• Borrowers demand loanable funds for
home building, plant/equipment, and
inventory financing.
• The supply of loanable funds available
for financial investment may come from
decreasing money balances or past
savings.
Sources of Supply of and
Demand for Loanable Funds
Notice that households, businesses, and governmental units are both
suppliers and demanders of loanable funds. During most periods,
households are net suppliers of funds, whereas the federal government
is almost always a net demander of funds.
Supply of Loanable Funds (SU)
Consumer savings
Business savings (depreciation and retained earnings)
State and local government budget surpluses
Federal government budget surplus (if any)
Federal Reserve increases the money supply (M)
Demand for Loanable Funds (DU)
Consumer credit purchases
Business investment
Federal government budget deficits
State and local government budget deficits
Loanable Funds Theory of
Interest Rate Determination
Loanable Funds Theory of
Interest Rate Determination
Loanable Funds Theory of
Interest Rate Determination
Loanable Funds Theory of
Interest Rate Determination
Price Expectations and
Interest Rates
• Expected inflation, ex ante, is embodied in
nominal interest rates -- The Fisher Effect.
– Investors want compensation for expected decreases
in the purchasing power of their wealth.
– If investors feel the prices of real goods will increase
(inflation), it will take increased interest rates to
encourage them to place their funds in financial
assets.
Fisher Effect
• The formula for the Fisher equation is:
1  i   1  r 1  Pe 
where
i  the observed nominal rate of interest,
r  the real rate of interest,
Pe  the expected annual rate of inflation.
Fisher Effect (continued)
• From the Fisher equation, with a little algebra,
we see that the nominal (contract) rate is:
i  r  Pe  r * Pe 
• From this equation we see that a lender gets
compensated for:
– rent on money loaned,
– compensation for loss of purchasing power on the
principal,
– compensation for loss of purchasing power on the
interest.
Fisher Effect (continued)
• Contract rate example for: 1-year $1000 loan
when the loan parties agree on a 3% rental rate
for money and a 5% expected rate of inflation.
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Items to pay
Principal
Rent on money
PP loss on principal
PP loss on interest
Total Compensation
Calculation
Amount
$1,000.00
$1,000 x 3%
30.00
$1,000 x 5%
50.00
$1,000 x 3% x 5%
1.50
$1,081.50
Fisher Effect (concluded)
• The third term in the Fisher equation is
approximately equal to zero, so it is
dropped in many applications. The
resulting equation is referred to as the
approximate Fisher equation and is the
following:
i  r  Pe
Price Expectations and
Interest Rates
• Actual realized ex-post rates of return reflect
the impact of inflation on past investments or
on investors.
– r = i - Pa, where the annual "realized" rate of
return from past securities purchases, r, equals the
annual nominal rate minus the actual annual rate of
inflation.
– With ever-increasing rates of inflation, investors'
inflation premiums, Pe, may lag actual rates of
inflation, Pa, yielding low or even negative actual
real rates of return.
Three-Month Treasury Bill
Rates
Annual Percentage Rate
20
15
10
5
0
-5
-10
May-96
Aug-93
Nov-90
Mar-88
Jun-85
Sep-82
Dec-79
Mar-77
Jun-74
Sep-71
Jan-69
Month-Year
Nominal Rates
Realized Real Rates
Impact of Inflation on Loanable
Funds Theory of Interest
Interest Rate Changes and
Changes in Inflation
15
10
5
)
0
Month-Year
Three-Month Treasury Bills
Ten-Year Treasury Notes
Rate of Inflation (CPI)
May-96
Aug-93
Nov-90
Mar-88
Jun-85
Sep-82
Dec-79
Mar-77
Jun-74
Sep-71
-5
Jan-69
Annual Percentage Rate
20
Interest Rate Changes and
Changes in Inflation (concluded)
• What do we learn from the previous
slide?
– Interest rates change with changes in
inflation.
– Short-term interest rates change more than
long-term interest rates for a given change in
inflation.