Download Document

Interest Rates and
Bond Prices
Chapter 5
© 2003 South-Western/Thomson Learning
Learning Objectives

Why the interest rate represents the time
value of money

What are compounding and discounting

Why interest rates and bond prices are
inversely related
Slide 2
Learning Objectives

The major determinants of interest rates

The relationship between nominal and real
interest rates

How interest rates fluctuate over the
business cycle
Slide 3
The Time Value of Money
 Money
represents purchasing
power …
 Short of funds for goods or
services?
1. Borrow now and purchase now
2. Save now and purchase later
 The higher the interest rates
 the less appealing is #1
 the more appealing is #2
Slide 4
The Time Value of Money
Lending in present Borrowing in future
ENABLES
ENABLES
 Spending in the
future the sum of
what is lent plus the
interest earned
Slide 5
 Spending in the
present, but requires
paying back in the
future what is
borrowed plus
interest
Compounding and Discounting

Compounding Future Values
 What is the future value of
money lent (or borrowed) today
AMOUNT REPAID = PRINCIPAL + INTEREST
amount of interest
INTEREST = PRINCIPAL x INTEREST RATE
Slide 6
Compounding and Discounting
substituting equation into yields
AMOUNT REPAID = PRINCIPAL + ( PRINCIPAL x INTEREST RATE )
AMOUNT REPAID = PRINCIPAL x ( 1 + i )
V1 = V0 ( 1 + i )
Slide 7
Compounding and Discounting
V1 = the funds to be received by the
lender at the end of one year
V0 = the funds lent now
This is present value
Slide 8
Compounding and Discounting
In the second year
V2 = V0 (1 + i )2
Vn = V0 (1 + i )n
Slide 9
Discounting: Present Values

Discounting is backward-looking
What is the PRESENT VALUE of money to be
received (or paid) in the future?
expressed
V0 = Vn / (1 + i )n
Slide 10
Discounting: Present Values
RECAP


Compounding: finding the value of a
future sum.
Discounting: finding the present value of a
future sum

Future value: Vn of a sum, V0 invested
today for n years is V0 ( 1 + i )n

Present value: V0, of the sum Vn, to be
received in n years is Vn / ( 1 + i )n
Slide 11
Interest Rates, Bond Prices,
and Present Value
To compute the present value of each coupon
payment and the present value of the final
repayment of the face value on the maturity
date.
P = C1 / ( 1 + i )1 + C2 / ( 1 + i )2 + … + Cn / ( 1 + i )n
+ F / ( 1 + i )n
Slide 12
P = the price (present value) of the bond
C = the coupon payment on the bond (C1 in year 1, C2 in year 2
etc.
F = the face or par value of the bond
i = the interest rate
n = the number of years to maturity (on a five-year bond, n=5)
Interest Rates, Bond Prices,
and Present Value

Discount from par - raises the yield on the
bond, called the yield to maturity

Premium above par – a price above par
value
There is an inverse relationship between the price of
outstanding bonds trading in the secondary market and the
prevailing level of market interest rates.
If bond prices are rising, then interest rates are falling, and
vice versa.
Slide 13
Interest Rates, Bond Prices,
and Present Value
RECAP

The price of the bond is the discounted
value of the future stream of income over
the life of the bond.

When the interest rate increases, the price
of the bond decreases.

When the interest rate decreases, the
price of the bond increases.
Slide 14
Determinants of Interest Rates

Demand for loanable funds –
 downward-sloping demand curve indicates
that DSU’s are willing to borrow more at lower
interest rates

Supply of loanable funds – originates
 The household, business, government and
foreign SSUs who are prepared to lend
 The Fed, which, in its ongoing attempts to
manage the economy’s performance, supplies
reserves
Slide 15
Exhibit 5–3
The Supply of and Demand for Funds
Slide 16
Determinants of Interest Rates

Changes in the demand for loanable
funds
 Movements in gross domestic product
(GMP)
 When GMP rises
 Firms & households become more willing
and able to borrow
 Firms expand inventory & engage in
investment spending
Slide 17
 Households willing to borrow, increased
incomes, and/or improved employment outlook
Exhibit 5–4
A Shift in the Demand for Funds
Slide 18
Determinants of Interest Rates

Changes in the demand for loanable funds
 Increase their purchases of goods and
services, particularly
 Auto
 Durable goods
Items that require financing
 Houses
Easier to make the interest and
principal payments on new debt
 Increase in anticipated productivity of
capital investment

Slide 19
• Lead to a greater demand for capital investment &
hence increase the demand for loanable funds
Determinants of Interest Rates

Changes in the supply of funds
 Monetary policy
 Disequilibrium – the quantity supplied of funds
exceeds the quantity demanded
 As interest rates fall, DSUs & SSUs revise their
borrowing and lending plans
 Increase in the money supply will lower the
interest rates
 Decrease in the money supply will raise the
interest rates
Slide 20
A Shift in the Supply of Funds
i = f ( Y+,M¯ )
The interest rate is a positive function of
income or GDP, Y and negative function of
the money supply, M
Slide 21
Exhibit 5–5
A Shift in the Supply of Funds
Slide 22
Determinants of Interest Rates
RECAP

The demand for loanable funds originates from
DSUs

The quantity demanded is inversely related to the
interest rate

The supply of loanable funds originates from SSUs
and from Fed

The quantity supplied is directly related to the
interest rate

If the money supply increases, the supply of
loanable funds increases and the interest rate
falls: i = f ( Y+,M¯ )
Slide 23
Inflation and Interest Rates

Lenders are concerned about
 Nominal interest
 Inflation
Slide 24
Inflation and Interest Rates
Nominal interest rate is not an adequate
measure of the real return on an interestbearing financial asset unless there is
assurance of price stability.
Appropriate measure is the real interest
rate, which is the return on the asset
corrected for changes in the purchasing
power of money.
Slide 25
Inflation and Interest Rates
Money illusion is said to occur when investors
react to nominal changes even though no changes
in real interest rates or other real variables have
occurred.
i = r + pe
The equation says that nominal interest rate has
parts: a real interest rate, r, and an inflation
premium
Slide 26
i = r - pe
Inflation and Interest Rates

Major price indexes
 Consumer Price Index (CPI)
CPI is designed to measure changes in the
cost of goods and services purchased by a typical
urban consumer
 Producer Price Index (PPI)
PPI measures the changes in the cost of goods
and services purchased by a typical producer
 Inflation rate is generally measured by the
Slide 27
percentage change in one of these price
indexes.
Inflation and Interest Rates
Expectations of inflation affect portfolio choices
that help determine the demand and supply of
loanable funds
i = f ( Y+,M¯, p+ e )
Nominal interest rate is positively related to the
expected inflation rate
Slide 28
Inflation and Interest Rates
RECAP
Slide 29

The nominal interest rate is the real interest rate
plus the expected inflation rate

Money illusion occurs when investors react to
nominal changes when no real changes occurred

If expected inflation increases, the nominal
interest rate will rise

Nominal interest rates are correlated with
expected inflation i = f ( Y+,M¯, p+ e )
The Cyclical Movement of
Interest Rates
Slide 30

Stages of the business cycle are the
recession trough, expansion, and peak

Interest rates tend to fluctuate procyclically-that is, they move with the
business cycle, rising during expansions
and falling during recessions