EC223 Chapter 4 – Understanding Interest Rates Week 4
Measuring Interest Rates
-Different debt instruments have very different streams of cash payments to the holder – known as cash
flows – with very different timing
Present Value
-Based on the fact that a dollar paid to you one year from now is less valuable to you than a dollar paid to
you today
-Simple loan – the lender provides the borrower with an amount of funds that must be repaid to the
lender at the maturity date, along with an additional payment for interest
PV = Current value
n
(1 + i)
-The concept of present value allows us to figure out today’s value (price) of a credit market instrument
at a given simple interest rate, I, by just adding up to the individual present values of all the future
payments received
Four Types of Credit Market Instruments
1. A simple loan – the lender provides the borrower with an amount of funds that must be repaid to the
lender at the maturity date along with an additional payment for the interest
2. A fixed-payment loan – the lender provides the borrower with an amount of funds, which must be
repaid by making the same payment every period consisting of part o the principal and interest for a set
number of years
3. A coupon bond – pays the owner of the bond a fixed interest payment every year until the maturity
date, when a specified final amount (face value) is repaid. The bond’s coupon rate is the dollar amount of
the early coupon payment expressed as a percentage of the face value of the bond
4. A discount bond – bought at a price below its face value and the face value is repaid at the maturity
date
Yield to Maturity
-The interest rate that equates the present value of cash flow payments received froma debt instrument
with its value today
Simple Loan
PV = Cash flow in one year
n
(1 + i)
-The simple interest rate equals the yield to maturity
Fixed-Payment Loan
-The borrower makes the same payment to the bank every month until the maturity date, when the loan
will be completely paid off
-We equate today’s value of the loan with its present value
LV = Fixed payment + Fixed payment + Fixed payment + ….. + Fixed payment
2 3 n
(1 + i) (1 + i) (1 + i) (1 + i)
Coupon Bond
-Same strategy used for the fixed-payment loan: equate today’s value of the bond with its present value
P = Coupon payment + Coupon payment + Coupon payment + ….. + Coupon payment
(1 + i) (1 + i)2 (1 + i) (1 + i) EC223 Chapter 4 – Understanding Interest Rates Week 4
-Three facts emerge:
-When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate
-The price of a coupon bond and the yield to maturity are negatively related; that is, as the yield
to maturity rises, the price of the bon falls. As the yield to maturity Falls, the price of the bond
rises
-The yield to maturity is greater than the coupon rate when the bond price is below its face value
-These three facts are true for any coupon bond
-Bond price and the yield to maturity are negatively related
-When the yield to maturity equals the coupon rate, the bo

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