Understanding Interest Rates

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G-345- Topic 1--Chap 4
Understanding Interest Rates

Four Types of Credit Market
Instruments
Simple loan
Discount bond
Coupon bond
Fixed-payment loan

Time Lines for Credit Market
Instruments

Measuring Interest Rates
Present Value:
A dollar paid to you one year from now is less valuable than a dollar paid to you today
Why?
A dollar deposited today can earn interest and become
$1 x (1+i) one year from today.

Let i = .10
In one year $100 X (1+ 0.10) = $110
In two years $110 X (1 + 0.10) = $121 or 100 X (1 + 0.10)

2

In three years $121 X (1 + 0.10) = $133 or 100 X (1 + 0.10)3
In n years
$100 X (1 + i ) n

Discounting the future
What is the value today of a future return?
PV of $133 received in 3 years is $133/(1+0.10)3

Generally:

Time Line
One cannot directly compare payments scheduled in different points in the time line

Year
PV

$100

$100

$100

$100

0

1

2

n

100

100/(1+i)

100/(1+i)2

100/(1+i)n

$110

$121

Yield to Maturity
We know the price of a debt instrument and the future payment schedule

The interest rate that equates the present value of cash flow payments received from a debt instrument with its value today.

Yield to Maturity
Question: did I make a sound investment?
If I pay a price P today for a set of future payments, what is the interest rate at which I could invest P and get the same set of future payments?

Simple Loan
PV = amount borrowed = $100
CF = cash flow in one year = $110 n = number of years = 1
$110
$100 =
(1 + i )1
(1 + i ) $100 = $110
$110
(1 + i ) =
$100
i = 0.10 = 10%
For simple loans, the simple interest rate equals the yield to maturity

Fixed Payment Loan
The same cash flow payment every period throughout the life of the loan
LV = loan value
FP = fixed yearly payment n = number of years until maturity
FP
FP
FP
FP
LV =


 ...+
2
3
1 + i (1 + i ) (1 + i)
(1 + i) n

Coupon Bond
Using the same strategy used for the fixed-payment loan:
P = price of coupon bond
C = yearly coupon payment
F = face value of the bond n = years to maturity date
C
C
C
C
F
P=


. . . +

2
3
n
1+i (1+i ) (1+i )
(1+i) (1+i ) n

Relationship Between Price and Yield to
Maturity

• 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
• The yield to maturity is greater than the coupon rate when the bond price is below its face value

Consol or Perpetuity
• A bond with no maturity date that does not repay principal but pays fixed coupon payments forever.

i =

C
-------P

• For coupon bonds, this equation gives the current yield, and easy way to calculate approximation to the yield to maturity. Discount Bond (P = $900, F=
$1000)

Yield on a Discount Basis idb =

(F – P)
F

x

360
(number of days to maturity)

One year bill, P = $900, F = $1000

idb =

$1000 – $900
$1000

x

360
365

=0.099 = 9.9%

Two Characteristics
1.
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