Fundamentals of Finance Lecture 3 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 1i one year from today ID: 578320
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Slide1
Understanding Interest Rates
Fundamentals of Finance – Lecture 3Slide2
Measuring Interest RatesPresent 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. Slide3
Time Line
$100
$100
Year
0
1
FV
100
2
$100
$100
n
110
121
100/(1+i)
n
It’s impossible to
directly compare payments scheduled in different points in the time
line!Slide4
Simple Present ValuePV = today’s (present) value
FV = future cash flow (payment)
i
= the interest rateSlide5
Yield to Maturity
The interest rate that equates the present value of cash flow payments received from a debt instrument with its value today.Slide6
Five Basic Types of Debt Instruments
Simple Loan Contracts
Fixed-Payment
Loan Contracts
Coupon
Bond
(Zero-Coupon) Discount Bond
Consol (or Perpetuity)Slide7
Type 1: Simple Loan
Borrower issues to lender a contract stating a
loan value
(principal) LV ($) and interest payment I ($).
Today
the borrower receives LV from lender.
One year from now the lender receives back from the borrower an amount LV+I.
Example: One-Year Deposit AccountDeposit LV = $100; Interest payment I = $10Borrower’s end-of-year payment = $100 + $10 .Slide8
Simple Loan cont’dSlide9
Type 2: Fixed Payment Loan
Today a borrower issues to a lender a
contract with
a stated loan value LV ($), an annual
fixed payment
FP ($/Yr), and a maturity of N
years.Today the borrower receives LV from the lender.For the next N successive years, the
lender receives from borrower the fixed payment FP.FP includes principal and interest payments.Example: 30-year fixed-rate home mortgageSlide10
Fixed Payment Loan cont’dSlide11
Type 3: Coupon Bond
Today a seller offers for sale in a bond market a
bond with
stated annual
coupon payment C ($/yr), face (
or par
) value F ($), and a remaining maturity of N years.Today the bond seller receives from a buyer a price P ($/bond) as determined in the bond market.
For next N successive years, the bond holder receives the fixed annual payment C from original bond issuer.At maturity, the bond holder also receives the
face value F from the original bond issuer.Examples: 30-year
corporate bond, Central Government Treasury notes (1-10yrs) and bonds (≥ 10yrs)Slide12
Coupon Bond cont’dSlide13
Type 4: Discount BondToday a seller offers for sale in a bond market a
bond with
a stated face value F ($) and remaining
maturity of
N years.
Today
the bond seller receives from a buyer a price P ($/bond) as determined in the bond market.At the end of N years the bond holder receives
the face value F from the original bond issuer.Example: Treasury Bills Maturity < 1yr., typically offered
in 1mo., 3mo., & 6 mo. Maturities.Slide14
Discount Bond cont’dSlide15
Type 5. Consol (or Perpetuity)
Today a seller offers for sale in a bond market a
bond with
a stated annual coupon payment C ($/Yr) and
no maturity
date (i.e., bond exists “in perpetuity”).
Today the bond seller receives from a buyer a price P ($/bond) as determined in the bond market.
In each future year the bond holder receives the coupon payment C from the original bond issuer.Example: Consols were originally issued by UK in
1751, and remain a small part of UK’s debt portfolio.Slide16
Consol (or Perpetuity) cont’d
A bond with no maturity date that does not repay principal but pays fixed coupon payments forever
For coupon bonds, this equation gives the current yield, an easy to calculate approximation to the yield to maturitySlide17
Other Measures of Interest Rate
Current yield
:
where is the
current yield, P is the price of the coupon bond, and C is the yearly coupon payment.
Yield on a Discount Basis:
Where F is the face value of the bond, P is the price of the bond, and d stands for the days to maturity=Slide18
The Distinction Between Interest Rates and Returns
Rate of Return
:Slide19
The Distinction Between Interest Rates and Returns (cont’d)
The return equals the yield to maturity only if the holding period equals the time to maturity.
A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period.
The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change.
The more distant a bond’s maturity, the lower the rate of return that occurs as a result of an increase in the interest rate.
Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise.Slide20
The Distinction Between Real and Nominal Interest Rates
Nominal interest rate
makes no allowance for inflation.
Real interest rate
is adjusted for changes in price level so it more accurately reflects the cost of borrowing.
Ex ante real interest rate is adjusted for expected changes in the price level.
Ex post real interest rate is adjusted for actual changes in the price level.Slide21
Fisher Equation