Understanding Interest Rates 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 (1+i) one year from today.

Time Line $100 Year01 FV100 2 $100 n /(1+i) n It’s impossible to directly compare payments scheduled in different points in the time line!

Simple Present Value PV = today’s (present) value FV = future cash flow (payment) i = the interest rate

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

Five Basic Types of Debt Instruments 1.Simple Loan Contracts 2.Fixed-Payment Loan Contracts 3.Coupon Bond 4.(Zero-Coupon) Discount Bond 5.Consol (or Perpetuity)

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 Account Deposit LV = $100; Interest payment I = $10 Borrower’s end-of-year payment = $100 + $10.

Simple Loan cont’d

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 mortgage

Fixed Payment Loan cont’d

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)

Coupon Bond cont’d

Type 4: Discount Bond Today 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.

Discount Bond cont’d

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.

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 maturity

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=

The Distinction Between Interest Rates and Returns Rate of Return :

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.

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.

Fisher Equation