1. Pricing of Bonds

2. Outline  Time Value of Money Concepts  Valuation of Fixed Income Securities  Pricing zero coupon bonds  Price/Yield Relationship  The Relationship between coupon rate, required yield, and price  Relationship between bond price and time if interest rates are unchanged  How to account for accrued interest?

3. Time Value of Money  Future value of a single cash flow  Present value of a single cash flow  Future value of a series of cash flows  Present value of a series of cash flows  Present value of an annuity

4. Valuation of Fixed Income Securities  Process of determining the fair market value of a financial asset on the basis of present value of the expected cash flows  Three step process: –Estimate the expected cash flows –Determine the appropriate interest rate or interest rates to discount the cash flows –Compute the present value of the expected cash flows in step 1 by discounted them with interest rate(s) in step 2

5. Estimating Cash Flows  Holding aside the risk of default, the cash flows of fixed income securities are easy to project Payment of coupon/interest Repayment of principal  When will investors find it difficult to estimate the cash flows of a fixed-income security?

6. Determining the Discount Rate or Rates  What is the minimum rate that an investor should require?  How much more than the minimum interest rate should the investor require?  Should the investor require the same interest rate for each estimated cash flow or a unique interest rate for each estimated cash flow?

7. Discount Rate  The minimum interest rate that an investor should require is the yield available in the market place on a default-free cash flow  In the United States, this is the yield on a U.S. Treasury security, known as the base interest rate for each maturity  Premium over the base interest rate on a Treasury security that investors will require reflects the additional risks that the investor faces by acquiring a security not issued by the U.S. government

8.  Discount Rate = Base Interest Rate + Risk Premium/Spread over Treasuries  What determines the spread?

9. Value of a Bond  Depends on the present value of expected cash flows from the bond  Need to estimate –Expected cash flows –The appropriate required yield/discount rate  What are the expected cash flows for a plain-vanilla bond?

10. Pricing Zero-Coupon Bonds  Bonds that do not pay any periodic coupon payments.  Instead the investor realizes interest as the difference between the maturity value and the purchase price of the bond  Example

11. Price/Yield Relationship  Price of bond changes in the opposite direction from the change in the required yield

12. Coupon Rate, Required Yield, and Bond Price  Par bonds  Discount bonds  Premium bonds