Pricing of Bonds 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? 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 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 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? 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? 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 Discount Rate = Base Interest Rate + Risk Premium/Spread over Treasuries What determines the spread? 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? 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 Price/Yield Relationship Price of bond changes in the opposite direction from the change in the required yield Coupon Rate, Required Yield, and Bond Price Par bonds Discount bonds Premium bonds