Pricing of Bonds

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Pricing of Bonds
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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?

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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

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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

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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?

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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?

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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

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• Discount Rate Base Interest Rate Risk
  Premium/Spread over Treasuries
• What determines the spread?

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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?

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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

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Price/Yield Relationship

• Price of bond changes in the opposite direction
  from the change in the required yield

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Coupon Rate, Required Yield, and Bond Price

• Par bonds
• Discount bonds
• Premium bonds