Bond Prices Rise as the Interest Rates Fall


If i goes up, 1+i goes up, 1/(1+i) goes down for i > -1, (1/(1+i))j goes down for i > 0. So if the payments are positive, then the sum must also go down Similarly, i down -> PV up
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Bond Prices Rise as the Interest Rates Fall

Basic principle in evaluating known flows

cash flows are then evaluated using them
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8.3 Coupon Bonds, Current Yield, and Yield to Maturity

A change in market interest rates causes a change in the opposite direction in the market values of all existing contracts promising fixed payments in the future
Chapter 8 Contents




8.1 Using Present Value Formulas to Value Known Flows 8.2 The Basic Building Blocks: Pure Discount Bonds 8.3 Coupon Bonds, Current Yield, and Yield-toMaturity 8.4 Reading Bond Listings 8.5 Why Yields for the same Maturity Differ 8.6 The Behavior of Bond Prices Over Time
pmt 1 PV 1 i 1 i
n

60
400 1 1 0.015 1.015 $15,752.11
4

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Note

Volatile market rates imply volatile market values
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8.2 The Basics Building Blocks: Pure Discount Bonds


We can always analyze any fixed income contract into a sum of pure discount bonds A pure discount bond is a security that promises to pay a specified single cash payment (face value or par value) at a specified date called its maturity date
An increase in the required rate of return always leads to a decrease in the value of a fixed income security The proof is very easy

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First Solution Method
960 890 810 1000 100 P 100 100 1000 1000 1000 P $1076.00
1 3 1 2 1 1
1,000 i0,3 1 7.28% 810 100 100 1000 100 P 2 1.0417 1.0600 1.07283 P $1,075.91
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8.1 Using Present Value Formulas to Value Known Flows

You have been offered the opportunity to purchase a mortgage. The remaining life of the mortgage is 60 months, with payment of $400. Your required rate of return is 1.5% / month.
1 1 1 1 pmt1 * pmt2 * ... pmtn1 * pmtn * 1 i 1 i 1 i 1 i
1
2
n 1
n
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Using Pure Discount Bonds to Value other Bonds

Value a bond that pays its $100 coupon at the end of each year for 3-years, and its par value of $1,000 in 3-years
Financial Calculator

Alternatively, using your financial calculator (remember to set the correct defaults) you obtain
I PV PM T FV
N
6 0 1 .5 % ? -4 0 0 0 1 5 ,7 5 2 .1 1
Yield Curve

A typical yield curve:
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Chapter 8: Valuation of Known Cash Flows: Bonds
Objective
Valuation of fixed income securities Explain why bond prices change
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A coupon bond obligates the issuer to

make periodic payments of interest (called coupon payments) to the bond holder until the bond matures at which time the face value of the bond is also paid to the bond holder and the contract is satisfied

You have discovered three pure discount bonds (each with a $1,000 par value) that mature in 1, 2, and 3 years, and that are trading at $960, $890, and $810 respectively
N
I
PV
PMT FV
60 1.6% ? -400 0 15,354.66
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Using Present Value Formulas to Value Known Flows
Conclusion

The first method uses the fact that a coupon bond is the sum of pure discount bonds