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# chap07 - Chapter 7 Bonds and Their Valuation Chapter 7...

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Bonds and Their Valuation Chapter 7

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Chapter 7 Topic Overview 2 Bond Characteristics Annual and Semi-Annual Bond Valuation Reading Bond Quotes Finding Returns on Bonds Bond Risk and Other Important Bond Valuation Relationships
Bond Characteristics 3 Par (or Face) Value ( M ) = stated face value that is the amount the issuer must repay, usually \$1,000 Coupon Interest Rate Coupon ( INT ) = Coupon Rate x Face Value Maturity Date = when the face value is repaid. A legal contract called the bond indenture specifies these values. This makes a bond’s cash flows look like this:

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Bond Valuation Discount the bond’s cash flows at the investor’s required rate of return. the coupon payment (INT) stream (an annuity). the par (M) value payment (a lump sum). V = INT (PVA r, n) + M /(1+r) n 4 0 0 1 1 2 . . . 2 . . . n n INT INT INT INT INT+M INT+M
Bond Valuation Example #1 5 Duff’s Beer has \$1,000 par value bonds outstanding that make annual coupon payments. These bonds have a 7.5% annual coupon rate and 15 years left to maturity. Bonds with similar risk have a required return of 9%, and Moe Szyslak thinks this required return is reasonable. What’s the most that Moe is willing to pay for a Duff’s Beer bond?

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0 1 2 3 . . . 15 1000 ? 75 75 75 . . . 75 r = 9%
Let’s Play with Example #1 7 Homer Simpson is interested in buying a Duff Beer bond but demands an 7.5 percent required return. What is the most Homer would pay for this bond?

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0 1 2 3 . . . 15 1000 ? 75 75 75 . . . 75 r = 7.5%
Let’s Play with Example #1 some more. 9 Barney (belch!) Gumble is interested in buying a Duff Beer bond and demands on a 6 percent required return. What is the most Barney (belch!) would pay for this bond?

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0 1 2 3 . . . 15 1000 ? 75 75 75 . . . 75 r = 6%
Lesson from Example 1: Bond Prices and Interest Rates have an inverse relationship! 11

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Another Example 1 Lesson: Bond Premiums and Discounts 12 What happens to bond values if required return is not equal to the coupon rate? The bond's price will differ from its par value P 0 < par value r > Coupon Interest Rate DISCOUNT = P 0 > par value r < Coupon Interest Rate PREMIUM = P 0 = par value r = Coupon Interest Rate PAR =
Bonds with Semiannual Coupons 13 Double the number of years, and divide required return and annual coupon by 2. V V d = = INT INT /2 /2 (PVA (PVA r/2,2n r/2,2n ) + M ) + M /(1+r/2) 2n

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Semiannual Example 14 Kwickee-Mart has an \$1000 par value bond with an annual coupon rate of 6% that pays coupons semiannually with 20 years left to maturity. What is the most you would be willing to pay for this bond if your required return is 7% APR?
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chap07 - Chapter 7 Bonds and Their Valuation Chapter 7...

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