P b bondvalue at 0 pv c 1 r c 1 r 2 c 1 r n f 1 r n p

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P B = BondValue at 0 = PV 0 = C (1 + r ) + C (1 + r ) 2 + ............ + C (1 + r ) n + F (1 + r ) n ! P B = BondValue at 0 = C 1 " (1 + r ) " n r # $ % & ' ( + F (1 + r ) n
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12 iClicker Bond Pricing Example N Consider a bond with the following cash flows: 0 1 2 3 ……… .. 29 30 Periods N ---|------|------|------|-----------------------|------|--- 50 50 50 ……… . 50 50 Cash 1000 Flows N Suppose the effective periodic interest rate to discount these cash flows is 4%. N What is the price of the bond at t = 0? a) $ 1,000.00 b) $ 864.60 c) $ 1,808.32 d) $ 1,172.92 e) None of the above?
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13 iClicker Bond Pricing Example N Consider a bond that has the following cash flows: 0 1 2 3 ……… .. 29 30 Periods N ---|------|------|------|-----------------------|------|--- 50 50 50 ……… . 50 50 Cash 1000 Flows N Suppose the effective periodic interest rate to discount these cash flows is 4%. 92 . 172 , 1 $ 32 . 308 $ 60 , 864 $ ) 04 . 1 ( 000 , 1 $ 04 . 0 ) 04 . 1 ( 1 50 $ ) 1 ( ) 1 ( 1 30 30 0 0 = + = + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = = + + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + = = B B n n B P PV P r F r r C PV P
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14 So What s the Big Deal? N Bonds have their own terminology. N Most bonds make semi-annual coupon (i.e. interest) payments. N It s easy to get confused about the coupon rate and the interest rate used to discount a bond s cash flows (the bond’s ytm or bey). A bond s coupon rate is typically equal to market interest rates when a bond is issued . N The coupon rate determines the bond s annual coupon (i.e. interest) payments, which are the cash flows associated with the bond. To price a bond, we use an appropriate market interest rate (also called the yield-to-maturity ( ytm) or bond-equivalent yield (bey) ) to discount the bond s cash flows. Over time, market interest rates change, while the coupon rate of a bond, once issued, remains constant. As market interest rate change, so do prices of bonds that were issued in the past.
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15 More on the Yield-to-Maturity N The interest rate used to discount a bond s cash flow to determine the bond s price. N Also, by definition, the interest rate that equates the present value of a bond s cash flow with its price. N It s also equal to investors required rate of return for investments with the same characteristics. N The ytm is the rate at which demand for bonds equals supply of bonds (of this type). N The ytm is also called bond-equivalent-yield (bey). N It measures the average return on the bond if held to maturity (and coupon payments can be reinvested at the ytm). N Both ytm and bey are nominal interest rates (as were APRs we discussed earlier). N With semi-annual coupon-payments, ytm = r semi *2. In this case the effective annual yield is r Yr =(1+r semi ) 2 – 1. N More generally, with k coupon payments per year, ytm is equal to r k *k., where r k is the effective periodic yield.
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16 BSL: Bond Terminology N Face value F : $$$ amount that bondholder gets at maturity of the bond. Often equal to $1,000 for corporate bonds. Par value, Principal : Other terms for face value.
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