Class 10 Completed

# N maturity date at which the bond disappears or

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N Maturity : Date at which the bond disappears or expires/matures, which is when the bond issuer (borrower) pays the bond holder (lender) the face value (plus one last coupon, typically). N Time to maturity : Number of periods or years until bond matures. N Coupon payments : Periodic interest payments (cash flows) associated with a coupon-paying bond. N Coupon rate c : Determines the annual coupon payments a bond makes as C = c * F When coupons are paid semi-annually, payments are equal to N Yield to maturity or bond-equivalent-yield : interest rate that equates present value of bond s cash flows to its price. Also equal to market interest rate used to discount a bond s cash flows to compute bond s price. A nominal interest rate. For bonds with semi- annual coupon payments, YTM = 2*r sem (while EAR=(1+r semi ) 2 – 1). N Current yield : Annual coupon payment divided by the current price. 2 * F c

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17 Bond Pricing Example (1) N Consider a bond with the following characteristics: Face Value F = \$1,000 Coupon rate c = 8% 25 years to maturity (25-year bond) Annual coupon payments Current market interest rate r = 8% N 1. Need to compute annual coupon payment C = c*F Here: C = 0.08*F = \$80 N 2. Calculate P B 000 , 1 \$ 02 . 146 \$ 98 . 853 \$ ) 08 . 1 ( 000 , 1 \$ 08 . 0 ) 08 . 1 ( 1 80 \$ ) 08 . 1 ( 000 , 1 \$ ) 08 . 1 ( 80 \$ ... .......... ) 08 . 1 ( 80 \$ ) 08 . 1 ( 80 \$ 25 25 25 25 2 0 = + = + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = + + + + = = B B P P PV
18 Bond Pricing Example (2) N Consider the same bond as before, right after the 5 th coupon payment has been made. N Assume market interest rates are still 8% N What is P B now? Bond is now a 20-year bond – Surprise? – Coincidence? NOT: Whenever the market interest rate is equal to a bond s coupon rate the bond s price is equal to its face value. 000 , 1 \$ 55 . 214 \$ 45 . 785 \$ ) 08 . 1 ( 000 , 1 \$ 08 . 0 ) 08 . 1 ( 1 * 80 \$ 20 20 = + = + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = B P

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19 iClicker Bond Pricing Example (3) N Consider the same bond again, right after the 5 th coupon payment has been made, but in a different scenario. N Suppose the market interest rate has risen to 10% now. N What is P B in this case? Bond is still a 20-year bond Bond is trading at a discount to par value (or below par ). What happened?. N Interest rate used to discount future cash flows increased, so the present value of these future cash flows has to decrease. 73 . 829 \$ 64 . 148 \$ 09 . 681 \$ ) 1 . 1 ( 000 , 1 \$ 1 . 0 ) 1 . 1 ( 1 * 80 \$ 20 20 = + = + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = B P
20 What happened? N The interest rate for similar bonds in the market has gone up. N This means investors now require a return of 10%. N Coupons only pay 8% of face value, so nobody would buy this bond at face value. N The market price of the bond has to fall to give investors a built-in price appreciation return. At maturity, the issuer buys back the bond at face value, so at maturity the price will equal \$1,000.

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