# Bonds b A bond is a promisory note whose holder is entitled to a stream of coupon payments (usually semi-annual), plus a par/face value payment at maturity.

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Bonds b A bond is a promisory note whose holder is entitled to a stream of coupon payments (usually semi-annual), plus a par/face value payment at maturity.

Bond Characteristics b Face or par value b Coupon rate Zero coupon bondZero coupon bond b payments Accrued InterestAccrued Interest

Different Issuers of Bonds b b U.S. Treasury Notes and BondsNotes and Bonds b Corporations b Municipalities b International Governments and Corporations b Innovative Bonds Indexed BondsIndexed Bonds FloatersFloaters

Provisions of Bonds b Secured or unsecured b Call provision b Convertible provision b Put provision (putable bonds) b Floating rate bonds b Sinking funds

Bond Prices & Yields P B =Price of the bond C t = interest or coupon payments T = number of periods to maturity r t = semi-annual discount rate or the semi-annual yield to maturity

Example: pricing a bond b A 10-yr, 8% coupon bond, with face = \$1,000 b C t = 40 (SA), P= 1000, T= 20 periods, r t = 3% (SA) P B = \$1,148.77 t=1 + 20 = P B 40 1 ( 1+.03) t 1000 1 ( 1+.03 ) 20 __________

Bond Prices and Discount Rates Prices and discount rates (required rates of return) have an inverse relationship b When discount rates get very high the value of the bond will be very low b When discount rates approach zero, the value of the bond approaches the sum of the cash flows

Prices and Discount Rates b Price Discount Rate

Yield to Maturity b b Interest rate that makes the present value of the bonds payments equal to its price b Solve the bond formula for r

Yield to Maturity Example b 10 yr Maturity, Coupon Rate = 7%, Price = \$950 b Solve for r = semiannual yield r = 3.8635%

Yield Calculations b Bond Equivalent Yield 7.72% = 3.86% x 2 b Effective Annual Yield (1.0386) 2 - 1 = 7.88% b Current Yield =Annual Coupons/ Market Price = \$70 / \$950 = 7.37 %

Realized Return versus YTM b Holding Period Return Changes in rates affects returnsChanges in rates affects returns Reinvestment of coupon paymentsReinvestment of coupon payments Change in price of the bondChange in price of the bond

Holding-Period Return: Single Period b HPR = [ I + ( P 0 - P 1 )] / P 0 where I = interest payment P 1 = price in one period P 0 = purchase price

Holding-Period Example b CR = 8% YTM = 8%N=10 years Semiannual CompoundingP 0 = \$1000 In six months, the rate falls to 7% P 1 = \$1068.55 HPR = [40 + ( 1068.55 - 1000)] / 1000 HPR = 10.85% (semiannual)

Holding-Period Return: Multiperiod b Requires actual calculation of reinvestment income b Solve for the Internal Rate of Return using the following: Future Value: sales price + future value of couponsFuture Value: sales price + future value of coupons Investment: purchase priceInvestment: purchase price

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