Bond Valuation Problems 3. Interpreting Bond Yields Suppose you buy a 9 percent coupon, 15-year bond today when it’s first issued. If interest rates suddenly rise to 15 percent, what happens to the value of your bond? Why? Answer: $649.16

Bond Valuation Problems 5. Bond Yields N&N Co. has 11 percent coupon bonds on the market with 8 years left to maturity. The bonds make annual payments. If the bond currently sells for $1,110.70 what is its YTM? Answer: 9%

Bond Valuation Problems 6. Coupon rates Merton Enterprises has bonds on the market making annual payments, with 14 years to maturity, and selling for $950. At this price, the bonds yield 7.5 percent. What must the coupon rate be on Merton’s bonds? Answer: 6.911%

Bond Valuation Problems 22. Interest Rate Risk Bond J is a 4 percent coupon bond. Bond K is a 10 percent coupon bond. Both bonds have 10 years to maturity, make semi-annual payments and have a YTM of 9 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?

Bond Valuation Problems 23. Bond Yields BrainDrain Software has 12 percent coupon bonds on the market with 9 years to maturity. The bonds make semiannual payments and currently sell for 125.32 percent of par. What is the current yield on BrainDrain bonds? The YTM? The effective annual yield? Answer: CY=9.58% YTM=8% EAR=8.16%

Example. Decomposition of total return when YTM at the end of a period is same as YTM at the beginning of the period then total realized return=YTM at the beginning of the period = capital gains yield + interest income for instance: coupon rate=9% annual coupon N=10 years P=$882.22 P10=882.22= 90 PVIFAk,10 + 1000PVIFk,10 k=11%=YTM at the beginning of the period

Example. Decomposition of total return after 1 year if YTM is still 11% P9= 90 PVIFA11%,9 + 1000PVIF11%,9=$889.26 total realized return=0.798%+10.202% =11% =YTM at the beginning of the period

Example. Decomposition of total return if YTM rises to 13% at the end of the period P9=$794.73 total realized return=-9.917%+10.202% =0.285%  YTM at the beginning of the period Note: To be able to calculate realized return for more than one period we need to make assumptions about reinvestment rates.

Bond Valuation Problems 40. Holding Period Yield The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY). Suppose you buy a 10 percent coupon bond making annual payments today for $1,064.18. The bond has 10 years to maturity. What rate of return do you expect on your investment? Two years from now, the YTM on your bond has declined by 3 percent, and you decide to sell. What price will your bond sell for? What is the HPY on your investment assuming that you reinvest coupons at HPY? Compare this yield to the YTM when you first bought the bond. Why are they different? Answer: 1,064.18=100 PVIFA10,k + 1,000 PVIF10,k YTM=9% b. New YTM=9%-3%=6% $1,248.39=100 PVIFA8,6% + 1,000 PVIF8,6% 1,064.18=100 PVIFA2,HPY + 1,248.39 PVIF2,HPY HPY=17.361% note this assumes you could reinvest $100 coupon at 17.361%