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BKM_Sol_Ch_10 - Chapter 10 Bond Prices and Yields Chapter...

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Chapter 10 - Bond Prices and Yields Chapter 10 Bond Prices and Yields 1. a. Effective annual rate on three-month T-bill: % 00 . 10 1000 . 0 1 ) 02412 . 1 ( 1 645 , 97 000 , 100 4 4 = = - = - b. Effective annual interest rate on coupon bond paying 5% semiannually: (1.05) 2 – 1 = 0.1025 = 10.25% Therefore, the coupon bond has the higher effective annual interest rate. 2. The effective annual yield on the semiannual coupon bonds is 8.16%. If the annual coupon bonds are to sell at par they must offer the same yield, which requires an annual coupon of 8.16%. 3. The bond callable at 105 should sell at a lower price because the call provision is more valuable to the firm. Therefore, its yield to maturity should be higher. 4. The bond price will be lower. As time passes, the bond price, which is now above par value, will approach par. 5. True. Under the expectations hypothesis, there are no risk premia built into bond prices. The only reason for long-term yields to exceed short-term yields is an expectation of higher short-term rates in the future. 6. c A “fallen angel” is a bond that has fallen from investment grade to junk bond status. 7. Uncertain. Lower inflation usually leads to lower nominal interest rates. Nevertheless, if the liquidity premium is sufficiently great, long-term yields can exceed short-term yields despite expectations of falling short rates. 10-1
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Chapter 10 - Bond Prices and Yields 8. If the yield curve is upward sloping, you cannot conclude that investors expect short-term interest rates to rise because the rising slope could be due to either expectations of future increases in rates or the demand of investors for a risk premium on long-term bonds. In fact the yield curve can be upward sloping even in the absence of expectations of future increases in rates. 9. a. The bond pays $50 every six months. Current price: [$50 × Annuity factor(4%, 6)] + [$1000 × PV factor(4%, 6)] = $1,052.42 Assuming the market interest rate remains 4% per half year, price six months from now: [$50 × Annuity factor(4%, 5)] + [$1000 × PV factor(4%, 5)] = $1,044.52 b. Rate of return = months six per % 00 . 4 0400 . 0 42 . 052 , 1 $ 90 . 7 $ 50 $ 42 . 052 , 1 $ ) 42 . 052 , 1 $ 52 . 044 , 1 ($ 50 $ = = - = - + 10. a. Use the following inputs: n = 40, FV = 1000, PV = –950, PMT = 40. You will find that the yield to maturity on a semi-annual basis is 4.26%. This implies a bond equivalent yield to maturity of: 4.26% × 2 = 8.52% Effective annual yield to maturity = (1.0426) 2 – 1 = 0.0870 = 8.70% b. Since the bond is selling at par, the yield to maturity on a semi-annual basis is the same as the semi-annual coupon, 4%. The bond equivalent yield to maturity is 8%. Effective annual yield to maturity = (1.04) 2 – 1 = 0.0816 = 8.16% c. Keeping other inputs unchanged but setting PV = –1050, we find a bond equivalent yield to maturity of 7.52%, or 3.76% on a semi-annual basis. Effective annual yield to maturity = (1.0376) 2 – 1 = 0.0766 = 7.66% 10-2
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Chapter 10 - Bond Prices and Yields 11. Since the bond payments are now made annually instead of semi-annually, the bond equivalent yield to maturity is the same as the effective annual yield to maturity. The inputs are: n = 20, FV = 1000, PV = –price, PMT = 80. The resulting yields for the three bonds are: Bond equivalent yield = Effective annual yield $950 8.53% $1,000 8.00% $1,050 7.51% Bond Price
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