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ch_10_sol - CHAPTER 10 BOND PRICES AND YIELDS 1 a Effective...

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CHAPTER 10: BOND PRICES AND YIELDS 1. a. Effective annual rate on 3-month T-bill: 4 – 1 = (1.02412) 4 – 1 = .10 or 10% b. Effective annual interest rate on coupon bond paying 5% semiannually: (1.05) 2 – 1 = .1025 or 10.25% Therefore, the coupon bond has the higher effective annual 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 YTM should be higher. 4. Lower. As time passes, the bond price, which now must be 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. The fallen angel is a bond that has fallen from investment grade to junk bond status. 7. Uncertain. Lower inflation will usually lead to lower nominal interest rates. Nevertheless, if the liquidity premium is sufficiently great, long-term yields may exceed short-term yields despite expectations of falling short rates. 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 either be due to expectations of future increases in rates or due to the demand of investors of a risk premium on long-term bonds. In fact the yield curve can be upward sloping even in the absence of any expectations of future increases in rates. 9. a. The bond pays $50 every 6 months Current price: $50 × Annuity factor(4%, 6) + $1000 × PV factor(4%, 6) = $1052.42 10-1
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Assuming the market interest rate remains 4% per half year: Price 6 months from now: $50 × Annuity factor(4%, 5) + $1000 × PV factor(4%, 5) = $1044.52 b. Rate of return = = = = .04 or 4% per six months 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 = .087 = 8.7% 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 = .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 = .0766 = 7.66% 11. Since the bond now makes annual payments instead of semi-annual payments, the bond equivalent yield to maturity will be 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 Price Bond equivalent yield = Effective annual yield $ 950 8.53% $1000 8.00% $1050 7.51% The yields computed in this case are lower than the yields calculated when the coupon payments were semi-annual. All else equal, annual payments make the
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