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51757878-5830Chap003 - Chapter 03 Interest Rates and...

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Chapter 03 - Interest Rates and Security Valuation Answers to Chapter 3 Questions 1. 935 = 75(PVIFA rr, 5 ) + 980(PVIF rr, 5 ) Ψ rr = 8.83% 2. 980 = 75(PVIFA Err, 3 ) + 990(PVIF , 3  ) Ψ Err = 7.97% 3. V b = 1,000(.08) (PVIFA 9%, 10) + 1,000(PVIF 9%, 10) = $935.82 4. EXCEL Problem: Bond Value = $1,268.27 Bond Value = $1,169.36 Bond Value = $1,000.00 Bond Value = $862.01 5. $1,100 = 1,000(.12) (PVIFA ytm/2, 10(2) ) + 1,000(PVIF ytm/2, 10(2) ) => ytm = 10.37% 2 6. EXCEL Problem: Yield to Maturity = 9.87% Yield to Maturity = 9.19% Yield to Maturity = 7.69% Yield to Maturity = 5.97% 7. V b = 1,000(.07) (PVIFA 14%/4, 4(4) ) + 1,000(PVIF 14%/4, 4(4) ) = $788.35 4 8. $863.73 = 1,000(.08) (PVIFA 10%, n) + 1,000(PVIF 10%, n) => n = 12 years 9. a. V b = 1,000(.1) (PVIFA 6%/2, 10(2) ) + 1,000(PVIF 6%/2, 10(4) ) = $1,297.55 2 b. V b = 1,000(.1) (PVIFA 8%/2, 10(2) ) + 1,000(PVIF 8%/2, 10(4) ) = $1,135.90 2 c. From parts a. and b. of this problem, there is a negative relation between required rates and fair values of bonds. 10. a. Premium bond b. Par bond c. Discount bond d. Discount bond e. Premium bond f. Discount bond 11. a. 985 = 1,000(.09) (PVIFA ytm/2, 15(2) ) + 1,000(PVIF ytm/2, 15(2) ) Ψ ytm = 9.186% 2 b. 915 = 1,000(.08) (PVIFA ytm/4, 10(4) ) + 1,000(PVIF ytm/4, 10(4) ) Ψ ytm = 9.316% 4 c. 1,065 = 1,000(.11) (PVIFA ytm, 6 ) + 1,000(PVIF ytm, 6 ) Ψ ytm = 9.528% 3-1
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Chapter 03 - Interest Rates and Security Valuation 12. a. V b = 1,000(.06) (PVIFA 10%/2, 12(2) ) + 1,000(PVIF 10%/2, 12(2) ) = $724.03 2 b. V b = 1,000(.08) (PVIFA 10%/2, 12(2) ) + 1,000(PVIF 10%/2, 12(2) ) = $862.01 2 c. V b = 1,000(.10) (PVIFA 10%/2, 12(2) ) + 1,000(PVIF 10%/2, 12(2) ) = $1,000.00 2 d. From parts a. through c. in this problem, there is a positive relation between coupon rates and present values of bonds. 13. a. V b = 1,000(.06) (PVIFA 8%/2, 12(2) ) + 1,000(PVIF 8%/2, 12(2) ) = $847.53 2 b. V b = 1,000(.08) (PVIFA 8%/2, 12(2) ) + 1,000(PVIF 8%/2, 12(2) ) = $1,000.00 2 % change in bond value versus part (a) = ($1,000 - $847.53)/$847.53 = 17.99% c. V b = 1,000(.10) (PVIFA 8%/2, 12(2) ) + 1,000(PVIF 8%/2, 12(2) ) = $1,152.47 2 % change in bond value versue part (b) = ($1,152.47 - $1,000)/$1,000 = 15.25% d. From these results we see that as coupon rates increase, price volatility decreases. 14. a. V b = 1,000(.10) (PVIFA 8%/2, 10(2) ) + 1,000(PVIF 8%/2, 10(2) ) = $1,135.90 2 b. V b = 1,000(.10) (PVIFA 8%/2, 15(2) ) + 1,000(PVIF 8%/2, 15(2) ) = $1,172.92 2 c. V b = 1,000(.10) (PVIFA 8%/2, 20(2) ) + 1,000(PVIF 8%/2, 20(2) ) = $1,197.93 2 d. From these results we see that there is a positive relation between time to maturity and the difference between present values and face values on bonds.
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