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Exercise 2: Bond

Exercise 2: Bond. 1) 7 year bond, 7% coupon rate semiannually, 8% required return. Bond Value = C (PVIFA i/2,nx2 ) + Par (PVIF i/2,nx2 ). Coupon per period = 7% x 1,000 ÷ 2. = 35. Vb = 35 (PVIFA 8%/2,7x2 ) + 1,000 (PVIF 8%/2,7x2 ). Vb = 35 (PVIFA 4% , 14 ) + 1,000 (PVIF 4% , 14 ).

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Exercise 2: Bond

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  1. Exercise 2: Bond

  2. 1) 7 year bond, 7% coupon rate semiannually, 8% required return. Bond Value = C (PVIFA i/2,nx2) + Par (PVIF i/2,nx2) Coupon per period = 7% x 1,000 ÷ 2 = 35 Vb = 35 (PVIFA8%/2,7x2) + 1,000 (PVIF8%/2,7x2) Vb = 35 (PVIFA 4% , 14 ) + 1,000 (PVIF 4% , 14 ) Vb = 35 (10.5631) + 1,000 (0.5775) Vb = $ 947.21

  3. 2) coupon rate 10% per annum. Maturity 10 years. case 1: interest rate 12% case 2: interest rate 8% Bond Value = C (PVIFA i,n) + Par (PVIF i,n) Coupon = 10% x 1,000 = 100 Case 1: Vb = 100 (PVIFA12%,10) + 1,000 (PVIF12%,10) Vb = 100 (5.6502) + 1,000 (0.3220) = $ 887.02 Case 2: Vb = 100 (PVIFA8%,10) + 1,000 (PVIF8%,10) Vb = 100 (6.7101) + 1,000 (0.4632) =$1,134.21

  4. 3.1) Bond paying 10% semiannual. 3 yrs to maturity. YTM 18% Coupon per period = 10% x 1,000 / 2 = $ 50 i per period = 18% / 2 = 9% number of periods = 3 years * 2 = 6 periods Vb = 50 (PVIFA 9%,6) + 1,000 (PVIF 9%,6) Vb = 50 (4.4859) + 1,000 (0.5963) = $ 820.60

  5. 4) $1,000 par bond paying coupon 11% semiannually. Remaining period 8 years. Market price $ 900. Coupon per period = 11% x 1,000 / 2 = $ 55 i per period = 14% / 2 = 7% number of periods = 8 years * 2 = 16 periods

  6. 4.1) what should be the price of bond if required rate = 14% Vb = 55 (PVIFA 7%,16) + 1,000 (PVIF 7%,16) Vb = 55 (9.4466) + 1,000 (0.3387) = $ 858.26

  7. 4) $1,000 par bond paying coupon 11% semiannually. Remaining period 8 years. Market price $ 900. Par value = $ 1,000 Market price = $ 900 Bond value = $ 858.26 4.2) Market price = $ 900, Par value = $ 1000 Market price < Par value  Bond is traded at “Discount” 4.3) Market price = $ 900, Bond value $ 858.26 Market price > Bond value  Bond is “Overpriced”

  8. 4.4) $1,000 par bond paying coupon 11% semiannually. Remaining period 8 years. Market price $ 900. Find YTM = coupon per year + [(par – price) ÷ n] (par + price) ÷ 2 **coupon per year = 11% x 1000 = $ 110 **n = 8 years = $ 110 + 12.5 950 = $ 110 + [(1,000 – 900) ÷ 8] (1,000 + 900) ÷ 2 = 0.1289 = 12.89 %

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