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Exercise 2: Bond

Exercise 2: Bond. SOLUTION Courtesy of A. Marisa. 1. Bond Value= R (PVIFA k b/2 , n*2 ) + Par (PVIF k b/2 , n*2 ). 1) 7 year bond, 7% coupon rate semiannually, 8% required return. Coupon per period = 7% x 1,000 ÷ 2. = 35. Vb = 35 (PVIFA 8%/2,7x2 ) + 1,000 (PVIF 8%/2,7x2 ).

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Exercise 2: Bond

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  1. Exercise 2: Bond SOLUTION Courtesy of A. Marisa 1

  2. Bond Value= R (PVIFAkb/2, n*2) + Par (PVIFkb/2, n*2) 1) 7 year bond, 7% coupon rate semiannually, 8% required return. 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 2

  3. 2) coupon rate 10% per annum. Maturity 10 years. case 1: interest rate 12% case 2: interest rate 8% Bond Value= R (PVIFAkb, n) + Par (PVIFkb, 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 3

  4. 3.1) Bond paying 10% semiannual. 3 yrs to maturity. YTM 18% Coupon per period = 10% x 1,000 / 2 = $ 50 kb 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 4

  5. 3.2) If the market rate is changed to 13%, what is the value of bond in the eighth year? PV of coupon payment = R x [1 - (1÷(1 +i)n)] ÷ i = 50 x [1 - (1 ÷ (1.065)4)] ÷ 0.065 = 50 x 3.4258 = 171.29 PV of PAR = 1000 / (1+0.065)4 = 777.32 Value of Bond = 171.29 + 777.32 = $948.61

  6. 4.1) what should be the price of bond if required rate = 14% 4) $1,000 par bond paying coupon 11% annually. Remaining period 8 years. Market price $ 900. Coupon per period = 11% x 1,000 = 110 kb per period = 14% number of periods = 8 years Vb = 110 (PVIFA14%,8) + 1,000 (PVIF 14%,8) Vb = 110 (4.6389) + 1,000 (0.3506) = $ 860.88 6

  7. Par value = $ 1,000 Market price = $ 900 Bond value = $ 860.88 4) $1,000 par bond paying coupon 11% semiannually. Remaining period 8 years. Market price $ 900. 4.2) Market price = $ 900, Par value = $ 1000 Market price < Par value  Bond is traded at “Discount” 4.3) Market price = $ 900, Bond value $860.88 Market price > Bond value  Bond is “Overpriced” 7

  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 + [(1,000 – 900) ÷ 8] (1,000 + 900) ÷ 2 = $ 110 + 12.5 950 = 0.1289 = 12.89 % 8

  9. 5) 10 year-bond, 6% conpon rate semiannually, required rate of return is 12%, 4 years to maturity, market price is $800. 5.1) Should you buy this bond? Explain. You should buy this bond, as market price is cheap. 5.2) Is it underpriced or overpriced? Explain. It is underpriced, since the market price is lower than fair value. Vb = 30 (PVIFA6%,8) + 1,000 (PVIF 6%,8) Vb = 30 (6.2098) + 1,000 (0.6274) = $ 813.69

  10. 5) 10 year-bond, 6% conpon rate semiannually, required rate of return is 12%, 4 years to maturity, market price is $800. 5.3) Find YTM and current yield. YTM= coupon per year + [(par – price) ÷ n] (par + price) ÷ 2 = $60 + [(1,000 – 800) ÷ 4] = 12.22% (1,000 + 800) ÷ 2 Yc = R/P = 60/800 = 7.5% 5.4) If investors buy, do they have capital gain or loss? Explain. Capital gain since par is higher than market price Capital gain = 1,000 – 800 =200

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