Question 2 (10 marks) Grand Ltd has issued a 3-year bond with a face value of $1
ID: 1171839 • Letter: Q
Question
Question 2 (10 marks) Grand Ltd has issued a 3-year bond with a face value of $1000 and which pays a coupon of 6, 10% p.a. Coupon payments are made semi-annually. 5.80% ?.?. Assume a yield to maturity of a) Calculate the value of the bond (3 marks) b) Calculate the effective annual yield (EAY) of the bond. (As a percentage to two decimal (2 marks) places) Suppose you bought 100 bonds at the price you indicated in a) above. After one year, immediately after the 2nd coupon payment, you sell the bonds at a yield of 6.1% pa. c) i. Calculate the price (per bond) you obtained from the sale. (2 marks) i. At the time you sold your bonds, was the bond a premium bond, a discount bond or a bond that trades at par? Explain why, with reference to the coupon rate (3 marks) PREMIUM IDISCOUNT / PAR (Circle one) Why?Explanation / Answer
Par Value = $ 1000, Coupon = 6.1 % payable semi-annually, YTM = 5.8 % and Tenure = 3 years or 6 half-years
Semi-Annual Coupon = 0.061 x 0.5 x 1000 = $ 30.5
(a) Let the bond price be Pm
Therefore, Pm = 30.5 x (1/0.029) x [1-{1/(1.029)^(6)}] + 1000/(1.029)^(6) = $ 1008.15
(b) Interest per 6 month period = 2.9 %
Therefore, Effective Annual Yied = (1.029)^(2) - 1 = 5.88 %
(c) (i) The sale price of the bond would be equal to the sum of the present value of the remaining coupons and par value redemption discounted at the then existing yield of 6.1 %
As the yield at 6,1 % is equal to the annual coupon rate, the bond price should be equal to its par value.
Therefore, sale price per bond = $ 1000
(ii) The bond was trading at par when it was sold as the bond's yield was equal to its coupon rate at the time of the sale.
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