Question 5 Mark purchases a bond. A 1000 par value two-year bond with semiannual

Question

Question 5 Mark purchases a bond. A 1000 par value two-year bond with semiannual coupons at a rate of 8% convertible semiannually, is bought to yield 6% convertible semiannually. The initial price of the bond was 1037.17. Then, m months after purchase, before a coupon is paid, Mark decides to sell the bond. Using the semi-theoretical method, the full price of the bond at this time is 1063.04. Using the semi-theoretical method, what would be the book value of the bond at this time (m months after purchase)? (a) 1229.7 (b) 1179.7 (c) 1129.7 (d) 1079.7 (e) 1029.7

Explanation / Answer

Bond price * (1+ytm/2)n/6 = full price

= 1063.04 / 1037.17 = 1.02

Apply logarithm on both sides

n*LN(1.03) = LN(1.02)

n/6 = LN(1.02) / LN(1.03)

n/6 = 0.83

n = 0.83*6 = 5 months

Interest for 5 months = 40*((1+0.03)5/6 - 1) / 0.03 = 33.25

Book price = 1063.04 - 33.25 = 1029.79 (Option E)

You can eliminate other options by looking, as all the options have higher price than full price

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