A 10 year bond is redeemable at par of $100,000. The bond has semi-annual coupon
ID: 2792419 • Letter: A
Question
A 10 year bond is redeemable at par of $100,000. The bond has semi-annual coupons of $4,000. The bond is bought to yield 6% convertible semi-annually. Two years and 7 months after purchase, calculate the market price based on the theoretical method less the market price based on the semi-theoretical method.
Theoretical Method Market Price:
(Round answer to nearest dollar)
Semi-Theoretical Method Market Price:
(Round answer to nearest dollar)
Market Price based on theoretical method less the Market Price based on the semi-theoretical method:
Explanation / Answer
Par Value =$100,000
Semi-Annual Coupons =$4,000
Yield = 6% or 3% per semi-annual period
Bond Price at 2.50 years = 4000x{(1-(1+0.03)-15)/0.03} + 100,000/(1+0.03)15
= 4000x11.9379 + 64,186.19
= 47,751.74 + 64,186.19
= 111,937.94
Bf(2y7m) =$111,937.94 x (1 + 0.03)1/6 = 111,937.94 x 1.0049 =$112,490.75
Theoretical Method
Fr(1m) = 4000 x {(1+0.03)1/6 - 1)/0.03} =$ 4000 x 0.1646 =$658.48
Bond Price =$ 112,490.75 - 658.48 =$111,832.27
Semi-Theoretical Method
Fr(1m) = 4000 x 1/6 =$ 4000 x 0.1667 =$666.67
Bond Price =$ 112,490.75 - 666.67 =$111,824.09
Difference in Prices = Theoretical Price - Semi-Theoretical Price
= $111,832.27 - 111,824.09
= $8.18
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