Answers
Let the bind with coupons be Bond A and the bond without coupons be bond B
Bond Price = ∑(Cn / (1+YTM)n )+ P / (1+i)n
Where
- n = Period which takes values from 0 to the nth period till the cash flows ending period
- Cn = Coupon payment in the nth period
- YTM = interest rate or required yield
- P = Face Value of the bond
Therefore using this formula we get,
Soln for A:
Price of bond A when the interest is 3% = $159.71
Price of Bond B when the interest is 3% = $74.41
When interest is at 6%
Price of bond A = $129.44
Price of Bond B = $55.84
Soln for B:
When the interest rises from 3 to 6 %,
Price of Bond A falls by $30.27 which is 18.95% decrease (30.27/159.71*100)
whereas,
Price of bond B falls by $18.57 which is 24.95% decrease (18.57/74.41*100)
Therefore the Price of bond B falls by a larger percentage than the price of bond A. This is because Bond A offers coupons of $10 every year. With this, the value of the bonds goes up at the end of every year. With the change in interest rate, though bond A decreases more in terms of value, in terms of percentage, Bond B falls by a larger percentage
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