Question

6. Consider two bonds. Each has a face value of $100 and matures in 10 years. One has no coupon payments, and the other pays $10 per year. a. Calculate the price of each bond if the interest rate is 3 percent and if the inter- est rate is 6 percent. b. When the interest rate rises from 3 per- cent to 6 percent, which bond price falls by a larger percentage? Explain why.

Answer 1

Let the bind with coupons be Bond A and the bond without coupons be bond B

Bond Price = ∑(C_n / (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
• C_n = 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