Question

# A callable bond with a \$1,000 par value and a 7.5% coupon rate pays interest semiannually....

A callable bond with a \$1,000 par value and a 7.5% coupon rate pays interest semiannually. The bond matures in 20 years but is callable in 5 years at a price of \$1,100. Today, the bond sells for \$1,055.84. What is this bond’s yield to call expressed as a bond equivalent yield?

 3.49% 3.90% 6.18% 6.98% 7.80%

Face(Par) Value = \$1000

Semi-annual coupon payment = \$1000*7.5%*1/2 = \$37.5

No of years to call = 5

n = 5*2 = 10

Price = \$1055.84

To calculate the Yield to call(YTC) we eill use Trial and Error method, First we take YTC as 6%

Semi-annual YTC = 6%/2 = 3%

Price = \$ 319.88 + \$744.09

Price = \$ 1063.97

Now, since the price at YTC 6% is higher & closer than the current price, we will take a little higher YTC as 7%

Semi-annual YTC = 7%/2 = 3.5%

Price = \$ 311.87 + \$708.92

Price = \$ 1020.79

Now calculating the YTC,

YTC = 6.18% (approx)

So, this bond’s yield to call expressed as a bond equivalent yield is 6.18%

hence, Option C