Question

A bond has a $1,000 par value, 20 years to maturity, and pays a coupon of 5.5% per year, annually. The bond is callable in ten years at $1,075. If the bond’s yield to maturity is 5.89% per year, what is its yield to call? Question 13 options: A) 5.87% B) 6.57% C) 6.11% D) 6.43% E) 6.68%

Answer 1

6.68% , option E is correct

Step-by-step explanation:

The price of the bond can be computed using the below formula for bond price calculation:

bond price=face value/(1+r)^n+coupon*(1-(1+r)^-n)/r

face value is $1000

r is the yield to maturity which is 5.89%

coupon=face value*coupon rate=1000*5.5%=55

n is the number of coupons the bond would pay which is 11 coupons over 20 years

bond price=1000/(1+5.89%)^20+55*(1-(1+5.89%)^-20)/5.89%

bond price=$ 954.87

The yield on the call can be determined using excel rate function as further explained below:

=rate(nper,pmt,-pv,fv)

nper is the number of coupons the bond would pay before being called in ten years' time i.e 10 coupons

pmt is the is the amount of annual coupon=$1000*5.5%=$55

pv is the current price of $954.87

fv is the call price which is $1,075

=rate(10,55,-954.87,1075)=6.68%