Question

A 20-year fixed coupon bond has 12 years left until maturity.  It has a 7% coupon rate paid SEMI-ANNUALLY.  If the price of the bond is $850, what is the annual yield?

a. 9.08%

b. 4.56%

c. 9.11%

d.4.54%

e. 8.60%

Answer 1

Face Value of the bond = $1000

Price of the Bond = $850

Time to maturity = 12 years

Annual coupon rate = 7%

Annual coupon payment = Annual coupon rate*Face Value = 7%*1000 = 70

The bond pays coupons semi-annually hence we will consider semi-annual coupon payments and time to maturity in semiannual periods

Semiannual coupons = null coupon arte/2 = 70/2 = 35

No. of semiannual periods = 12*2 = 24

Method 1: Yield calculation using ba ii plus calculator

Input the following values in ba ii plus calcultor

N = 24

PV = -850

PMT = 35

FV = 1000

CPT -> I/Y [Press CPT and then press I/Y]

We get, I/Y = 4.538818132

Note that this is the semi-annual Yield. To get the annual Yield we need to multiply it by 2

Annual Yield or YTM = 4.538818132%*2 = 9.077636263% ~ 9.08% (Rounded to two decimals)

Answer -> 9.08% (Option a)

Method 2: Yield calculation using Excel

We can compute the Yield of the bond using the RATE function in Excel as shown below:

=RATE(24,35,-850,1000) = 4.538818132%

Note that this is the semi-annual Yield.

To get the annual Yield we need to multiply it by 2

Annual Yield or YTM = 4.538818132%*2 = 9.077636263% ~ 9.08% (Rounded to two decimals)

Annual Yield = 9.08%

Answer -> 9.08% (Option a)