Question

Smackdown Inc. has a bond outstanding with a 9% annual coupon rate, a market price of $1,050, and a face value of $1,000. If the bond matures in 5 years and interest is paid on a semi-annual basis, what is the annual YTM? Assume the next coupon payment will occur in 6 months.

A. The YTM is less than 6%.

B. The YTM is equal to or greater than 6% but less than 7%.

C. The YTM is equal to or greater than 7% but less than 8%.

D. The YTM is equal to or greater than 8% but less than 9%.

E. The YTM is equal to or greater than 9%.

Answer 1

Face value of the bond = $1000

Annual coupon rate = 9%

The coupon is paid semiannually. So we will take the semi-annual coupon payments and semi-annual periods to maturity.

Semi-annual coupon payments = (9%/2)*1000 = 45

Time to maturity = 5 years

Semi-annual periods = 5*2 = 10

Present value of the bond = $1050

Method 1: Using BA II plus calculator

We can calculate the semiannual YTM of the bond using BA II Plus calculator as shown below

N = 10

PV = -1050

PMT = 45

FV = 1050

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

We get I/Y = 3.887007883%

Note that this is the semi-annual YTM because we have considered semi-annual coupon payments

Annual YTM = 3.887007883%*2 = 7.774015766% ~ 7.77% (Rounded to two decimals)

Answer -> C. The YTM is equal to or greater than 7% but less than 8%

Method 2: Using Excel

We can calculate the YTM of the bond using the RATE function in Excel as shown below:

=RATE(10,45,-1050,1000) =  3.887007883%

Annual YTM =  3.887007883%*2 = 7.774015766% ~ 7.77% (Rounded to two decimals)

Answer -> C. The YTM is equal to or greater than 7% but less than 8%