Question

Assume the market price of a 6​-year bond for Margaret Inc. is ​$775​, and it has a par value of $ 1,000. The bond has an annual interest rate of 7​% that is paid semiannually. What is the yield to maturity of the​ bond?

The yield to maturity of the bond is

Answer 1

Face value of the bond = FV = 1000

Annual interest rate = 7%, the bond pays interest semiannually

So, semi-annual interest rate = 7%/2 = 3.5%

Semiannual interest payment = 3.5%*1000 = 35

Time to maturity = 6 years

No. of semiannual periods = 6*2 = 12

The current price of the bond = 775

We can calculate the YTM of the bond using ba ii plus calculator and also using Excel

Method 1: Using ba ii plus calculator

N = 12, PV = -775, PMT = 35, FV = 1000

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

we get, I/Y = 6.215535495

Note that this is the semi-annual YTM (as we have taken everything to be semi-annually)

So, Annual YTM = 6.215535495%*2 = 12.43107099%

Answer -> YTM = 12.43107099%

Method 2: Using Excel

We can calculate the YTM using the RATE function in Excel as shown below. As we have taken semi-annual interest payment and semiannual time period, we will get semi-annual YTM using the formula

=RATE(12,35,-775,1000) = 6.21553549542464%

Annual YTM = 6.21553549542464%*2 = 12.4310709908493%

Annual YTM = 6.21553549542464%*2 = 12.4310709908493%

Answer -> YTM = 12.4310709908493%