Question

a 6 year bond pays semiannually and is priced at $800. the ytm is 14%. what is the annual coupon rate?

Answer 1

Face value of the bond = $1000

The current price of the bond = $800

Time to maturity = 6 years

YTM = 14%

The bond pays semiannual coupons. So we will consider semiannual ytm and semiannual periods

Therefore, semiannual periods = 6*2 = 12

Semi-annual YTM = 14%/2 = 7%

We can calculate the semiannual coupon payment using both ba ii plus calculator and using excel

Method 1: Using ba ii plus

N = 12, I/Y = 7, PV = -800, FV = 1000

CPT -> PMT (Press CPT and then press PMT)

PMT = 44.81960227

Note that this is the semi-annual coupon payment

Semi-annual coupon rate = 44.81960227/1000 = 4.481960227%

Therefore, annual coupon rate = 4.481960227%*2 = 8.963920454

Answer -> Annual coupon rate = 8.963920454%

Method 2: Using PMT function in Excel

We can calculate the semiannual coupon payment using PMT function in Excel as shown below:

=PMT(7%,12,-800,1000) = 44.81960227

Semiannual coupon rate = 44.81960227/1000 = 4.481960227%

Annual coupon rate = 4.481960227%*2 = 8.963920454%

Answer -> Annual coupon rate = 4.481960227%*2 = 8.963920454%