A four-year 6% semi-annual-pay bond with a maturity value of $1,000 is trading at a yield-to-maturity (YTM)of 7%.What is this bond's current yield?

Question

Quizplus · Accepted Answer

The current yield formula is Annual Interest Payment / Current Market Price of the Bond x 100%.

To calculate the annual interest payment, we need to divide the coupon rate (6%) by 2 since the bond pays semi-annually. Thus, the annual interest payment is:

Annual Interest Payment = (6% / 2) x 1000 = $30

To calculate the current market price of the bond, we need to use the present value formula:

PV = PMT x [1 - 1/(1 + r)^n] / r + FV / (1 + r)^n

Where:
PMT = Semi-annual coupon payment = 6% / 2 x 1000 = $30
r = YTM / 2 = 7% / 2 = 3.5%
n = Number of semi-annual periods = 4 years x 2 = 8
FV = Maturity value = $1000

PV = $30 x [1 - 1/(1 + 3.5%)^8] / 3.5% + $1000 / (1 + 3.5%)^8 = $906.77

Now that we have the annual interest payment ($30) and the current market price of the bond ($906.77), we can calculate the current yield as follows:

Current Yield = Annual Interest Payment / Current Market Price of the Bond x 100%
Current Yield = $30 / $906.77 x 100% = 3.31%
Current Yield = 3.31% x 2 = 6.62% (to get the annual current yield)

The closest answer is B) 6.21% which is the best choice.

A Four-Year 6% Semi-Annual-Pay Bond with a Maturity Value of $1,000