Question

Carla Vista, Inc., has bonds outstanding that will mature in 8 years. The bonds have a face value of $1,000. These bonds pay interest semiannually and have a coupon rate of 4.6 percent. If the bonds are currently selling at $895.92, what is the yield to maturity that an investor who buys them today can expect to earn? (Round answer to 3 decimal place, e.g. 5.275%.)

Yield to maturity%?

What is the effective annual yield? (Round answer to 3 decimal places, e.g. 5.275%.)

Answer 1

Firstly, the Yield to Maturity of a bond refers to the return expected from the bond if it is held until it matures. YTM is similar to Internal Rate of Return which is a discounting rate at which Present Values of Cash Inflows (Interest Payment and Principal of a Bond) is equal to Cash outflows (Current Market Price of a bond).

In the above example it will be assumed that the Coupon Rate is 4.6% per annum.

Using Microsoft Excel, Click FORMULAS tab then select Financial Drop down and select RATE.

When the Window of this function is opened,
NPER is the total number of periods NPER = 8 x 2 = 16
PMT is the Coupon payment made each period PMT = 46/2 = 23
PV is the current market value of the bond PV = -895.92.

Please note that when you use a Microsoft Excel or a Financial Calculator the Outflows value are to be entered as Negative values.  

Therefore, the YTM % will be 8.959%

Secondly, Effective yield is a more accurate measure of the investor's return than calculating a simple annual interest rate (the yield for one period times the number of periods in a year) because effective yield takes compounding into account.

In the above case as the Interest is paid Semi annually, the number of payment periods in one year is 2.
Therefore, Effective annual yield can be calculated as:

(1 + (0.046/2))^2 - 1 = 4.652%

Effective annual yield = 4.652%