Question

1. One of the England’s largest corporation, who own the hair salon, “British Hairways” just expanded operations into the United States. At present, the firm has a 30 year, $10,000 par value bond outstanding, with a coupon rate of 4.3% percent paid semiannually and 15 years to maturity. The yield to maturity on this bond is 5.2 percent. A. What is the current value of the bond?   B. Once you have calculated the Present Value or the current price of the bond, what would be the Current Yield on this bond? C. Is it selling at a discount, par, or premium? D. What is the difference between the concepts of Yield to Maturity, Current Yield, and Coupon Rate? Please compare the three rate. Please show all work and be descriptive. Thanks!

Answer 1

a. Par value = 10000
Number of Periods = 30*2 =60
Coupon =4.3%*10000/2 = 215
Semi annual YTM = 5.2%/2 = 2.6%
Price of Bond = PV of coupons + PV of Par Value = 215*(1-(1+2.6%)^-60)/2.6% + 10000/(+2.6%)^60 =8640.25

b. Current Yield =Coupon*2/Price =215*2/8640.25 = 4.98%

c. The bond is selling at discount because price is less than par value.

d. In this case Current Yield > YTM > Coupon Rate This because the bond is at discount.

YTM is total  rate of return of a bond if held till maturity.It is the sum of current yield and capital gain.
Current yield is the annual coupon or interest dividend by price. In case of semi annual or quarterly coupon payment it has to be converted to annual payment. for calculation of current yield.
Coupon is the fixed interest paid annually or semiannually on bond par value.

If bond is at premium then Current yield< YTM < Coupon Rate