Question

3. Masters Corp. issues two bonds with 20-year maturities. Both bonds are callable at $1,050 in two years. The first bond is issued at a deep discount with a coupon rate of 4% and a price of $600 to yield 11.03%. The second bond is issued at par value with a coupon rate of 10%. Coupon is paid annually

a) What is the YTM of the par bond?

b) If you expect rates to fall to 5% in the next 2 years, would any bond be called (redeemed before maturity), if any? What do you expect be the yield of this bond (yield to call)

Answer 1

a) What is the YTM of the par bond?

The YTM of the par bond is equal to its coupon rate which is 10% therefore YTM of par band is 10%.

b) If you expect rates to fall to 5% in the next 2 years, would any bond be called (redeemed before maturity), if any? What do you expect be the yield of this bond (yield to call)

The bond will be called if YTM (Yield to maturity) is more than the YTC (yield to call) on the bond

If you expect rates to fall to 5% in the next 2 years then YTM of first bond = 11.03% - 5% = 6.03%

And YTM of second bond = 10% - 5% = 5%

Now calculate YTC of first bond

The formula to calculate the bond's yield-to-call (YTC) is as follows

P = the current market price of bond = $600

C = coupon payment = 4% of $1000 = $40

CP = the call price = $1,050 (assumed it as the maturity value if the bond is callable)

t = the number of years remaining until the call date = 2 years

YTC = the yield to call =?

The complete formula to calculate yield to call is:

P = C * {(1 – 1/ (1 + YTC) ^ t) / (YTC)} + (CP / (1 + YTC) ^t)

$600 = $40 *{(1- 1/ (1+ YTC) ^2)/ (YTC)} + ($1,050/ (1+YTC) ^2)

With the help of above equation and by trial and error method we can calculate the value of YTC = 38.16% per year

[Or you can use excel function for YTC calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(2,-40,600,-1050)” = 38.16%]

As the YTC is more than YTM therefore it will not called

Now calculate YTC of second bond

The formula to calculate the bond's yield-to-call (YTC) is as follows

P = the current market price of bond = $1000

C = coupon payment = 10% of $1000 = $100

CP = the call price = $1,050 (assumed it as the maturity value if the bond is callable)

t = the number of years remaining until the call date = 2 years

YTC = the yield to call =?

The complete formula to calculate yield to call is:

P = C * {(1 – 1/ (1 + YTC) ^ t) / (YTC)} + (CP / (1 + YTC) ^t)

$1000 = $100 *{(1- 1/ (1+ YTC) ^2)/ (YTC)} + ($1,050/ (1+YTC) ^2)

With the help of above equation and by trial and error method we can calculate the value of YTC = 12.35% per year

[Or you can use excel function for YTC calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(2,-100,1000,-1050)” = 12.35%]

As the YTC is more than YTM therefore it will also not called