Question

Ten years ago, a firm issued $1,000 par value, 30-year bonds with an 6.5% coupon rate and a 7% call premium. These bonds currently trade for $1,325 and are callable beginning 20 years from date of issuance. Assume semi-annual compounding.

a. Calculate the yield-to-maturity of these bonds today?

b. Calculate the yield-to-call on these bonds today?

Please show work!

Answer 1

a. Calculate the yield-to-maturity of these bonds today?

We have following formula for calculation of bond’s yield to maturity (YTM) for the case when it is not called (normal bond price calculation)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $1,325

M = value at maturity, or par value = $ 1000

C = coupon payment = 6.5% of $1000 = $65

n = number of payments (time remaining to maturity) = 20 years

YTM = interest rate, or yield to maturity =?

Now we have,

$1,325 = $65 * [1 – 1 / (1+YTM) ^20] /YTM+ 1000 / (1+YTM) ^20

By trial and error method we can calculate the value of YTM = 4.09% per year

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

“= Rate(N,PMT,PV,FV)”

“Rate(20,65,-1325,1000)” = 4.09%]

YTM = 4.09% per year

b. Calculate the yield-to-call on these bonds today?

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

P = the current market price of bond = $1,325

M = value at maturity, or par value = $ 1000

C = coupon payment = 6.5% of $1000 = $65

CP = the call price = 7% premium of par value = $1000 * (1+7%) = $1,070 (assumed it as the maturity value if the bond is callable)

t = the number of years remaining until the call date = 10 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)

$1,325 = $65 *{(1- 1/ (1+ YTC) ^10)/ (YTC)} + ($1,070/ (1+YTC) ^10)

With the help of above equation and by trial and error method we can calculate the value of YTC = 3.25% per year

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

“= Rate(N,PMT,PV,FV)”

“Rate(10,65,1325,-1070)” = 3.25%]

Therefore,

YTC = 3.25% per year