Question

It is now January 1, 2018 and you are considering the purchase of an outstanding bond that was issued on January 1, 2016. It has an 8.5% annual coupon and had a 20-year original maturity. (It matures on December 31, 2035.) There is 5 years of call protection (until December 31, 2020), after which time it can be called at 106 - that is, at 106%. of par, or $1060.00. Interest rates have declined since it was issued, and it is now selling at 118.06% of par, or $1,180.60.

What is the yield to maturity?

What is the yield to call?

Answer 1

a.            What is the yield to maturity?

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] /i + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $1,180.60

C = coupon payment = 8.5% of $1000 = $85

n = number of payments (time remaining to maturity) = 20 -2 = 18

YTM = interest rate, or yield to maturity =?

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

Now we have,

$ 1,180.60 = $85 * [1 – 1 / (1+YTM) ^18] /i + 1000 / (1+YTM) ^18

By trial and error method we can calculate the value of YTM = 6.74% per year

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

“= Rate(N,PMT,PV,FV)”

“Rate(18,-85,1180.60,-1000)” = 6.74%]

b.            What is the yield to call?

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

P = the current market price of bond = $1,180.60

C = coupon payment = 8.5% of $1000 = $85

CP = the call price = $1,060 (assumed it as the maturity value if the bond is callable)

t = the number of years remaining until the call date = 5-2 =3 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)

$1,180.60 = $85 *{(1- 1/ (1+ YTC) ^3)/ (YTC)} + ($1,060/ (1+YTC) ^3)

With the help of above equation and by trial and error method we can calculate the value of YTC = 3.92% per year

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

“= Rate(N,PMT,PV,FV)”

“Rate(3,-85,1180.60,-1060)” = 3.92%]