Question

4. Bond yields

Coupon payments are fixed, but the percentage return that investors receive varies based on market conditions. This percentage return is referred to as the bond’s yield.

Yield to maturity (YTM) is the rate of return expected from a bond held until its maturity date. However, the YTM equals the expected rate of return under certain assumptions. Which of the following is one of those assumptions?

The bond has an early redemption feature.

The bond will not be called.

Consider the case of Badger Corp.:

Badger Corp. has 9% annual coupon bonds that are callable and have 18 years left until maturity. The bonds have a par value of $1,000, and their current market price is $1,040.35. However, Badger Corp. may call the bonds in eight years at a call price of $1,060. What are the YTM and the yield to call (YTC) on Badger Corp.’s bonds?

	Value
YTM
YTC

If interest rates are expected to remain constant, what is the best estimate of the remaining life left for Badger Corp.’s bonds?

5 years

18 years

10 years

8 years

If Badger Corp. issued new bonds today, what coupon rate must the bonds have to be issued at par?

Answer 1

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 = $1,040.35

C = coupon payment = 9% of $1000 = $90

n = number of payments (time remaining to maturity) = 18 years

YTM = interest rate, or yield to maturity =?

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

Now we have,

$ 1,040.35 = $90 * [1 – 1 / (1+YTM) ^18] /i + 1000 / (1+YTM) ^18

By trial and error method we can calculate the value of YTM = 8.55% per year

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

“= Rate(N,PMT,PV,FV)”

“Rate(18,-90,1040.35,-1000)” = 8.55%]

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

P = the current market price of bond = $1,040.35

C = coupon payment = 9% of $1000 = $90

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 = 8 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)

$1,040.35 = $90 *{(1- 1/ (1+ YTC) ^8)/ (YTC)} + ($1,060/ (1+YTC) ^8)

With the help of above equation and by trial and error method we can calculate the value of YTC = 8.82% per year

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

“= Rate(N,PMT,PV,FV)”

“Rate(3,-85,1040.35,-1060)” = 8.82%]

	Value
YTM	8.52%
YTC	8.82%

If interest rates are expected to remain constant, what is the best estimate of the remaining life left for Badger Corp.’s bonds?

The best estimate for the remaining term is 18 years because the company would not call the bonds as YTM is less than the YTC.

If Badger Corp. issued new bonds today, what coupon rate must the bonds have to be issued at par?

The coupon rate to issue a bond at par is YTM which is 8.52%.