If the bond can be called at moment S at “Call price” and coupon is annual we can define Yield
To Call (YTC) as a rate that satisfies (*):
Example 7: You’ve just bought a 4% coupon 15 year bond with annual coupon payments. This
bond is callable in 7 years at a call price of $1050. Find its yield to call (YTC) if your purchasing
price was $950.
Solution: , so, to ﬁnd YTC we need to use either a ﬁnancial calculator or an approximation
Example 8: Today you found that your 15 year Disney callable bond that can be called in 5
years at a price of $1020 has YTM =6% and YTC=7%. If you believe that interest rates will not
change until bond’s maturity do you think this bond will be called?
Solution: Disney will end up paying its debtholders 6% if the bond is not retired. They would not
want to pay 7%, so, the bond will not be called..
Many municipal bonds are callable. If the issuer does not call the bonds when they can, this probably
means that interest rates on bonds with similar maturities are higher than the interest that they are paying
you. This means that the issuer would likely have to pay new bondholders more than they are paying you.
A good rule is to only buy callable bonds if both the yield-to-call and yield-to-maturity are attractive to you
and if you would be indifferent as to whether the bonds are called early or not.
Real/nominal returns and risk free rates:
The standard assumption is that Treasury Bills – the shortest governmental bonds are the safest
bonds. Return of these bonds is called “the Risk Free rate”.
As you understand, this return, even though presumed not risky, is still a “nominal” rate.
Nominal in this context means “not real” or “not adjusted for inﬂation”.
Thus, if a T-bill offer 3% annual return but inﬂation during this year is projected to be 2% you
need to expect to receive approximately 1% real return if you invest in this bond (using Fisher
formula: ). Example 9 (from question 6-23): Maritime Construction (MC) needs to borrow $50 million for 5
years. The company estimates that the real risk-free rate of return is currently 2%, expected
inﬂation per annum for the period is 3% and the risk premium on its bonds is 2.5%. The
company wants to issue a 5 year 7 % coupon bond (coupon is paid annually). Find its