Question

A company's 25 year bonds have 6 years to maturity and currently have a market price of $1,050. Its coupon rate is 8 percent and its required rate of return, rd, is 9 percent. By how much is the bond mispriced?

Possible Answer:

Bond Price=c/(1+i) + c/(1+i)^2 + c/(1+i)^3...+ c/(1+i)^n + M/(1+i)^n= c[1 – (1+i)^-n]/i + M(1+i)^-n

c=80
i=0.09
M=1000
Bond price= $955.14
Mispriced= 1050 - 955.14= $94.86

How is c=80 and M=1000?

Answer 1

Company bonds usually have a nominal value (paid at maturity) of $1000, hence M=1000.
It promises $80 per annum (at the end of the year).
There are six years left.

Present value of a series of A=$80, n=6, i=1.09
P=A*[P/A,.09,6)
=A((1+.09)^6-1)/(.09*(1+.09)^6)
=$358.87

Present value of a future value of $1000 in six years at i=.09
P=F*[F/A,.09,6]
=F/(1+i)^n
=1000/(1.09^6)
=596.27

Total=358.87+596.27=955.14 as you had it.