There are two bonds in the market: Bond A will pay only $80 of
interest every year until its maturity in 30 years; this bond pays no
maturity value. Bond B will pay only $1000 at its maturity in 30
years. Both bonds have a YTM of 10%. Because there are no 30-year
couppon bonds anymore, my boss at Merrill Lynch proposes that I buy
both bonds, combine them and then sell them as one unit to investors.
If I expect that investors would like to make an 9% yield to maturity
on such a bond package, I extimate that investors will pay for this
combined bond: what?

Holla,

The key to answering a question like this is to get a decent diagram
or table showing all of the cashflows and to then figure out how best
to discount them back to the present.

Here's the table of cashflows

Year         Bond A          Bond B        Combined
  0
  1            80              0              80
  2            80              0              80
  .            .               .              .
  .            .               .              .
 29            80              0              80
 30            80             1000           1080

The main trick of the question is to figure out what rate you should
be discounting the cashflows back at. The stated YTM of 10% is the
price at which you could buy bonds A and B. But when it comes to
selling the combined cashflows to investors, they are demanding a 9%
yield, so you should use that to price the combined package. If you
give them less than a 9% yield they will not buy the bond. If you give
them more than that, they will buy but you are losing out on potential
profits.

So we discount back the cashflows to calculate the price using the
formula :

P = Sum{CFi/(1+r)^i}

(where sum means sum over i from 1 to 30, CFi is the cashflow in year
i, r is the discount rate (9%) and ^i means raised to the power i).

The easiest way of valuing the package is to use the bond formula :

    C (         1   )      FV
P = - (1 -  --------) + -------
    r (     (1+r)^n))   (1+r)^n

     80 (          1    )      1000
  = --- (1 -  ----------) + ---------
    .09 (     (1.09)^30))   (1.09)^30

  = 821.89 + 75.37 = 897.26

Hence investors would be prepared to pay 897.26

Regards

calebu2-ga

Useful resource
http://www2.bc.edu/~balduzzp/sylmf880f02a.html - Course on fixed
income from Boston College.

P.S. While the question doesn't ask for it, you can calculate the
price of each individual bond as by using r = 0.1 to get Pa = 754.15,
Pb = 57.31 for a combined total of 811.46.

By buying these bonds and repackaging you would be netting roughly
$85.80 per $1000 face value of bonds.