What is the maximum price to pay for a 7%, 30 yr, $1000 par value bond?

Question

the answer is $795, but I can't figure out the procedure.

Answer 1

The procedure to figure the *maximum* price to pay for such a bond would be the value of the payments (periodic interest payments and principal payment at maturity), discounted to present value at the risk-free rate, i.e. the rate for US Treasury securities with a similar duration.

The price you really *should* pay depends on how much risk of default there is or - in other words - how creditworthy the issuer is.

The $795 figure appears to be either (a) wrong, or (b) based on some other assumptions or information you haven't provided us in your question. The reason it can't possibly be right is that the current US Treasury rates are well under 7% ... thus a risk-free bond with a coupon of 7% should have a price higher than it's face amount, not lower.

EDIT (based on edit to the question, which supplies "some other assumption or information"):

The additional information is apparently intended to specify that you should price the bond so it earns 9%. To do this, discount all the payments (the coupon and the payment at maturity) to present value using a discount rate of 9%.

If you assume the bond pays $70 of interest annually, with the first payment one year from today, and pays $1,070 at maturity, you get a present discounted value of $794.53, which seems to be what you're looking for.

In the real world, bonds more typically pay interest semi-annually (i.e. every six months). This would produce a present value that is only slightly different: $793.62.