Value of a bond?

Question

Wilson Company will issue $300,000,000 of 7%, $1000 Par bonds on November 15, 2004. The bonds will pay interest semiannually and mature on November 15, 2011.
a)What is the value of an individual bond from this issue to an investor who purchases the Wilson bond on the date of issue (November 15, 2004) assuming they require an 8% return?

Answer 1

Here is how to do this problem:

1. figure out the cash flows together with the time until it comes. This is a seven year bond -- so there are 14 payments in total. The first 13 payments are for a half year's interest. The interest payment is one half of 7% of the value of the bond. This is 0.5*0.07*1000 = $35. The 14th andf final payment includes the last interest payment and the return of principal -- so it is $1035.

2. Find the present value of each cash flow discounting at 8%. Note that since it compounds twice per year (semiannually) this means that the rate is 4% every half year.

The PV of each cash flow is:

PV = C * (1.04)^(2*T)

where C is the cas flow (either 35 or 1035)
T is the time until the cash flow (0.5, 1, 1.5, 2, . . . , 6.5, 7)

Then add up all the flows to get the value.