pv and fv formulas
Need help with Market price of a bond!!!?
Please explain how the textbook arrived at this answer. The question is The company intends to issue 20 year bonds with a face value of $1000. The bonds carry a coupon rate of 9% and interest is paid semiannually. On the issue date, the market interest rate for bonds issued by companies with similar risk is 12% compounded semiannually. Compute the market price of one bond on the date of issue.
The solution is
N= 20 yrs X 2 = 40
I= 12/2=6
PMT=1000 X .09 X (1/2) = 45
FV= 1000
PV= 774.31
If you could please explain this I would really appreciate it. This is homework, but I am not being graded on it. As you can see I already have the solution, but I would really appreciate if you could explain the formula used to arrive PV= 774.31. I understand up to that point. Thanks.
Answer:
The price of bond is the sum of:
1. Present value of interest
2. Present value of principal
In computing price of bond, you have to consider the number of periods to maturity (40 periods) and the prevailing market interest rate (12 percent).
Prevailing interest rate is 6 percent semi – annually (12 percent divided by 2).
Interest is $45 (1000 * 0.09 * 1/2) semi-annually.
The present value of annuity at 6 percent for 40 periods is 15.04622.
The present value of 1 at 6 percent for 40 periods is 0.09722.
You can find these values at the present value table.
Interest = $45*15.04622 = 677.08
Principal = $1000 * 0.09722 = 97.23
Total $774.31
Excel Finance Class 21: Future Value Lump Sum Calculations, Simple & Compound Interest
