How to calculate the value of a bond that is priced to yield X%
I am currently practicing for a beginners exam in finance. One of the previous exams had the following question:
You own a 2 year, £1000, 7% bond, with semi-annual coupons.
If the bond is priced to yield 6%, calculate its value.
I assumed that "is priced to yield 6%" means that I can assume an interest rate of 6%, but I am unsure. I asked the lecturer and he gave me the hint
"This is the same as saying 'if interest rates are currently 6%,
what is a bond yielding 7% bond worth?"
When I assume an interest rate of 6 percent, my answer is 1076.
2*(35/1,03) + 2*(35/1,03^2) + 1000/1,03^2 = 1076.54
Is this correct?
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The idea is correct; the details are a little off. You need to apply it to the actual cash flow the bond would create.
The best advice I can give you is to draw a time-line diagram.
Then you would see that you receive £35 in 6 months, £35 in 12 months, £35 in 18 months, and £1035 in 24 months.
Use the method you've presented in your question and the interest rate you've calculated, 3% per 6 months, to discount each payment the specified amount, and you're done.
PS: If there were more coupons, say a 20 year quarterly bond, it would speed things up to use the Present Value of an Annuity formula to discount all the coupons in one step...
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