# 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?

## 1 Answer

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...