I was reading up on Bonds here on About.com Why Do Bond Prices and Yields Move in Opposite Directions?

In the second example it offers:

In this example, the opposite scenario occurs. The same company issues Bond A with a coupon of 4%, but this time yields fall. One year later, the company can issue new debt at 3.5%. What happens to the first issue? In this case, the price of Bond A needs to adjust upward as its yield falls in line with the newer issue. Again, Bond A came to the market at $1000 with a coupon of 4%, and its initial yield to maturity is 4%. The following year, the yield on Bond A has moved to 3.5% to match the move in prevailing rates (as reflected in the 3.5% yield on Bond B). Since the coupon stays the same, the price must rise to $1142.75. Due to this increase in price, the yield declines (because the $40 coupon divided by $1142.75 equals 3.5%).

After reading the part I bolded, I tried to compute it on my own:

40 / n = 3.5
40 / .035 = n
n = 1142.8571426

However, they come up with 1142.75. From what I gather its ultimately a fluctuation based on market anyways. But I'd still like to know. If I reverse and do 40 / 1142.85 I get 0.03500021875 while 40 / 1142.75 yields 0.03500328155. So how does one accurately round or compute this? Am I just missing something in my math?

  • Significant digits may be an idea to consider here as the 4% and 3.5% are only 1 or 2 significant digits. Both the values you give would round to 3.500% at 3 or 4 significant digits you do realize right? – JB King Jul 14 '14 at 6:00
  • @JBKing yes I saw that which is why I'm asking the correct way to round, which could be with significant digits. – Ender Jul 14 '14 at 13:46

With the formula you are using you assume that the issued bond (bond A) is a perpetual. Given the provided information, you can't really do more than this, it's only an approximation.

The difference could be explained by the repayment of the principal (which is not the case with a perpetual). I guess the author has calculated the bond value with principal repayment.

You can get more insight in the calculation from the excel provided at this website: http://breakingdownfinance.com/finance-topics/bond-valuation/fixed-rate-bond-valuation/

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