how to get money of bond grossprice?

Answer 1

The gross price of a bond is equal to the price times the accrued interest times the face value of a bond.

The price and accrued interest are always stated as a percent of face value (percent of Par). So if you have a price of 95.50 -- then the price is 95.5% of the face value. If the face value of the bond is $100,000 -- then the price of the bond is $95,500 -- not counting the accrued interest.

The value of a bond is broken into two parts -- the price and the accrued interest. The reason for this is taxes. Interest on a bond is taxable at the ordinary income tax rate while capital gains are taxes at the capital gains rate. To calculate the accrued interest, you first have to find the value of the next coupon payment (interest payment). In the US, most bonds pay twice per year. So, if the coupn rate on the $100,000 bond is 6%, then you will get 3% every six months -- or a $3,000 coupon payment . Since we usually calculate Accrued Interest (AI) as a percent, we will work with half the 6% rate -- or 3%.

Now that we know the coupon payment, we need to find out how much has accrued. This is a simple ratio of the number of days that have passed in the current 6-month period divided by the number of days in the period. This is where things get tricky. For corporate bonds, it is assumed that all months have 30 days and there are 360 days in a year. For US Treasury bonds, the actual number of days is used.

Let's look at an example. Suppose that you have a 6% corporate bond and a 6% treasury bond that both pay coupons on 12/15 and 6/15. Suppose that trade settlement is April 15.

For the corporate bond, you are 120 days into a 180 day period. This is two thirds. That means that 2/3 of the coupon payment (or 2%) has to be added to the price of 95.5 -- so the total price (including AI) is 97.5% This means that the bond will cost $975,000.

The Treasury bond uses the same idea, but will use the actual daycount. In non-leap years, the number of days between 12/15 and 4/15 is 121. The number of days in the six month coupon period is 182. This means that 121/182 of the 3% is accrued. This is 1.9945. That means that the Treasury will have a price of 95.5+1.9945 = 97.49451. So, the cost of the bond is $97,494.51.

In leap years, the AI would be 122/183 which is 2/3 -- so the total price would be 97.5


In this example, I am using the same price for the corporate and the T-Bond. The T-Bond would actually be worth more since it is safer and taxed differently.