# 30360 Daycount Count Convention to find NPV for Bonds

Using a 30/360 day count convention, how can you value the NPV of these cash flows and the discount factor? I know how to discount cash flows but how does it differ using a 30/360 approach? What is the approach that I should be using?

Date       Payments     Discount Factor    Discounted Value
12/31/2012  0               100.00%
6/30/2013   75,200
12/31/2013  50,600
6/30/2014   86,700
12/31/2014  77,000
6/30/2015   74,400
12/31/2015  25,200
6/30/2016   70,700
12/31/2016  81,800

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You are missing the rates in your question you need to derive your DFs. The only difference between day count convention is how you adjust your rate to convert to the actual rate applicable between the date of the cash flow and the date to which you pv the future cf.

Generally the following function applies: 1/((1+r/360)^360*T), where T is the time in years between the pv date and the cf date, given each month has 30 days and the year 360 days.

Example: r(t0, t1) = 5%, dcConvention = 30/360, t0 = 1 Jan 2013, t1 = 15 Mar 2013

T = 74 days / 360 days = 0.20555555

DF(t1) approx = 0.989775564

Edit This above calculation implies daily compounding. If rates are only annually compounded then the following function applies: 1/(1+r)^T which works out to be in this example:

1/(1+0.05)^0.2055555 = 0.990021

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Hi Matt, I am confused about this formula. DF=1/((1+r/360)^360*T). Why are we dividing r by 360. Shouldn't it be r/2 (if the bond is semi annual). How about in the scenario where my settlement date is t0=1/1/2013 and one of my coupon dates is t1=12/31/2013. – jessica Jul 18 '13 at 22:37
@jessica, then you get 360 days just as 30/360 suggests. Re coupon payment frequencies you made no mention of that in your question and nor does it matter for your actual problem. You look to discount a future cash flow, whether it be a semi-annually paid cash flow or annually paid cash flow. The formula to discount any cash flow, using 30/360 convention, is as stated above in my answer. – Matt Wolf Jul 19 '13 at 4:26
So the 360 portion of 30/360 is to assume daily compounding? Well, then where does the the "30" part play a role in the equation? – jessica Jul 19 '13 at 5:49
Please see my edit. The day count convention dictates the 'T', the time fraction applied in the discount factor function. It makes the assumption here that months are of 30 day length and years of 360 days. – Matt Wolf Jul 19 '13 at 7:26
@jessica, does that answer your question? – Matt Wolf Jul 19 '13 at 9:30

In the data provided, the Dec dates are all 31st. In the 30/360 conventions (Wikipedia has details of the different 30/360 versions), the factor is calculated from the difference in years, months and days separately; years count as 12 months, and months count as 30 days. Generally 31st gets lowered to 30 days.

In this manner, the distance between the first two dates (2012-12-31 and 2013-06-30) becomes 1 year, -6 months and 0 days (in the convention), and thus the factor for the dates (see Wikipedia explanation for details) comes out as exactly 0.5.

The 30/360 factors for the periods specified by those dates, then, are 0.5, 0.5, 0.5 etc.

Usually bonds have a fixed coupon rate, but those interest payments in the question and the neat fractions above do not square with each other, so something else is going on. In order to discount, you would need a rate to discount at. I thought I might retrieve it from the interest and a guess at the principal, but the interest payments vary too much to be a vanilla bond.

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