# DCF Zero Coupon Bond

Using a 30/360 day count what is the exact formula to discount this single zero coupon bond?

DayCount:   30/360
Start Date  6/25/2013
End Date    1/1/2020
Discount Rate   3.50%

Present Value
Ending Value    50,000,000
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Like we ask all other homework questions: What have you tried so far? – chrisaycock Jul 19 '13 at 1:35
Well the formula I am using is =50,000/(1+.035)^(something). The problem is I don't know what power to raise it too. Zero coupon bonds have n=1 frequency. Do I raise it to the ^(Diff.Date(6/25/2013,1/1/2020)/360) ? – jessica Jul 19 '13 at 1:40

## 1 Answer

• DF(t1) = 1/((1+r/360)^360*T)
• Using 30/360 Daycount convention, you get 2346 days to discount over.
• Your discount factor should work out to about 0.7961 and hence your PV of the cash flow should be about 39,803,337.23.
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Matt, I just don't understand where you are getting the r/360 and the 360*T. Shouldn't we be dividing the discount rate "r" by the frequency of the cashflows, which in this case is 1? Not to mention, 360*T=360*(#of days/360)=# of days. Why are you raising to the number of days? Not the number of years?s – jessica Jul 19 '13 at 5:44
It has to do with what compounding frequency you apply. If you compound annually then the 360 term would drop out. Please see my edited answer here: quant.stackexchange.com/questions/8497/… – Matt Wolf Jul 19 '13 at 7:31
@jessica, does that answer your question? – Matt Wolf Jul 19 '13 at 9:33