# DCF of Arbitrary Dates Cash Flows

I am having a problem understanding discounted cash flows. I appreciate your patience and help. Lets say I have a bond that I want to price.

Par: \$1000
Coupon Rate: %5.0
YTM: %5.0
Frequency: Semi-Annual – 2 (Paid on: 6/30/20XX,12/31/20XX)
Settlement Date: 8/15/2013
Maturity Date: 12/31/2014

12/31/2013  6/30/2014   12/31/2014  6/30/2014   12/31/2014
25        25        25          25           1025


This is the formula I know used to discount cash flows. CF/(1+r/n)^a, where, as I understand it, a=n*t. My question is when valuing bonds I have seen people using the typical a=1,2,3,4,…,n*t I have also seen formula’s where a=.5,1,1.5,2,2.5 when discounting semi-annual cash flows. I have also seen people using # of days a=280 for example when the cash flow is some arbitrary date.

For such a simple formula, this unbelievably complicated. Can someone please just explain to me how to find “a” . Is there a comprehensive formula I could use that can discount any cash flow no matter what the date is? Eg. Today is 03/14/2009 and the CF is due on 07/2/2010 for the same info above what would a be?

• Really Sorry Matt. I am still new to the forum. I promise to go back and check off one's where my question was answered. Appreciate your patience and help. – jessica Aug 15 '13 at 16:23
• The conversion between the dates and the year fraction is determined by the day counting convention you use. The following document explains this in more details: marchioro.webs.com/White-papers/… – Vincent Zoonekynd Aug 16 '13 at 9:19