Choosing Discount Exponents for Arbitrarily Dated Bond Cash Flows

Summary

The document asks how to choose the exponent in a discounted-cash-flow formula when bond payments do not fall on a simple sequence of whole coupon periods. It gives a semiannual coupon bond example with a settlement date between payment dates, then contrasts counting successive coupon periods with using fractional periods or elapsed days. It also asks how to handle a cash flow due on a date that is not aligned with the regular schedule.

The material identifies a real bond-pricing issue: the discount exponent depends on how time is measured between settlement and payment. However, it contains no answer or worked calculation, and it does not specify a day-count convention, yield-compounding convention, or treatment of accrued interest. Those choices are necessary to turn the question into a pricing method, so the example is useful as a statement of the problem but does not provide a complete valuation procedure.

Key ideas

• The discount exponent represents the time from settlement to a cash-flow date under a chosen convention.
• Regular coupon periods may produce whole or fractional period exponents depending on the settlement date.
• Arbitrary payment dates raise questions about measuring elapsed time, including through day-count conventions.
• A complete bond valuation also needs consistent yield-compounding and accrued-interest conventions.
• The document poses the problem but does not supply a solution or numerical valuation.

Tags

# DCF of Arbitrary Dates Cash Flows


# 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?

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