Calculating Simple-Interest Cost for a Delayed Cash Flow

Summary

The document explains how to estimate the opportunity cost of receiving a cash flow late when the stated annual rate uses an actual/actual day-count basis. For a delay shorter than the annual compounding period, it applies simple interest: multiply the annual rate by the fraction of a year represented by the delay, then apply that fraction to the cash amount. This yields the stated cost for a $1 million payment delayed 15 days at 6.5%. The method also explains why compounding a daily rate was not the convention used for this calculation.

The answer frames this as a market convention rather than a uniquely dictated mathematical choice. It contrasts the 15-day calculation with a separate book example that quotes a per-day cost, but does not resolve whether that example should be multiplied by 14 or 15. The guidance is limited to the stated convention and day-count setup; other instruments or conventions may handle accrual and timing differently.

Key ideas

• For a short delay, the example uses simple interest rather than compounding.
• The year fraction is calculated as elapsed days divided by 365 under the stated basis.
• The opportunity cost equals the principal multiplied by the annual rate and the delay year fraction.
• Short-period interest conventions are standard practices and can depend on the instrument.

Tags

# Calculating the Cost of Delay


# Calculating the Cost of Delay












I am working on a problem in Davidson and Herskovitz workbook titled the Mortgage-Backed Securities Workbook. The questions asks to find the total opportunity cost to the investor of having a $1 million cashflow delayed for 15 days and the current risk free interest rate is 6.5% actual/actual. I first converted 6.5% into a daily rate and then tried to compound the interest on 1 million dollars, but it was deemed incorrect. The correct answer is 2671.23.

Their is also an example, but this time the current risk free rate is 6.25% and the book tells us each delay costs 171.23. The investor is still supposed to receive 1 million. I am assuming one could take the 171 multiply it by 15 to get the total, but why not 14 to account for timing?

## Answer by nbbo2 (score 1, accepted)

https://quant.stackexchange.com/a/33462

These calculations are a matter of convention and standard practice (which are somewhat arbitrary, and not necessarily the way I would have defined it).

A compounding period is defined, which is by default 1 year (except for US treasuries where it is 6 months). For periods shorter than this, compounding is not used, but rather "simple interest" is used, which amounts to a linear interpolation. So for "15 days and the current risk free interest rate is 6.5% actual/actual" we would do (15/365)*0.065 = 0.0267123 . On 1 million it is 2671.23

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.