Calculating an FRN Invoice Total from Clean Price and Accrued Interest
Summary
The document explains how to reconcile a floating-rate note’s invoice total by separating principal value from accrued interest. Rather than discounting projected coupons and discount margin through a full cash-flow formula, the response starts with the displayed clean price and face value to obtain the principal amount. It then estimates accrued interest using the assumed index rate plus quoted margin, the stated day-count convention, and the actual number of accrued days.
The example uses Actual/360 accrual and shows that adding the calculated accrual to principal matches the invoice total displayed by Bloomberg. It also interprets other coupon accrual figures on the screen using coupon amount and period length. The response notes that the assumed index rate can be changed and suggests that a curve projection may be available instead. This is a practical reconciliation for the stated screen setup, not a general derivation of FRN valuation; different settings or rate assumptions can change the result.
Key ideas
- An FRN invoice total can be reconciled as principal plus accrued interest.
- Principal is obtained by applying the clean price to face value.
- Accrued interest depends on the assumed coupon rate, day-count convention, and elapsed accrual days.
- A projected index curve may replace a flat assumed index rate, changing accrued or projected cash flows.
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Full text
# How does Bloomberg arrive at FRN Total Price?
# How does Bloomberg arrive at FRN Total Price?
I already asked to help desk about pricing FRN, however the answer was not helpful.
I want to know how to get the value in the Invoice sector 'Total (USD)'
Using help desk's advice, I used this formula to get total price
formula : $((∑^{n-1}_{i=1}\frac{Coupon}{(1+(AR + DM)/100/freq)^i}) + \frac{FaceValue}{(1+(AR + DM)/100/freq)^{n-1}} + First Cpn)/(1+\frac{ITP+DM}{freq*100}*YF(StubPeriod))$
- AR = Assumed Rate(%)
- DM = Discount Margin(%)
- ITP = Index to Pay(%)
- YF = Year Frac
- freq = coupon payment frequency
- n = number of coupon payment
And Coupon Payment is below here
I tried many things; such as change daycount convention, method to calculate frequency, else.. , but I cannot not make accurate total price like bloomberg.
How to get accurate total price?
## Answer by Dimitri Vulis (score 2, accepted)
https://quant.stackexchange.com/a/64309
I may be missing something, but I think you're overcomplicating it. You don't need discount margin and all that jazz.
The clean price (entered in upper left corner) is 100.311% The face value (entered in the lower right corner) is 1,000 M. So "Principal" (next row below face value) is 1,003,110.00.
Now for the accrued. You see on the left that the quoted margin is 26 basis points, and the index rate is assumed to be 1 bp (you can change this). So the assumed coupon rate is 27 bps.
You know that the daycount convention is Actual / 360. And it says in the lower right corner that there are 71 days of accrual (actual days for your settlement date of 5/25). So, 0.000027 * 100,000,000.00 * 71 / 360 = 532.50 - exactly the number you see on the screen.
Adding up the 1,003,110.00 principal and the 532.50 accrued, you get the total of 1,003,642.50.
In the CSHF screen grab, 682.50 = 2700 * 91 / 360 corresponds to a 91-days coupon period, and 675 = 2700 * 90 / 360 to the 90-day periods.
If you prefer, you may be able to tell Bloomberg not to assume 1 bp SOFR to maturity, but to project it from some curve.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.