Please don't laugh at the silliness of this, since I suspect I am asking brain surgeons to tell me what the shape of a brain is. I was looking at the value of a deep-discount FRN. I have assumed that the usual discounted margin calculation has a drawback as regards principal investment, irrespective of all the other ones regarding discounting the premium/discount to generate a spread. I considered a 5 year FRN with a price of 80, and a spread of LIBOR flat. Fundamentally, the DM calculation (I think) takes the 20% discount which will generate a redemption payment greater than the initial investment at maturity, and discounts over the term of the FRN. For simplicity I assume annual coupons and a five year swap rate of 5% (I don't think the details matter). The spread payments = 4.62%, so the DM calculation = LIBOR + 4.62% ; but surely this would assume a principal of 100%? In fact the FRN only costs 80%, even though the LIBOR coupon that is received is on 100%. Consequently, the 'true' return should be generated by assuming that the coupon on 100% = 1.25 X LIBOR on 80%. Using the 5% swap rate as a (rough) proxy for the intermediate coupons, this means that the investor is receiving (5 × 1.25)% coupons on the investment = c.6.25% = LIBOR +125 (on 80). Adding this to the initial spread of 462 = LIBOR + 587. The simple DM appears to be a really bad way of estimating value on this. This issue would exist irrespective of the size of discount or premium, but I can't find it mentioned anywhere? This suggests that I am either making a really basic mistake, or that it is so obvious that no one can be bothered to talk about it. Can anyone tell me which it is?

It would appear I was making a really basic mistake - I have been calculating discounted margin incorrectly for about 20 years. I apologise for wasting your time.