Amortization According to LAC and SAC.
The distribution of profits and losses over time with respect to financial assets or payables that carry interest is known as amortization. The difference between the acquisition value and the payback amount is amortized throughout the term, either exponentially or linearly. The linear method is referred to as LAC (Linear Amortized Cost), whereas the exponential method is referred to as SAC (Scientific Amortized Cost).
LAC method.
Planned profit is distributed equally over the term. This calculation method assumes that the value of the positions is based on a constant annual amortization rate.
Where: BPnew = new book rate
BPold = old book rate
da = Duration in days between the last and the current amortization
Db = Duration in days between the last amortization and the final maturity date
SAC method.
When using SAC method, gains and losses are dispersed exponentially. The effective interest rate, which is derived from the cash flow, is used to compute the interest on the position. Every time a position is changed (by inflow, outflow, or valuation, for example), an amortization is carried out; however, this process is limited to once per position date.
Amortization is always carried out incrementally. This means that the amortization procedure is always applied to the entire position.
The system determines the difference from the newly calculated and previous amortized acquisition values and uses this amount to generate a write-up or write-down. The system uses the position currency to determine the values mentioned above. The write-up or write-down amount is then translated at the book exchange rate into the valuation currency.
Interest-related settings of the SAC method.
• Do not include interest. See also: SAC Procedure Without Interest
• Include interest, with accrued interest adjustment. See also: SAC Including Interest and Accrued Interest Adjustment
• Cash flow method in accordance with IAS39 (Include interest, without accrued interest adjustment). See also: SAC Procedure Including Interest (Cash flow method in accordance with IAS39)
This setting is important for figuring out the net present value (of the amortization) and the effective interest rate.
The 'Do not include interest' setting causes the algorithm to overlook interest rate flows. The 'Cash flow method according to IAS' option allows you to account for all interest rate flows. As a result, after interest payments, the net present value abruptly increases (see the example for details). This doesn't happen if you select the "Include interest, accrued interest correction" setting.
SAC procedure. Interest factor.
The effective interest rate of cash flow is determined with numerical methods. Particularly, it is based on an approximation method, and therefore, a detailed calculation or formula is not available. However, it can be easily determined whether the effective interest rate for the key date is correct or not. To do this, it is proposed to determine the interest factors for the individual flows: Interest factor = (1 + effective interest rate/100) ^ (days/360)
As on the picture, the net present value of the cash flow for June 15, 2005, is zero and the used effective interest rate of 13.85491999%.
SAC method including Interest (Cash flow method in accordance with IAS39).
The system considers all interest rate flows when you select the "Cash flow method according to IAS" option.
For reference, the net present value following the interest payments will suddenly increase in compare with “Do not include interest” option.
The calculation starts with the last valuation key date, which is November 1, 2005.
In order to illustrate the distinctions between the two interest-involved amortization methods, an analysis is limited to the key date valuations for December 29, 2005, and January 03, 2006.
For the purposes of this method demonstration, an effective interest rate of 30.7673016% is set. In the same way, the interest factor for each cash flow is equal to (1 + effective interest rate/100) ^ (days/360).
A new amortization value of 1,167,686.72 is obtained by adding the net present values of the two interest flows and the repayment that occurred after December 29, 2005. A write-up of 1,167,686.72 and 1,118,296.66) is 49,390.06 that is created as an amortization flow within the key date valuation.
The key date valuation of December 29, 2005 is the starting point of the calculation.
The amount of the net present values of the flows after January 03, 2005 (interest flow and a repayment) results in an amortization value of 1,115,088.74. A write-down of 1,115,088.74 and 1,167,686.72 is 52,597.98 that is created as the amortization flow. The book value (or the amortization) decreases, and this leads to a write-down. The amortization curve is therefore no longer continuous, instead it jumps when interest flows occur. You can avoid these jumps and an easier way to do this is the cash flow method with accrued interest adjustment. This creates accrued interest flows for the interest flows on the key date of the amortization. Therefore, the write-down as above do not occur.
SAC method including Interest with accrued interest adjustment.
Only securities are supported by this method. Loans are amortized using the cash flow method in accordance with IAS; no accrued interest is taken into account during this process.
The calculation starts with the last valuation key date, which is November 1, 2005. 1,091,257.02 is the updated amortized acquisition cost on key date - December 29, 2005. The system creates interest rate flows and an accrued interest flow when using the method with accrued interest adjustment
These flows have an effective interest rate of 28.7343312%. And in a similar way, for the cash flow: Interest factor = (1 + effective interest rate/100) ^ (days/360). Also, the interest of the cash flow is discounted using the interest factor (amount in position currency/interest factor).
The amount of the net present values of the flows after December 29, 2005 (two interest rate flows and repayment) results in a value of 1,185,346.95. Accrued interest is calculated for the amortization key date of December 29, 2005 to correct the amortization amount. Therefore, the amortization amount/net present value is 1,185,346.95 - 55,688.89 = 1,129,658.06 with this method for December 29, 2005. This results in a write-up of 1,129,658.06 and 1,091,257.02 as 38,401.04 for December 29, 2005.
For the key date of the most recent position change, which in this case is December 29, 2005, an artificial position inflow is established, and this generates the condition-based cash flow that is related for amortization.
These flows have an effective interest rate of 28.7343312%. And in a similar way, for the cash flow: Interest factor = (1 + effective interest rate/100) ^ (days/360). Also, the interest of the cash flow is discounted using the interest factor (amount in position currency/interest factor).
The amount of the net present values of the flows after January 03, 2005 (one interest rate flows and one repayment) results a value of 1,132,599.61. Accrued interest is calculated for the amortization key date of January 03, 2005 to correct the amortization amount. Therefore, the amortization amount/net present value is 1,132,599.61 - 311.11 = 1,132,288.49 with this method for for January 03, 2005. This results in a write-up of 1,132,288.49 and 1,129,658.06 as 2,630.43 for January 03, 2005. So, no write-down is created (as in the case of the IAS method).
LAC and SAC: the advantages and disadvantages of different methods and settings.
LAC calculation.
• Advantages
- Constant sign of calculated values of amortized costs.
- Transparent calculation procedure.
• Disadvantage
- Absent of effective interest rate in calculation formula.
SAC calculation including Interest.
• Advantages
- Amortized acquisition costs are calculated using the effective interest method
• Disadvantage
- Causes sudden jumps of the net present value after interest payments.
- Variable sign of calculated values of amortized costs.
SAC calculation including Interest and Accrued Interest Adjustment.
• Advantages
- Amortized acquisition costs are calculated using the effective interest method, in accordance with IAS 39.
- No jumps of the net present value after interest payments.
• Disadvantage
- Variable sign of calculated values of amortized costs.
Find more Information on LAC and SAC amortization methods.
Explore:
SAP Note 864857- Documentation for the SAC amortization
SAP Note 1828517- SAC: constant effective interest rate for amortization
SAP Help:
Example: Effective Interest Method (Cash Flow Method)
Example: Premium/Discount for an Interest Rate Instrument
Example: Discount for a Fixed-Interest Rate Transaction with Rollover
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