Valuation of compounded deferred tax assets for the banking sector, using the binomial CRR algorithm

Figures & data

Figure 1. Binomial projection of profits.

Figure 2. Spreading the carry-over of losses through the following years.

Table 1. Initial conditions

Tax	20%
Discount Rate	5%
Profit projection for 1st year	50.000€
sigma	0,8

Table 2. Losses, Projected Profits and Valuation of DTA, example 1 (in €), method 1A

Years Left to discount	0	1	2	3	4	5
Losses		40000	120000	50000	100000	30000
Mean Projected Profits		50000	66871,75	89436,61	119615,7	159978,2
Limited Losses		40000	76871,75	50000	100000	30000
Used Amount		50000	66871,75	89436,61	90563,39	0
Wrongfully used DTA	68000,00
Realistic DTA	52007,83

Table 3. Losses, projected profits and valuation of DTA, example 2 (in €), method 1A

Years Left to discount	0	1	2	3	4	5
Losses		40000	120000	50000	100000	30000
Mean Projected Profits		50000	51003,34	52026,81	53070,82	54135,78
Limited Losses		40000	61003,34	50000	55097,63	30000
Used Amount		50000	51003,34	52026,81	53070,82	30000
Wrongfully used DTA	68000,00
Realistic DTA	41198,11

Table 4. Losses, projected profits and valuation of DTA, example 3 (in €), method 1A

Years Left to discount	0	1	2	3	4	5
Losses		0	120000	0	100000	300000
Mean Projected Profits		50000	66871,75	89436,61	119615,7	159978,2
Limited Losses		0	116871,7	0	100000	269030,4
Used Amount		50000	66871,75	89436,61	119615,7	159978,2
Wrongfully used DTA	104000
Realistic DTA	81857,51

Figure 3. Binomial projection of profits.

Table 5. Adjustment of negative profits for method 1B

	2º year	3º year	4º year	5º year
# of elements	2	4	8	16
Smallest element	P-d	P-2d	P-3d	P-4d
Value of smallest element	22466,45	−5067,1	−32600,7	−60134,2
2º Smallest element	P + u	P-d + u	P-2d+u	P-3d+u
Value of 2º smallest element	111277	83743,49	56209,94	28676,39
Mean Projected Profits w/o adjustment	66871,75	83743,49	100615,2	117487
Mean Projected Profits with adjustment	66871,75	85010,27	104690,3	121245,4

Table 6. Example 1 using method 1B

Years Left to discount	0	1	2	3	4	5
Losses		40000	120000	50000	100000	30000
Mean Projected Profits		50000	66871,75	85010,27	104690,3	121245,4
Limited Losses		40000	76871,75	50000	100000	30000
Used Amount		50000	66871,75	85010,27	94989,73	0
Wrongfully used DTA	68000,00
Realistic DTA	51971,41

Table 7. Example 2 using method 1B

Years Left to discount	0	1	2	3	4	5
Losses		0	120000	0	100000	300000
Mean Projected Profits		50000	66871,75	85010,27	104690.3	121245,4
Limited Losses		0	116871,75	0,00	100000	210946
Used Amount		50000	66871,75	85010,27	104690.3	121245,4
Wrongfully used DTA	104000,00
Realistic DTA	72567,34

Table 8. Losses, Arbitrary Projected Profits and Valuation of DTA, example 4 (in €)

Years Left to discount	0	1	2	3	4	5
Losses		0	120000	0	100000	300000
Mean Projected Profits		20000	0	110000	0	0
Limited Losses		0	20000	0	100000	10000
Used Amount		20000	0	110000	0	0
Wrongfully used DTA	104000,00
Realistic DTA	22813,95

Figure 4. Binomial tree for DTA calculation.

Figure 5. Components of each state in the binomial tree.

Table 9. Initial conditions used to illustrate the binomial method

Tax	20%
Discount Rate	5%
Profit projection for 1st year	100.000€
sigma	0,8
Previous Losses Vector	(130.000; 70.000; 80.000)€

Figure 6. Example with state evolution in the binomial tree.

Table 10. Parallelism of same conditions using method 1A (in €)

Years Left to discount	0	1	2	3
Losses		130000	70000	80000
Mean Projected Profits		100000,00	133743,49	178873,22
Limited Losses		100000	70000	80000
Used Amount		100000,00	133743,49	16256,51
Wrongfully used DTA	56000,00
Realistic DTA	46118,07

Figure 7. Example allowing for negative profits, Method 2B.

Table 11. Parallelism of same conditions using method 1B (in €)

Years Left to discount	0	1	2	3
Losses		130000	70000	80000
Mean Projected Profits		100000	133743	136277
Limited Losses		100000	70000	80000
Used Amount		100000	133743	16257
Wrongfully used DTA	56000,00
Realistic DTA	46118,07