Valuation of non-regulated
projects
N.V. Nederlandse Gasunie
Appendices
Groningen, April 2007 Rijksuniversiteit GroningenFaculty of Management and Organization Supervisor RuG: Dr. J.H. von Eije
Gasunie: Dr.ir. B.M. Visser Author : Remôn te Morsche
Valuation of non-regulated Projects
Valuation of non-regulated projects
N.V. Nederlandse Gasunie
Master thesis Technology Management (TBW program)
Discrete Technology
Cluster Financial Management
Rijksuniversiteit Groningen
First supervisor RuG: Dr. J.H. von Eije
Second supervisor RuG: Mr. drs. H.A. Ritsema
Supervisor Gasunie: Dr. ir. B.M. Visser
Author: R.H.A. te Morsche
Groningen, April 2007
Table of contents
Table of contents ... 1
Appendix I Risk free rate ... 2
Appendix II Beta ... 3
Appendix III Deduction of r0 from rs... 8
Appendix IV Interpolated default percentages for year 1 to 10. ... 9
Appendix V Calculation of the WACC’s for four current calculation methods of Gasunie. ... 10
Appendix VI Default percentages in comparison with spreads. ... 16
Appendix I Risk free rate
Appendix I Risk free rate
Table AI.1: Calculation of the risk free rate.
(Source: Bloomberg, 15 November 2006)
DBR 4 07/04/16 Govt 17-07-2006 3.99 19-09-2006 3.78 Date Yld Ytm Mid 18-07-2006 4.01 20-09-2006 3.77 16-05-2006 4.01 19-07-2006 3.98 21-09-2006 3.75 17-05-2006 4.07 20-07-2006 3.98 22-09-2006 3.69 18-05-2006 4.03 21-07-2006 3.95 25-09-2006 3.66 19-05-2006 3.98 24-07-2006 3.95 26-09-2006 3.65 22-05-2006 3.91 25-07-2006 3.96 27-09-2006 3.67 23-05-2006 3.93 26-07-2006 3.98 28-09-2006 3.69 24-05-2006 3.89 27-07-2006 3.94 29-09-2006 3.71 25-05-2006 3.87 28-07-2006 3.92 02-10-2006 3.69 26-05-2006 3.88 31-07-2006 3.92 03-10-2006 3.73 29-05-2006 3.89 01-08-2006 3.93 04-10-2006 3.69 30-05-2006 3.93 02-08-2006 3.93 05-10-2006 3.71 31-05-2006 3.98 03-08-2006 3.97 06-10-2006 3.75 01-06-2006 3.99 04-08-2006 3.90 09-10-2006 3.76 02-06-2006 3.92 07-08-2006 3.90 10-10-2006 3.81 05-06-2006 3.96 08-08-2006 3.90 11-10-2006 3.80 06-06-2006 3.98 09-08-2006 3.93 12-10-2006 3.80 07-06-2006 4.00 10-08-2006 3.93 13-10-2006 3.83 08-06-2006 3.93 11-08-2006 3.98 16-10-2006 3.83 09-06-2006 3.93 14-08-2006 4.00 17-10-2006 3.80 12-06-2006 3.91 15-08-2006 3.97 18-10-2006 3.81 13-06-2006 3.86 16-08-2006 3.93 19-10-2006 3.84 14-06-2006 3.89 17-08-2006 3.92 20-10-2006 3.84 15-06-2006 3.94 18-08-2006 3.90 23-10-2006 3.87 16-06-2006 3.93 21-08-2006 3.86 24-10-2006 3.87 19-06-2006 3.97 22-08-2006 3.81 25-10-2006 3.88 20-06-2006 3.99 23-08-2006 3.82 26-10-2006 3.85 21-06-2006 4.01 24-08-2006 3.81 27-10-2006 3.81 22-06-2006 4.05 25-08-2006 3.79 30-10-2006 3.79 23-06-2006 4.07 28-08-2006 3.79 31-10-2006 3.74 26-06-2006 4.09 29-08-2006 3.82 01-11-2006 3.70 27-06-2006 4.09 30-08-2006 3.80 02-11-2006 3.74 28-06-2006 4.09 31-08-2006 3.76 03-11-2006 3.77 29-06-2006 4.06 01-09-2006 3.74 06-11-2006 3.79 30-06-2006 4.06 04-09-2006 3.74 07-11-2006 3.74 03-07-2006 4.09 05-09-2006 3.78 08-11-2006 3.75 04-07-2006 4.07 06-09-2006 3.83 09-11-2006 3.74 05-07-2006 4.13 07-09-2006 3.81 10-11-2006 3.71 06-07-2006 4.11 08-09-2006 3.78 13-11-2006 3.74 07-07-2006 4.06 11-09-2006 3.80 14-11-2006 3.71 10-07-2006 4.08 12-09-2006 3.84 15-11-2006 3.70 11-07-2006 4.05 13-09-2006 3.79 12-07-2006 4.08 14-09-2006 3.79 Average 3.88 13-07-2006 4.04 15-09-2006 3.77 14-07-2006 3.98 18-09-2006 3.83
n
yield
Average
n 1 t∑
==
tAppendix II Beta
Table AII.1: Calculation of the Beta.
(Source: Bloomberg, 16 October 2006)
Company Raw Beta Total debt Equity D/E tax rate Unlevered Beta (Raw) Gas Transmission Fluxys 0.43 14.34 85.66 0.17 34.46 0.39 Average 0.39 Gas BG Group PLC 1.52 6.14 93.85 0.07 40.89 1.46 Gas de France SA 0.92 13.47 86.62 0.16 30.42 0.83 Gas Natural SDG SA 1.12 23.81 76.19 0.31 22.93 0.90 Average 1.07 some Gas OMV AG 1.81 14.91 85.09 0.18 24.90 1.60 RWE AG 0.97 42.13 57.86 0.73 32.19 0.65 EVN AG 0.71 29.51 70.48 0.42 13.47 0.52 Electrabel SA 0.50 15.70 84.30 0.19 9.51 0.43
Italgas SpA not av. 19.80 80.20 0.25 43.63
Statoil ASA 1.25 7.99 92.01 0.09 60.00 1.21 E.on AG 0.97 22.03 77.79 0.28 24.25 0.80 Endesa SA 1.23 40.99 59.01 0.69 14.30 0.77 RWE AG 0.97 42.13 57.86 0.73 32.19 0.65 Suez SA 1.17 33.05 66.96 0.49 30.42 0.87 Average 0.83 Airport BAA 0.32 41.06 58.94 0.70 29.72 0.21 Average 0.21 Infrastructure Abertis Infreastructuras SA 1.07 25.69 74.31 0.35 30.27 0.86 Autostrade SpA not av. 18.11 81.89 0.22 41.68
Average 0.86 Water Kelda Group PLC 0.50 40.24 59.76 0.67 27.31 0.34 Pennon Group PLC 0.94 48.97 51.03 0.96 30.13 0.56 United Utilities PLC 0.52 48.57 51.43 0.94 27.38 0.31 Average 0.40
Appendix II Beta
Electricity
Electricite de France 0.95 31.08 68.92 0.45 17.03 0.69
National Grid PLC 0.31 45.81 54.19 0.85 31.59 0.20
Red Electrica de Espana 0.65 42.85 57.15 0.75 33.81 0.43
Scottish & Southern Energy PLC 0.66 18.53 81.47 0.23 30.21 0.57
Terna Spa 0.59 35.61 64.39 0.55 39.52 0.44
Average 0.47
US Pipeline
Duke Energy Corp 0.90 36.59 63.41 0.58 32.23 0.65
Dynegy Inc 1.27 55.98 44.02 1.27 32.74 0.68
El Paso Corp 1.28 59.17 38.09 1.55 60.00 0.79
Equitable Resources Inc 0.67 17.29 82.71 0.21 35.00 0.59
NiSource Inc 0.58 50.29 49.71 1.01 31.95 0.34
Oneok Inc 1.02 50.07 49.92 1.00 32.08 0.61
PG&E Corp 0.67 42.59 57.41 0.74 37.00 0.46
Questar Corp 1.31 13.02 86.98 0.15 36.70 1.20
Western Gas Resources Inc 1.25 11.14 88.86 0.13 35.03 1.16
Williams Cos Inc 1.55 34.92 65.08 0.54 43.29 1.19
Average 0.77
Category Weight Unlevered category Beta Product
Gas Transmission 5 0.39 1.94 Gas 3 1.07 3.20 some Gas 2 0.83 1.67 Airport 2 0.21 0.43 Infrastructure 2 0.86 1.72 Water 2 0.40 0.80 Electricity 2 0.47 0.93 US Pipeline 1 0.77 0.77 Total 19 11.46
Weighted average unlevered 0.60 category Beta
Levered beta Gasunie 0.84
Total Debt = Short term Debt + Long term Debt D/E = Total Debt / Total Equity
Tc is the corporate tax rate (25.5 % for Gasunie)
Unlevered Beta = y Debt/Equit * ) T -(1 (1 Beta Raw c + Industry D/E = 35/65
Levered Beta Gasunie = Weighted average unlevered category Beta * [1+ (1-Tc)*
Equity Debt
Appendix II b
In the footnote on page 24 was already stated that formula (3.11) can only be used with a fixed debt level. Formula (3.11) is the following one:
)
Equity
Debt
*
)
T
-(1
(1
*
+
c=
asset equityβ
β
In the previous part of this appendix the assumption was made that this formula could be used. However when a firm has a target debt level formula (3.10) should be used which is the following formula:
)
Equity
Debt
(1
*
+
=
asset equityβ
β
Now four options will be investigated to find a levered beta for Gasunie:
• comparable companies have a fixed debt level and Gasunie has a fixed debt level; • comparable companies have a target debt level and Gasunie has a fixed debt level; • comparable companies have a fixed debt level and Gasunie has a target debt level; • comparable companies have a target debt level and Gasunie has a target debt level.
Comparable companies have a fixed debt level and Gasunie has a fixed debt level
This option is already investigated in the first part of this appendix and leads to a levered beta for Gasunie of 0.84.
Comparable companies have a target debt level and Gasunie has a fixed debt level
To calculate the levered beta for Gasunie this way, first the comparable companies have to be unlevered again, but now with formula (3.10) instead of formula (3.11). After this the weighted average unlevered category beta is levered for Gasunie with formula (3.11). These calculations are shown in table AII.2:
Table AII.2: Calculation of the beta with target debt level for comparable companies.
Company Unlevered Beta Gas
BG Group PLC 1.43
Gas de France SA 0.80
Gas Transmission Gas Natural SDG SA 0.85
Fluxys 0.37 Average 1.03
Appendix II Beta
some Gas Electricity
OMV AG 1.54 Electricite de France 0.65
RWE AG 0.56 National Grid PLC 0.17
EVN AG 0.50 Red Electrica de Espana 0.37
Electrabel SA 0.42 Scottish & Southern Energy PLC 0.54
Italgas SpA Terna Spa 0.38
Statoil ASA 1.15 Average 0.42
E.on AG 0.76
Endesa SA 0.73
RWE AG 0.56 US Pipeline
Suez SA 0.78 Duke Energy Corp 0.57
Average 0.78 Dynegy Inc 0.56
El Paso Corp 0.50
Airport Equitable Resources Inc 0.55
BAA 0.19 NiSource Inc 0.29
Average 0.19 Oneok Inc 0.51
PG&E Corp 0.38
Infrastructure Questar Corp 1.14
Abertis Infreastructuras SA 0.80 Western Gas Resources Inc 1.11
Autostrade SpA Williams Cos Inc 1.01
Average 0.80 Average 0.66 Water Kelda Group PLC 0.30 Pennon Group PLC 0.48 United Utilities PLC 0.27 Average 0.35
Category Weights Unlevered category Beta Product
Gas Transmission 5 0.37 1.84 Gas 3 1.03 3.08 some Gas 2 0.78 1.56 Airport 2 0.19 0.38 Infrastructure 2 0.80 1.59 Water 2 0.35 0.70 Electricity 2 0.42 0.84 US Pipeline 1 0.66 0.66 Total 19 10.65
Weighted average unlevered 0.56
category Beta
Levered beta Gasunie 0.79
Comparable companies have a fixed debt level and Gasunie has a target debt level
For this calculation the weighted unlevered category beta of the first part of this appendix of 0.60 can be used. Now the levered beta for Gasunie can be calculated with formula (3.10). This leads to a levered beta for Gasunie of 0.93.
Comparable companies have a target debt level and Gasunie has a target debt level
To calculate the levered beta for Gasunie this way the weighted average unlevered category beta of 0.56 is used. Next this number is levered with formula (3.10). This leads to a levered beta for Gasunie of 0.86.
To summarize the following numbers have been found:
Table AII.3: The levered beta of Gasunie for different debt structures.
Levered beta Gasunie
Comparable companies have a fixed debt level and Gasunie has a fixed debt level
0.84Comparable companies have a target debt level and Gasunie has a fixed debt level
0.79Comparable companies have a fixed debt level and Gasunie has a target debt level
0.93Comparable companies have a target debt level and Gasunie has a target debt level
0.86Average 0.86
Conclusion
The average levered beta for Gasunie for the four different methods is 0.86 which is very near the beta of 0.84 that was found when only formula (3.11) was used. The conclusion can be drawn that the levered beta of Gasunie is somewhere in the range from 0.79 – 0.93. If a future project is expected to have a high risk it is better to choose the higher beta of 0.93. If a future project is expected to have a lower risk profile the lower beta of 0.79 comes in sight.
Appendix III Deduction of r0 from rs
Appendix III Deduction of r0 from rs
Ross et al. (2005) give the following equation for the levered cost of equity:
)
r
(r
*
)
T
-(1
*
S
B
r
r
s=
0+
c 0- bIn this case we want to know r0 and not rs so some mathematics is needed. First substitute:
)
T
-(1
*
S
B
x
=
cThis leads to:
This finally can be rewritten to:
pr.
Debt
*
x)
(1
x
)
r
-(r
*
r
r
0 f 0 m f+
+
+
=
β
(
Substituting for x again you get:pr.
Debt
*
)
T
1
(
*
S
B
1
)
T
1
(
*
S
B
)
r
-(r
*
r
r
c c f m 0 f 0−
+
−
+
+
=
β
)
x
1
D
x
r
x)
(1
)
r
-(r
x
1
D
x
r
x
r
)
r
-(r
x
1
D
x
r
x
)
r
-(r
x
1
r
x
1
)
D
(r
x
)
r
-r
(
x)
(1
r
)
r
-(r
*
]
S
B
)
T
1
(
1
[
r
r
x
1
r
x
r
r
r
x
r
x)
(1
r
)
r
-(r
x
r
r
pr f f m 0 pr f f f m 0 pr f f m 0 f pr f f m 0 f f m c 0 f s : Substit. b s 0 b s 0 b 0 0 s+
+
+
+
=
+
+
+
+
=
+
+
+
+
+
=
+
+
+
+
+
=
−
+
+
=
+
+
=
+
=
+
+
=
β
β
β
β
β
Appendix IV Interpolated default percentages for year 1 to 10.
Table AIV.1: Interpolated default percentages for year 1 to 10.
Years after Issuance
1 2 3 4 5 6 7 8 9 10 Average AAA Marginal 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.00 0.00 Cumulative 0.00 0.00 0.00 0.00 0.03 0.03 0.03 0.03 0.03 0.03 0.00 Interpol. Def. % 0.00 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.03 0.03 AA Marginal 0.00 0.00 0.33 0.17 0.00 0.00 0.00 0.00 0.03 0.02 Cumulative 0.00 0.00 0.33 0.50 0.50 0.50 0.50 0.50 0.53 0.55 0.06 Interpol. Def. % 0.06 0.11 0.17 0.22 0.28 0.33 0.39 0.44 0.50 0.55 A Marginal 0.01 0.10 0.02 0.09 0.04 0.10 0.05 0.20 0.11 0.06 Cumulative 0.01 0.11 0.13 0.22 0.26 0.36 0.41 0.61 0.72 0.78 0.08 Interpol. Def. % 0.08 0.16 0.23 0.31 0.39 0.47 0.55 0.62 0.70 0.78 BBB Marginal 0.25 3.42 1.52 1.44 0.92 0.57 0.80 0.26 0.17 0.35 Cumulative 0.25 3.66 5.13 6.49 7.35 7.88 8.62 8.85 9.01 9.33 0.97 Interpol. Def. % 0.97 1.94 2.90 3.84 4.78 5.71 6.63 7.54 8.44 9.33 BB Marginal 1.23 2.62 4.53 2.15 2.49 1.14 1.67 0.67 1.76 3.78 Cumulative 1.23 3.82 8.17 10.15 12.39 13.39 14.83 15.40 16.89 20.03 2.21 Interpol. Def. % 2.21 4.37 6.49 8.55 10.57 12.55 14.48 16.37 18.22 20.03 B Marginal 3.19 7.14 7.85 8.74 6.22 4.28 3.88 2.39 2.07 0.87 Cumulative 3.19 10.10 17.16 24.40 29.10 32.14 34.77 36.33 37.65 38.19 4.70 Interpol. Def. % 4.70 9.17 13.44 17.51 21.38 25.07 28.59 31.95 35.14 38.19 CCC Marginal 6.70 14.57 16.16 11.28 3.36 10.26 5.35 3.25 0.00 4.18 Cumulative 6.70 20.29 33.17 40.71 42.70 48.58 51.33 52.92 52.92 54.88 7.65 Interpol. Def. % 7.65 14.71 21.24 27.26 32.83 37.97 42.71 47.10 51.14 54.88
Valuation of non-regulated Projects
Appendix V Calculation of the WACC’s for four current calculation
methods of Gasunie.
This appendix is written as an extra for financial management of Gasunie. At the moment Gasunie uses four different financial methods to calculate the net present value of non-regulated projects. This appendix is meant to give financial management an extra insight in the results of the different calculation methods in comparison with the method described in this thesis. The four methods that Gasunie uses at the moment will be described first.
Method I of Gasunie
The first method uses two different WACC’s. This method assumes that contracts that have already been signed with shippers can be considered almost risk-free. For these contracts a very low cost of capital of 5 % is used. The potential cash inflows from the capacity that has not been sold (yet) are much less certain and are therefore discounted with a much higher cost of capital. For the first group a WACC of 5 % is used and for the second group a WACC of 10 % is used.
Method II of Gasunie
The second method uses one WACC for all the cash flows. A WACC of 7.5 % is used to discount all the cash flows. For the capacity that has not been sold (yet) an adjustment is made in the cash flows. The method assumes that the cash flows of the unsold capacity will be in the range of 75 % of the value of contracts that have been signed already. Therefore the value of the cash flows of the potential contracts is multiplied by a factor of 0.75 to derive at an estimate of the potential value. (This means that the potential value of these contracts is reduced by 25 % in the calculations).
Method III of Gasunie
The third method uses the same WACC as method II: 7.5 %. The difference is that this method assumes that the capacity that has been sold already has a higher value than the capacity that has not been sold yet. Because the cash flows of the contracts that have been sold already can considered to be quite certain, banks might be willing to give money to Gasunie in advance of the project for these “certain” cash flows. To estimate the amount of money banks might be willing to give in exchange for these contracts, these cash flows are discounted with a discount rate of 5 %. Estimated is that approximately 80 % of the “certain” cash flows can be exchanged with a bank when the shipper is AAA. When the shipper is BBB estimated is that approximately 70 % of the “certain” cash flows can be exchanged with a bank. The cash flows of the capacity that has not been sold yet and the remaining 20 % and/or 30 % of the “certain” cash flows are discounted with a higher discount rate. The discount rate for these cash flows is 7.5 %.
Method IV of Gasunie
The fourth method uses one WACC, just like method two. A WACC of 6% is used to discount all the cash flows. The difference with the other methods is the fact that it also takes the credit rating of the contracting party in consideration. The risks that originate because of a lower credit rating are put in the cash flows, but the method does not say anything on the fact how this should be done. For the calculations made in this chapter the same method as described in chapter five will be used. Just like method II this method assumes that the cash flows of the unsold capacity have to be reduced. For the calculations in this paragraph a reduction of 25 % will be used. Therefore the value of the cash flows of the potential contracts is multiplied by a factor of 0.75 to derive at an estimate of the potential value.
Management of the corporate finance department is wondering how the WACC’s of the different methods have to be adjusted to arrive at a present value of the cash flows that is equal to the value when you:
• Use a WACC of 6.5 %;
• Reduce the cash flows of firms with the default probabilities according to the credit ratings (table 5.3.);
• Reduce the cash flows of potential contracts with 25 % to get cash flows for calculations.
For such a calculation first the following example is used (see also figure AV.1):
• For the first ten years two contracts with a cash flow of € 10,000,000 have been signed: * 10 year contract with an AAA firm.
* 10 year contract with a BBB firm.
• The capacity with a potential cash flow of € 20,000,000 of year 11 to 20 has not been sold yet.
First the present value of these contracts is calculated for the WACC of 6.5 described earlier (all the
risk is put into the cash flows).
This leads to the following present values:
• €10,000,000, 10 years, AAA, WACC 6.5 %, PV: €72 million • €10,000,000, 10 years, BBB, WACC 6.5 %, PV: €69 million • 75 % of €20,000,000, year 11 to 20, WACC 6.5 %, PV: € 57 million
Valuation of non-regulated Projects
Figure AV.1: Calculation of the WACC’s for four current calculation methods, example 1.
Now the other four methods are explored to arrive at the same NPV by changing the WACC.
Method I
• €10,000,000, 10 years, AAA, WACC 5.0 %, PV: €77 million • €10,000,000, 10 years, BBB, WACC 5.0 %, PV: €77 million • €20,000,000, year 11 to 20, WACC 11 %, PV: €44 million
Total PV: € 198 million
Method II
• €10,000,000, 10 years, AAA, WACC 7 %, PV: €71 million • €10,000,000, 10 years, BBB, WACC 7 %, PV: €71 million • 75 % of €20,000,000, year 11 to 20, WACC 7 %, PV: € 56 million
Total PV: € 198 million
AAA
10 years € 10 millionBBB
10 years € 10 million Not sold 10 years potential € 20 million Year 0 Year 20Method III
• 80 % of €10,000,000, 10 years, AAA, WACC 5.0 %, PV: €62 million • 70 % of €10,000,000, 10 years, BBB, WACC 5.0 %, PV: €54 million • Remaining €5,000,000, 10 years, WACC 10 %, PV: €32 million • €20,000,000, year 11 to 20, WACC 10 %, PV: €51 million
Total PV: € 198 million
Method IV
The calculation is done the same as the method described earlier with the WACC of 6.5 %, because the reduction of the cash flows for method IV in this example is done in the same way. (However method IV itself does not say anything about how this reduction should be done, therefore certain assumptions are made. Otherwise no calculation would be possible) =>
WACC = 6.5 %
Now another example will be given to give some more insight in the WACC’s of the different methods.
Figure AV.2: Calculation of the WACC’s for four current calculation methods, example 2.
AAA
10 years € 10 millionBBB
10 years € 10 millionNot sold
10 years potential € 30 million Year 0 Year 20Not sold
10 years potential € 10 millionValuation of non-regulated Projects
• For the first ten years two contracts with a cash flow of € 10,000,000 have been signed: * 10 year contract with an AAA firm.
* 10 year contract with a BBB firm.
• A contract with a potential cash flow of € 10,000,000 per year is still available for the first 10 years.
• The capacity with a potential cash flow of € 30,000,000 of year 11 to 20 has not been sold yet.
Again, first the present value of these contracts is calculated for the WACC of 6.5 % described earlier (all the risk is put into the cash flows).
This leads to the following present value:
• € 10,000,000, 10 years, AAA, WACC 6.5 %, PV: €72 million • € 10,000,000, 10 years, BBB, WACC 6.5 %, PV: €69 million • 75 % of € 10,000,000, 10 years, WACC 6.5 %, PV: €54 million • 75 % of € 30,000,000, year 11 to 20, WACC 6.5 %, PV: €86 million
Total PV: € 280 million
Now the other four methods are explored to arrive at the same NPV by changing the WACC.
Method I
• € 10,000,000, 10 years, AAA, WACC 5.0 %, PV: € 77 million • € 10,000,000, 10 years, BBB, WACC 5.0 %, PV: € 77 million • € 10,000,000, 10 years, WACC 11 % , PV: € 60 million • € 30,000,000, year 11 to 20, WACC 11 %, PV: € 66 million
Total PV: € 280 million
Method II
• € 10,000,000, 10 years, AAA, WACC 7 %, PV: €71 million • € 10,000,000, 10 years, BBB, WACC 7 %, PV: €71 million • 75 % of € 10,000,000, 10 years, WACC 7%, PV € 53 million • 75 % of € 30,000,000, year 11 to 20, WACC 7 %, PV: € 84million
Method III
• 80 % of €10,000,000, 10 years, AAA, WACC 5.0 %, PV: €62 million • 70 % of €10,000,000, 10 years, BBB, WACC 5.0 %, PV: €54 million • Remaining €15,000,000, 10 years, WACC 10 %, PV: €93 million • € 30,000,000, year 11 to 20, WACC 10 %, PV: € 72 million
Total PV: € 280 million
Method IV
Calculation is the same as method described earlier with WACC of 6.5 =>
WACC = 6.5 %
Summarizing:
Example I
Example II
Method
CoC
CoC not certain
Method
CoC
CoC not certain
I
5%
11%
I
5%
11%
II
7%
d.n.a.
II
7%
d.n.a.
III
5%
10%
III
5%
10%
IV
6.5%
d.n.a.
IV
6.5%
d.n.a.
Conclusion:
Since the two examples lead to the same (rounded off) results, the numbers can considered to be quite robust. Interesting to see is that the WACC’s found in the numerical examples are almost the same as the WACC’s used in the four methods by Gasunie. A part of this is the result of the fact that all the missing information of the different methods has been completed with methods described in this thesis.
Valuation of non-regulated Projects
Appendix VI Default percentages in comparison with spreads.
In chapter 5, table 5.3 about default probabilities is depicted. This table will be used to reduce the cash flows in the discounted cash flow model for non-regulated projects. Financial management of Gasunie is wondering whether these different reduction percentages are correlating with the spreads of different ratings over government bonds. This appendix is written to check this correlation. To do this a fictive loan is created. The interest payment by the receiving party is calculated by adding the default spread to the risk free rate for different credit ratings. This is done for four different credit ratings: AAA, AA, A and BBB. For this paragraph the credit spreads of Bloomberg provided by JPMorgan are used. These credit spreads have already been presented in table 4.2.
In the second column of table AVI.1 the spreads for different ratings are depicted. When you add these spreads to the risk free rate of 3.9 % you get the interest percentages shown in the third column of table AVI.1. For example for a BBB firm the interest percentage is 3.9 % + 1.08 % = 4.98 %.
Table AVI.1: Default spreads according to different credit rating agencies. Risk free rate Loan
3.9 1000
Rating Spread % Interest %
AAA 0.12 4.02
AA 0.35 4.25
A 0.64 4.54
BBB 1.08 4.98
Now the yearly cash flows can be calculated. A BBB firm will be used as an example. The calculations for the firms with the other credit ratings are done in the same way. For a loan of € 1000 an annual interest payment is made of 4.98 % * € 1000 = € 49.80. The annual interest payments are reduced by the default probabilities depicted in table 5.3. For example in year one this leads to a
reduced cash flow of
)
€
49.31
100
%
0.97
-(1
*
49.80
€
=
.After 10 years the loan of € 1000 is repaid to the lender. This € 1000 is also reduced by the probability of default. For the BBB firm this leads to a value after ten years of
907
€
)
100
%
9.3
-(1
*
1000
€
=
Now the interest payments and the repayment of the loan have been reduced with the probabilities of default, they are discounted with the risk free rate (3.9 %). For the BBB firm this leads to a NPV of € 1004 which is a bit higher than the original € 1000. This means that the default spread is slightly higher than you would expect according to the reductions of the interest payments with the percentages of table 5.3. However for the BBB firm these differences are very small. For a firm with a credit rating between AAA and A the differences are a little higher but not disturbing. This means that the default percentages in the real world are a bit lower than you would expect according to the default spreads (for higher rated firms).
Table A VI.2: NPVs of loans with different spreads and default percentages. Cash flow in year
1 2 3 4 5 6 7 8 9 10 NPV AAA Interest 40.2 40.2 40.2 40.2 40.2 40.2 40.2 40.2 40.2 40.2 € 328 red.loan 1000 € 682 € 1,010 AA Interest 42.5 42.5 42.4 42.4 42.4 42.4 42.3 42.3 42.3 42.3 € 345 red.loan 995 € 678 € 1,024 A Interest 45.4 45.3 45.3 45.3 45.2 45.2 45.2 45.1 45.1 45.0 € 369 red.loan 992 € 677 € 1,045 BBB Interest 49.3 48.8 48.4 47.9 47.4 47.0 46.5 46.0 45.6 45.2 € 386 red.loan 907 € 618 € 1,004
Valuation of non-regulated Projects
Tables and figures.
List of figures:
Figure AV.1: Calculation of the WACC’s for four current calculation methods, example 1……….12
Figure AV.2: Calculation of the WACC’s for four current calculation methods, example 2……….13
List of tables: Table AI.1: Calculation of the risk free rate………..………...2
Table AII.1: Calculation of the Beta………..………..3
Table AII.2: Calculation of the beta with target debt level for comparable companies……..……...5
Table AII.3: The levered beta of Gasunie for different debt structures………..……….7
Table AIV.1: Interpolated default percentages for year 1 to 10………..………...9
Table AVI.1: Default spreads according to different credit rating agencies………...16