Monday, August 15, 2011

Yet more on LEC

As I mentioned in my last post, I’ll present a talk to the Sydney branch of the Australian Solar Energy Society next Tuesday.  The talk is entitled “Comparison of Levelised Electricity Cost for Large-Scale Solar Projects”.

I’m sure to be questioned about my methodology for estimating the Levelised Electricity Cost (LEC).  By way of explanation, I’m mainly interested in international comparisons rather than being able to give a definitive statement to potential investors or to the Department of Taxation.  So my methodology ignores inflation and taxation.  I have stated my assumptions in every post in which I have discussed the cost of solar power; they are

          there is no inflation,
          taxation implications are neglected,
          projects are funded entirely by debt,
          all projects have the same interest rate (8%) and payback period (25 years), which means that the required rate of capital return is 9.4%,
          all projects have the same annual maintenance and operating costs (3% of the total project cost), and
          government subsidies are neglected.

Further commentary on my LEC methodology has been given in the posts on Real cost of coal-fired power, LEC – the accountant’s view and Cost of solar power (10).

For completeness, I’m now going to give a full model including taxation and inflation.  The model will be applied to the Kogan Creek installation I described in Cost of Solar Power (7).  The capital cost of this project was AUD 105 million and the annual output is stated to be 44 GWhr/yr.

WARNING: This is not exciting stuff and I just can’t think of any way to make it easy reading!  Basically, the requirement is to study the construction and entries in a spreadsheet.  In essence, future Profit & Loss accounts and future balance sheets are presented (in future $), which are then discounted back into present $.  Changes in the sum of NPAT plus equity are calculated, both for individual years and on average over years since the start of the project.  This leads to a quantity called average TSR (present $), which is truly the bottom line; the goal is for this to hit a shareholder-specified target such as 0.05.

Here are the assumptions for the full model:

cost
[AUD]
105,000,000
interest rate
[-]
0.075
depreciation period
[yrs]
25
annual output
[MWhr/yr]
44,000
tax rate on profits
[-]
0.3
debt fraction
[-]
0.5
{annual O&M costs}/{total cost}
[-]
0.03
inflation rate
[-]
0.025
estimated LEC
[AUD/MWhr]
320

Here are the financial details for the first three years (all figures in AUD millions):

Year
0
1
2
3
sales (future $)

14.080
14.432
14.793
O&M (future $)

3.150
3.229
3.309
EBITDA (future $)

10.930
11.203
11.483
depreciation (future $)

4.200
4.200
4.200
EBIT (future $)

6.730
7.003
7.283
interest payments (future $)

3.938
3.623
3.308
pre-tax profit (future $)

2.793
3.381
3.976
taxation (future $)

0.838
1.014
1.193
NPAT (future $)

1.955
2.367
2.783
NPAT (present $)

1.955
2.309
2.649
* cumulative NPAT (present $)

1.955
4.264
6.912
depreciated assets (future $)

100.800
96.600
92.400
borrowings (future $)
52.500
48.300
44.100
39.900
equity (future $)

52.500
52.500
52.500
* equity (present $)

52.500
51.220
49.970
sum of items marked *
52.500
54.455
55.483
56.883
average TSR (present $)

0.037
0.028
0.028

Acronyms:

O&M              Operations and Maintenance expenses
EBITDA         earnings before interest, taxation, depreciation and allowances
EBIT               earnings before interest and taxation
NPAT             nett profit after tax
TSR                 total shareholder return

Note that the annual depreciation figure is used to reduce borrowings, which means that interest payments decrease with time.

The last line is the key to it all – in words it is the cumulative nett profit after tax plus the equity, all expressed in today’s $, divided by the initial investment, and then expressed as an average over the total numbers of years that have elapsed.  That is the number that should eventually hit the target specified by the investors.  In this example, it will be 0.050.

The spreadsheet then continues uneventfully until year 13 when the borrowings hit zero.  Here are four years from the spreadsheet around that time.

Year
12
13
14
15
sales (future $)
18.474
18.936
19.409
19.895
O&M (future $)
4.133
4.236
4.342
4.451
EBITDA (future $)
14.341
14.670
15.067
15.444
depreciation (future $)
4.200
4.200
4.200
4.200
EBIT (future $)
10.141
10.500
10.867
11.244
interest payments (future $)
0.473
0.158
0.000
0.000
pre-tax profit (future $)
9.669
10.342
10.867
11.244
taxation (future $)
2.901
3.103
3.260
3.373
NPAT (future $)
6.768
7.239
7.607
7.871
NPAT (present $)
5.158
5.383
5.518
5.570
* cumulative NPAT (present $)
43.990
49.373
54.892
60.461
depreciated assets (future $)
54.600
50.400
46.200
42.000
borrowings (future $)
2.100
0.000
0.000
0.000
equity (future $)
52.500
50.400
46.200
42.000
* equity (present $)
40.013
37.475
33.514
29.725
sum of items marked *
84.003
86.849
88.406
90.186
average TSR (present $)
0.050
0.050
0.049
0.048

Thereafter, not much dramatic happens.  The installation earns a bit more than 5% annually after tax, as expressed in today’s $, and the value of the asset continues to depreciate until there is no residual value after 25 years.  For the parameters that have been chosen, the average TSR (present $) after 25 years is 0.050.

I therefore conclude that, with taxation and inflation included and for parameter settings as given in the first table, the LEC is around AUD 320 per MWhr.  Note that the eventual LEC depends on the assumptions that have been made.  This needs to be systematically explored with the spreadsheet, but I’ll give one example.  If I make only one change, namely to set the debt fraction to be 0.65, then LEC = AUD 287 per MWhr ensures that the average TSR (present $) turns out to be 0.05.

My original estimate of the LEC for the Kogan Creek development was AUD 295 per MWhr.  In view of the analysis and discussion above, I think that’s a reasonably robust estimate, and certainly useful for the purposes of international comparisons.

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