The Swansea Bay tidal lagoon debate tends to focus on its cost. The figure usually quoted is £168/MWh for the feed-in tariff or ‘strike price’ needed to enable it to go ahead. If you were wondering where this number came from, how it was derived, and whether it is still correct, then you’ve come to the right place.

The number is from a report commissioned by Tidal Lagoon Power (TLP) from Pöyry management consultants in 2014. The study’s objective was to find the minimum level of feed-in tariff that would make the plant commercially viable. The answer it gave was £168/MWh for a period of 35 years and it was calculated using the assumptions listed in Table 1 below.

Table 1: Assumptions used by Pöyry
Parameter	Unit	Value
Annual energy production (AEP)	GWh/year	495
Construction time	years	3
Capital cost	£M	913
Capex phasing	Dimensionless	Year 1: 45% Year 2: 30% Year 3: 25%
Wholesale electricity price	£/MWh	65
Operating cost	£M/year	9.8
Operating life	Years	120
Duration of feed-in tariff	Years	35
Transmission loss	Dimensionless	0.8%
PPA discount	Dimensionless	7%
Use of system charges	£/MWh	1.50
Discount rate	Dimensionless	6.5%

The following Octave function returns the NPV of the project according to Pöyry's assumptions.

function npv = swansea_bay_npv(strike_price)

    year = 1:123;

    AEP(1:3) = 0;    
    AEP(4:123) = 495e3; %MWh/y;
   
    use_of_system_charge = AEP .* 1.5; %GBP/MWh
  
    transmission_loss_adjustment = 1 - 0.8/100;
    AEP = AEP .* transmission_loss_adjustment;
    
    capital_cost = 913e6; %GBP
    capex = zeros(1, 123);
    capex(1) = capital_cost * 0.45; %year 1
    capex(2) = capital_cost * 0.3;  %year 2
    capex(3) = capital_cost * 0.25; %year 3
    
    % Operation starts in year 3 (index 4)
    opex(1:3) = 0;
    opex(4:123) = 9.8e6; %GBP
    
    wholesale_price = 65; %GBP/MWh
    
    PPA_discount = AEP .* wholesale_price .* 7/100;
    
    tariff_duration = 35; %years
    
    price = zeros(1, 123);
    price(4:tariff_duration+3) = strike_price;
    price(tariff_duration+4:123) = wholesale_price;
    revenue = price .* AEP;
    revenue = revenue .- PPA_discount .- use_of_system_charge;
    
    expenditure = capex .+ opex;
    
    net_cash_flow =  revenue .- expenditure;
    
    discount_rate = 6.5 / 100; 
    discount_factor = (1 + discount_rate) .^ year;
    
    discounted_cash_flow = net_cash_flow ./ discount_factor;
    
    npv = sum(discounted_cash_flow);

endfunction

And the following script uses Octave’s ‘fsolve’ function solve for the strike price that makes the NPV zero.

printf("Swansea bay tidal lagoon\n");

% The function "swansea_bay_npv" can only accept a scalar argument but the
% function "fsolve" requires a vector argument, so it is necessary to wrap it 
% in another function first. 

function w = wrapper(x)    
    w = zeros(size(x));
    for i = 1:length(x)
        w(i) = swansea_bay_npv(x(i));
    endfor     
endfunction

f = @(x) wrapper(x);
y = fsolve(f, 100);
printf("Required strike price = %.2f\n", y);

Gratifyingly, it comes out at £167.91/MWh (yes!). I expect the original calculation was done using a large complex spreadsheet containing dozens, if not hundreds, of formulae. The above code snippets show that exactly the same calculation can be done in just 39 lines (not including comments) of plain text that are almost completely self-explanatory.

This result is not the levelised cost of energy (LCOE). It is the strike-price needed to give investors their desired rate of return given that the plant gets the strike price only for part of its life and the ‘wholesale’ price for the remainder.

Having done this we can now easily and quickly look at what happens when we vary some of the assumptions. The first one to look at is the duration of the tariff. Pöyry and TLP chose 35 years, probably because that's what Hinkley C got. However, the Hendry report, which was published two years after the Pöyry report, says:

‘The CFD element of TLP’s proposal for Swansea Bay is for a 90 year contract term …’ (page 78)

so lets see what happens when we change the tariff duration to 90 years while keeping everything else the same. This could be a good way of getting the headline strike price down to something less hair raising without actually reducing the total amount of subsidy. The result is £156.87/MWh.

This is not as big a reduction as I was expecting, and certainly not as big as implied by a January 2016 report from Wales Online entitled ‘Big drop in Swansea Bay tidal lagoon subsidy cost makes project a ‘no-brainer’ says Sir Terry Matthews’ and subtitled ‘The lower strike price of £100 per megawatt hour would be built around a longer subsidy period of 90 years instead of 35’. I don't know how they came to that conclusion, because increasing the duration of the feed-in tariff from 35 to 90 years is not sufficient to get the strike price down to £100/MWh. Also, it isn’t correct to say that lower payments over a longer period equate to lower susbidy costs. Just as with home and car loans, if you spread the payments over a longer period you pay more in total.

The next things to vary are the capital cost and the annual energy production. These have changed since Pöyry wrote their report. As I remarked in an earlier post, media reports of the capital cost have been gradually going up, from £650M in June 2013, through £850M in February 2014, £1bn in June 2015 to £1.3bn (double the 2013 estimate) now. Figure 1 below shows these numbers plotted on graph.

Figure 1: Values of the capital cost of the Swansea Bay tidal lagoon as reported in the media.

The fact that the project is ready to start construction may mean that this trend has come to an end, but it is also possible that the cost will continue to increase during the construction phase in line with standard construction industry practice of bidding low and growing the project afterwards.

Figure 2 below shows a screenshot from TLP's website, taken today (23 February) showing the current values of capital cost (£1.3bn) and annual energy production (530GWh).

Putting these numbers into the calculation gives £198.75/MWh for a 90 year tariff duration and £214.82/MWh for a 35 year duration.

It doesn’t stop there, however. While it is plausible that the sea wall may last for 120 years the turbines, generators and associated mechanical and electrical equipment probably won't. The plant will probably need to be repowered at least once during its lifetime. Unfortunately there aren’t any publicly available data on how much this will cost.

The Hendry report wouldn’t discuss the Swansea Bay strike price due to confidentiality, but it looks like they are going to need something not unadjacent to £200/MWh even with a 90 year contract.

Addendum (25 February)

It has just occurred to me that it might be worth exploring what happens if you tweak the discount rate. The above results were calculated using a discount rate of 6.5%, which is the same as Pöyry used in their calculation. Table 2 below summarises these results:

Table 2: Summary of results calculated with discount rate of 6.5%
Tariff duration years	Capital cost £M	AEP GWh/y	Required strike price £/MWh
35	913	495	167.908
90	913	495	156.87
90	1300	530	198.746
35	1300	530	214.816

6.5% must have been TLP's desired rate of return on the project, otherwise they wouldn't have told Pöyry to use it. However, if they were prepared to accept a lower rate of return they could ask for a lower strike price from the government. If, for example, the government were prepared to offer £100/MWh over 90 years, and TLP to accept 2.75%, then the project would be a goer. Table 3 below lists the same results calculated with a discount rate of 2.75%.

Table 3: Summary of results calculated with discount rate of 2.75%
Tariff duration years	Capital cost £M	AEP GWh/y	Required strike price £/MWh
35	913	495	90.053
90	913	495	81.823
90	1300	530	99.524
35	1300	530	116.413

If they want to get down to the Hinkley level of £92.5/MWh, but over 90 years instead of 35, then 2.45% would do the trick, as shown in Table 4 below:

Table 4: Summary of results calculated with discount rate of 2.45%
Tariff duration years	Capital cost £M	AEP GWh/y	Required strike price £/MWh
35	913	495	82.606
90	913	495	76.344
90	1300	530	92.386
35	1300	530	107.504

And finally, 1.97% would get them to complete parity with Hinkley.

Table 5: Summary of results calculated with discount rate of 1.97%
Tariff duration years	Capital cost £M	AEP GWh/y	Required strike price £/MWh
35	913	495	69.591
90	913	495	67.746
90	1300	530	81.259
35	1300	530	92.183

I don't know whether they will be able to find investors who will accept any of these lower rates of return. If the government were to offer them a low interest soft loan then the equity investors could earn a bit more while keeping the weighted average the same. Maybe that is what Charles Hendry means when he talks about ‘the design of its financing structure’.

Given that the project is a ‘pathfinder’ it would be reasonable for them to accept a lower rate of return. The difference could be regarded as an ‘investment’ in the production of know-how that will enable a full commercial return to be earned on subsequent projects. It would also incentivise them to develop further projects in order to realise its value.

Howard Rudd

Swansea Bay tidal lagoon, what is its real cost?

Addendum (25 February)