**Appendix A**

The purpose of the PF model is to produce plant cost estimates for various generating technologies. The PF model is essentially a dynamic, multi-period post-tax discounted cash flow optimization model which solves for multiple generating technologies, business combinations, and revenue possibilities through simultaneous convergen<sup>t</sup> price, debt-sizing, taxation and equity return variables. These outputs are similar in nature to levelized cost estimates but with a level of detail beyond the typical LCoE

model because corporate or project financing, credit metrics and taxation constraints are co-optimized. Model logic, derived in [48,54], is as follows:

Costs increase annually by a forecast general inflation rate (CPI). Prices escalate at a discount to CPI. Inflation rates for revenue streams π*Rj* and cost streams π*Cj* in period (year) *j* are calculated as follows:

$$
\pi\_j^R = \left[1 + \left(\frac{\mathbb{CPI} \times a\_R}{100}\right)\right]^l, \text{ and } \pi\_j^C = \left[1 + \left(\frac{\mathbb{CPI} \times a\_C}{100}\right)\right]^l \tag{A1}
$$

Energy output *oij* from each plant (*i*) in each period (*j*) is a key variable in driving revenue streams, unit fuel costs and variable operations and maintenance costs. Energy output is calculated by reference to installed capacity *ki*, capacity utilisation rate *CFij* for each period *j*. Plant auxiliary losses *Aux<sup>i</sup>* arising from on-site electrical loads are deducted.

$$
\sigma\_j^{\bar{i}} = \mathbb{C}F\_j^{\bar{i}} \cdot k^{\bar{i}} \cdot \left(1 - A u x^{\bar{i}}\right) \tag{A2}
$$

Electricity price for the *ith* plant *pi*εis calculated in year one and escalated per Eq. (A1). Thus revenue for the *ith* plant in each period *j* is defined as follows:

$$R^i\_j = \left(o^i\_j \cdot p^{i\nu} \cdot \pi^R\_j\right) \tag{A3}$$

As outlined above, plant marginal running costs are a key variable and used extensively in *NEMESYS-PF*. In order to define marginal running costs, the thermal efficiency for each generation technology ζ*i* needs to be defined. The constant term "3600" is divided by ζ*i* to convert the efficiency result from % to kJ/kWh (i.e., the derivation of the constant term 3600 is: 1 Watt = 1 Joule per second and hence 1 Watt Hour = 3600 Joules). This is then multiplied by raw fuel commodity cost *fi*. Variable operations and maintenance costs *vi*, where relevant, are added which produces a pre-carbon short run marginal cost. Under conditions of externality pricing *CPj*, the CO2 intensity of output needs to be defined. Plant carbon intensity *gi* is derived by multiplying the plant heat rate by combustion emissions .*gi* and fugitive CO2 emissions *g*ˆ*i*. Marginal running costs in the *jth* period is then calculated by the product of short run marginal production costs by generation output ρ*ij* and escalated at the rate of π*Cj*.

$$\mathcal{S}\_{\hat{j}}^{i} = \left\{ \left| \left( \frac{\frac{3600}{\hat{\zeta}^{i}}}{1000} \cdot f^{i} + v^{i} \right) + \left( \hat{\mathcal{g}}^{i} \cdot \text{CP}\_{\hat{j}} \right) \right| \cdot o\_{\hat{j}}^{i} \cdot \pi\_{\hat{j}}^{\text{C}} \middle| \mathcal{g}^{i} = \left( \hat{\mathcal{g}}^{i} + \hat{\mathcal{g}}^{i} \right) \cdot \frac{\left( \frac{3600}{\hat{\zeta}^{i}} \right)}{1000} \right\} \tag{A4}$$

Fixed operations and maintenance costs *FOMij* of the plant are measured in \$/MW/year of installed capacity *FC<sup>i</sup>* and are multiplied by plant capacity *ki* and escalated.

$$FOM\_j^i = FC^i \cdot k^i \cdot \pi\_j^C \tag{A5}$$

Earnings before interest tax depreciation and amortization (EBITDA) in the *jth* period can therefore be defined as follows:

$$EBITDA^i\_j = \left[R^i\_j - \mathfrak{s}^i\_j - FOM^i\_j\right] \tag{A6}$$

Capital costs -*Xi*for each plant *i* are overnight capital costs and incurred in year 0. Ongoing capital spending for each period *j* is determined as the inflated annual assumed capital works program.

$$\mathbf{x}\_{j}^{i} = \mathbf{c}\_{j}^{i} \cdot \boldsymbol{\pi}\_{j}^{\mathbb{C}} \tag{A7}$$

Plant capital costs *Xi*0 give rise to tax depreciation (*dij*) such that if the current period was greater than the plant life under taxation law (*L*), then the value is 0. In addition, *xij* also gives rise to tax depreciation such that:

$$d\_j^i = \left(\frac{X^i}{L}\right) + \left(\frac{x\_j^i}{L+1-j}\right) \tag{A8}$$

From here, taxation payable τ*ij* at the corporate taxation rate (<sup>τ</sup>*c*) is applied to *EBITDAij* less interest on loans *Iij* later defined in (16), less *dij*. To the extent τ*ij* results in non-positive outcome, tax losses *Lij* are carried forward and offset against future periods.

$$\tau\_j^i = \text{Max}\{0, \left( EBITDA\_j^i - I\_j^i - d\_j^i - L\_{j-1}^i\right) \cdot \tau\_c\}\tag{A9}$$

$$L\_j^i = \operatorname{Min} \left( 0, \left( EBITDA\_j^i - I\_j^i - d\_j^i - L\_{j-1}^i \right) \cdot \tau\_c \right) \tag{A10}$$

The debt financing model computes interest and principal repayments on different debt facilities depending on the type, structure, and tenor of tranches. There are two types of debt facilities—(a) corporate facilities (i.e., balance-sheet financings) and (2) project financings. Debt structures include semi-permanent amortizing facilities and bullet facilities.

Corporate facilities involve 3- and 7-year money raised with an implied "BBB" credit rating. With project financings, two facilities are modeled. The first facility is nominally a 3-year bullet requiring interest-only payments after which it is refinanced with consecutive amortizing facilities and fully amortized over a 25-year period. The second facility commences with a tenor of 7 years as an amortizing facility, again set within a semi-permanent structure with a nominal repaymen<sup>t</sup> term of 25 years. The decision tree for the two tranches of debt is the same, so for the debt tranche where *T* = 1 or 2, the calculation is as follows:

$$\begin{cases} \text{i)} \begin{cases} > 1, DT^i\_j = DT^i\_{j-1} - P^i\_{j-1} \\ = 1, DT^i\_1 = D^i \cdot S \end{cases} \end{cases} \tag{A11}$$

*D<sup>i</sup>* refers to the total amount of debt raised for the project. The split (*S*) of the debt between each facility refers to the manner in which debt is apportioned to each tranche. In the model, 35% of debt is assigned to Tranche 1 and the remainder to Tranche 2. Principal *<sup>P</sup>ij*−<sup>1</sup> refers to the amount of principal repaymen<sup>t</sup> for tranche *T* in period *j* and is calculated as an annuity:

$$P\_j^i = \left(DT\_j^i / \left[\frac{1 - \left(1 + \left(R\_T^z + C\_T^z\right)\right)^{-n}}{R\_T^z + C\_T^z}\right]\right) \mathbf{z}\left\{\begin{array}{l} = VI\\ = PF \end{array}\right\}\tag{A12}$$

In (A12), *RT* is the relevant interest rate swap (3 yrs or 7 yrs) and *CT* is the credit spread or margin relevant to the issued debt tranche. The relevant interest paymen<sup>t</sup> in the *jth* period *Iij* is calculated as the product of the (fixed) interest rate on the loan by the amount of loan outstanding:

$$I\_j^i = DT\_j^i \times \left(R\_T^z + C\_T^z\right) \tag{A13}$$

Total debt outstanding *Dij*, total Interest *Iij* and total principle *Pij* for the *ith* plant is calculated as the sum of the above components for the two debt tranches in time *j*. For clarity, loan drawings are equal to *D<sup>i</sup>* in year 1 as part of the initial financing and are otherwise 0.

One of the key calculations is the initial derivation of *Di*. This is determined by the product of the gearing level and the overnight capital cost -*<sup>X</sup><sup>i</sup>*. Gearing levels are formed by applying a cash flow

constraint based on credit metrics applied by project banks and capital markets. The variable γ in the PF model relates specifically to the legal structure of the business and the credible capital structure achievable. The two relevant legal structures are vertically integrated (VI) merchant utilities (using "BBB" rated corporate facilities) and independent power producers using project finance (PF).

$$\text{if } f \circ \begin{cases} = VI, \mathit{Min} \left( \frac{\mathit{FFO}\_{j}^{i}}{P\_{j}} \right) \geq \delta\_{j}^{VI}.\mathit{Min} \left( \frac{\mathit{FFO}\_{j}^{i}}{D\_{j}^{i}} \right) \geq \omega\_{j}^{VI} \forall \ j \left| \mathit{FFO}\_{j}^{i} = \left( \mathit{EBITDA}\_{j}^{i} - \boldsymbol{x}\_{j}^{i} \right) \right. \\\ = \text{PF}, \mathit{Min} \left( \textup{DSCR}\_{j}^{i}, \mathit{LLCRR}\_{j}^{i} \right) \geq \delta\_{j}^{PF}, \ \forall \ j \left| \mathit{DSCR}\_{j} = \frac{\left( \mathit{EBITDA}\_{j}^{i} - \boldsymbol{x}\_{j}^{i} - \boldsymbol{x}\_{j}^{i} \right)}{P\_{j} + P\_{j}} \right| \mathit{LLCR}\_{j} = \frac{\sum\_{i=1}^{N} \left[ \left( \mathit{EBITDA}\_{j}^{i} - \boldsymbol{x}\_{j}^{i} - \boldsymbol{x}\_{j}^{i} \right) (1 + \boldsymbol{X}\_{2i})^{-} \right]}{D\_{j}} \end{cases} \tag{A14}$$

The variables δ*VI j* and ω*VI j* are exogenously determined by credit rating agencies. Values for δ*PFj* are exogenously determined by project banks and depend on technology (i.e., thermal vs. renewable) and the extent of energy market exposure, that is whether a power purchase agreemen<sup>t</sup> exists or not. For clarity, *FFOij* is "funds from operations" while *DSCRij* and *LLCRij* are the debt service cover ratio and loan life cover ratios. Debt drawn is:

$$D^i = X^i - \sum\_{j=1}^{N} \left[ EBITDA\_j^i - l\_j^i - P\_j^i - \tau\_j^i \right] \cdot (1 + K\_\varepsilon)^{-(j)} - \sum\_{j=1}^{N} x\_j^i \cdot (1 + K\_\varepsilon)^{-(j)} \tag{A15}$$

At this point, all of the necessary conditions exist to produce estimates of generalized long run marginal costs of the various power generation technologies. The relevant equation to solve for the price *pi*ε given expected equity returns (*Ke*) whilst simultaneously meeting the binding constraints of δ*VI j* and ω*VI j* or δ*PFj* given the relevant business combinations. The primary objective is to expand every term which contains *<sup>p</sup>i*<sup>ε</sup>. Expansion of the EBITDA and tax terms is as follows:

$$\begin{split} -X^i + \sum\_{j=1}^{N} \Big[ \Big( p^{i\varepsilon} \cdot \boldsymbol{\sigma}\_j^i \cdot \boldsymbol{\pi}\_j^R \Big) - \mathfrak{s}\_j^i - \boldsymbol{F} \boldsymbol{\mathcal{M}} \boldsymbol{d}\_j^i - \boldsymbol{l}\_j^i - \boldsymbol{P}\_j^i \\ - \Big( \Big( p^{i\varepsilon} \cdot \boldsymbol{\sigma}\_j^i \cdot \boldsymbol{\pi}\_j^R \Big) - \mathfrak{s}\_j^i - \boldsymbol{F} \boldsymbol{\mathcal{M}} \boldsymbol{d}\_j^i - \boldsymbol{l}\_j^i - \boldsymbol{d}\_j^i - \boldsymbol{L}\_{j-1}^i \Big) \cdot \boldsymbol{\pi}\_\varepsilon \Big] \cdot (1 + \boldsymbol{K}\_\varepsilon)^{-(j)} \\ - \sum\_{j=1}^{N} \boldsymbol{x}\_j^i \cdot (1 + \boldsymbol{K}\_\varepsilon)^{-(j)} - \boldsymbol{D}^i \end{split} \tag{A16}$$

The terms are then rearranged such that only the *pi*ε term is on the left-hand side of the equation: Let *IRR* ≡ *Ke*

$$\begin{split} \sum\_{j=1}^{N} (1 - \tau\_{\mathcal{E}}) \cdot p^{i\boldsymbol{\varepsilon}} \cdot \boldsymbol{o}\_{\boldsymbol{j}}^{i} \cdot \boldsymbol{\pi}\_{\boldsymbol{j}}^{R} \cdot (1 + \mathcal{K}\_{\boldsymbol{\varepsilon}})^{-(j)} \\ = \boldsymbol{X}^{i} \\ - \sum\_{j=1}^{N} \Big[ -(1 - \tau\_{\mathcal{E}}) \cdot \boldsymbol{\aleph}\_{\boldsymbol{j}}^{i} - (1 - \tau\_{\mathcal{E}}) \cdot \boldsymbol{F} \boldsymbol{\omup}\_{\boldsymbol{j}}^{i} - (1 - \tau\_{\mathcal{E}}) \cdot \left( \boldsymbol{I}\_{\boldsymbol{j}}^{i} \right) - \boldsymbol{P}\_{\boldsymbol{j}}^{i} + \tau\_{\mathcal{E}} \cdot \boldsymbol{d}\_{\boldsymbol{j}}^{i} \\ + \tau\_{\mathcal{E}} \boldsymbol{L}\_{\boldsymbol{j}-1}^{i} \cdot (1 + \mathcal{K}\_{\boldsymbol{\varepsilon}})^{-(j)} \Big] + \sum\_{j=1}^{N} \boldsymbol{x}\_{\boldsymbol{j}}^{i} \cdot (1 + \mathcal{K}\_{\boldsymbol{\varepsilon}})^{-(j)} + D^{i} \end{split} \tag{A17}$$

The model then solves for *pi*ε such that:

$$\begin{split} &p^{j\varepsilon} = \frac{\boldsymbol{X}^{j}}{\sum\_{j=1}^{N} (1-\mathsf{r}\_{\varepsilon}) \cdot p^{j\varepsilon} \cdot \boldsymbol{d\_{j}^{\varepsilon}} \cdot (1+\mathsf{K}\_{\varepsilon})^{-(j)}} \\ &+ \frac{\sum\_{j=1}^{N} \left( (1-\mathsf{r}\_{\varepsilon}) \cdot \boldsymbol{s^{j}} + (1-\mathsf{r}\_{\varepsilon}) \cdot \boldsymbol{\mathrm{F}} \mathrm{OM}\_{j}^{i} + (1-\mathsf{r}\_{\varepsilon}) \cdot \left(\boldsymbol{l}\_{j}^{i}\right) + \boldsymbol{P}\_{j}^{i} - \mathsf{r}\_{\varepsilon} \cdot \boldsymbol{d\_{j}^{\varepsilon}} - \mathsf{r}\_{\varepsilon} \boldsymbol{L\_{j}^{i}} \cdot (1+\mathsf{K}\_{\varepsilon})^{-(j)}\right)}{\sum\_{j=1}^{N} (1-\mathsf{r}\_{\varepsilon}) \cdot p^{j\varepsilon} \cdot \boldsymbol{d\_{j}^{\varepsilon}} \cdot (1+\mathsf{K}\_{\varepsilon})^{-(j)}} \\ &+ \frac{\sum\_{j=1}^{N} \boldsymbol{z^{j}}\_{j} \cdot (1+\mathsf{K}\_{\varepsilon})^{-(j)} + \boldsymbol{D}^{i}}{\sum\_{j=1}^{N} (1-\mathsf{r}\_{\varepsilon}) \cdot p^{j\varepsilon} \cdot \boldsymbol{d\_{j}^{\varepsilon}} \pi\_{j}^{R} \cdot (1+\mathsf{K}\_{\varepsilon})^{-(j)}} \end{split} \tag{A18}$$


**Table A1.** Corporate Finance Assumptions.
