In a previous post, I said Woodlawn Associates believes solar project sponsors (i.e., equity investors other than tax equity) expect to earn an 811% aftertax internal rate of return on their investments. As I said in that post:
Whether 811% is a good deal for the financier depends on its cost of capital. If a financier’s cost of capital is 10%, the net present value of its investment is essentially zero. On the other hand, if its cost of capital is 57%, the NPV of each solar system is several thousand dollars.
So how does one determine cost of capital for a project sponsor? First, we have to understand what we mean by “sponsor”. I use the term to mean the company that invests regular equity in project companies, which is usually a holding company subsidiary of a parent solar financing company:
Figure 1: Simplified Subsidiary Structure of Solar Finance Company,
and Sources of Capital
In this post I will first examine the cost of capital for project companies and then for sponsors/holding companies (the green boxes in Figure 1).
To do this type of analysis requires one to make a fair number of judgment calls about the correct values for certain inputs. Reasonable people may disagree about the particular values that should be used, and in any event they often vary over time. For efficiency, in this post I occasionally assert some such values. My intention is not to assert the oneandonly correct values, or the values that are correct right now, but to describe an overall approach to determining cost of capital that I believe to be sound. I would welcome discussion around alternative approaches or refinements.
Cost of Capital for Project Companies
Adjusted Present Value
A useful tool for determining the cost of capital for project companies is adjusted present value, or APV. Using APV, we calculate the value of a company by adding its value as if it were financed entirely with regular equity to the additional value created by using a particular type of financing. Once we have an APV, we can calculate the cost of capital.
To calculate APV for a solar project company we:
 Start with the investment required.
 Estimate the value of the aftertax cash flows from the project as if the sponsor were the only investor.
 Estimate the value of the benefits from using tax equity (net of transaction costs).
 Estimate the value of the tax benefits from using debt (net of transaction costs).
The sum of all this is the overall value of the enterprise, given how it is financed. For simplicity in this post let’s assume a project company with no debt. Debt is uncommon within project companies used for distributed solar. Formulaically, then, our APV will be:
Cost of Sponsor Equity if sponsor is only investor
To calculate the PV of the project as if it were financed will all sponsor equity, we need to know cost of sponsor equity for a company with no tax equity. The most widely accepted way to calculate the cost of equity is with the Capital Asset Pricing Model, or CAPM. It says an asset’s cost of equity is:
Where:
r_{asset} = the cost of equity for a firm financed with only equity
(i.e., the rate of return required for the underlying assets, since there is no leverage)
r_{f} = the riskfree rate of return
r_{m} = the expected return from equity in general
β_{asset} = a measure of an asset’s riskiness compared with assets in general
To avoid a long digression, let me assert some reasonable values:
r_{f} = 2.87%, the rate on the 10year U.S. treasury bond
r_{m}– r_{f} = 6%
β_{asset} = 0.5
The average asset beta for U.S. companies is 0.64 (per Aswath Damodaran at NYU). By comparison, Woodlawn Associates estimates the asset beta for U.S. regulated utilities to be 0.28. The asset beta for distributed solar assets should be between these two figures. Distributed solar projects typically have longterm contracted cash flows, so their beta should be lower than the market, but their returns are not moreorless guaranteed, like those of regulated utilities. As stated, we will use 0.5 in our example.
With those key values, we can calculate the cost of equity:
Calculating APV: An example
Now let’s calculate APV for a hypothetical project company. Recall the formula:
Suppose:
 We have a project with 3643 residential solar systems that requires a total investment of $100M.
 We forecast hypothetical aftertax cash flows from our solar assets as if they were financed with all sponsor equity and discount them at r_{asset}. We get $80M. ($80100 = don’t do this project without tax equity!)
 We forecast the additional cash flows that would be generated by our project if we use tax equity. We discount these at r_{asset} and get $44M. (Actually, using r_{asset} here is a simplification. Contact me if you want more details.)
The $100M investment generates total cash flows with a present value of $124M: $80M as an allequity project and $44M more with taxequity financing. The adjusted present value is:
Adjusted Cost of Capital
Now we can estimate the overall cost of capital for the project company. We simply take the project investment ($100M) and the sponsorequityonly cash flows from above and calculate the discount rate that will give us the same APV we calculated for our project with tax equity ($24M). In the example we set up, this turns out to be about 1.1%. This seemingly low cost of capital is reflecting the benefits of the tax equity financing.
We can use this adjusted cost of capital (r*) as a hurdle rate for similarlyfinanced projects, or to directly calculate their APVs. However, we should only use this for projects with very similar financial structures.
Why not WACC?
One of the most common tools in financial evaluations is weighted average cost of capital, or WACC. The formula for WACC is usually given as something like:
Where:
WACC = the weighted average cost of capital
r_{e} and r_{d} = the cost of equity and debt capital, respectively
E and D = the market value of the company’s equity and debt, respectively
V = E + D = the company’s total enterprise value
T = the marginal corporate tax rate
It might seem straightforward to simply replace the factors for debt in the above equation with some for tax equity and use this formula instead of calculating r* through APV. However, there are two problems with this.
First, the term (1T) accounts for the fact that companies can deduct interest from their taxable income—this is a tax benefit of using debt. However, in the case of tax equity the tax benefits change from period to period. They are quite significant when the tax investor is using the ITC in the first year of the project. They are lower—but still substantial—over the next several years, while the tax investor continues to benefit from accelerated depreciation. But they are much smaller (or even negative) during subsequent years. Thus it would be difficult to use the WACC formula because there is no stable factor, such as (1T), we could use to estimate the tax benefits consistently over the life of the project.
Second, the WACC assumes the relative ratio between the values of equity and debt are constant over the life of the project. Unfortunately, in a solar project company the relative ratios of the value of the tax equity and sponsor equity positions change a lot over the life of the project. This is expected and is proscribed in their partnership agreements, but it makes it difficult to use WACC.
Cost of (Levered) Equity
What project sponsors care about more than the cost of project capital is the value of their cash flows—the cash flows coming out of the project company and going to the holding company (see Figure 1). To calculate that, though, we need to know the cost of equity for the project given the way it is actually financed.
Most sponsors think of tax equity as a form of leverage because tax equity is, to some extent, senior to sponsor equity. We can modify the CAPM formula above to account for this additional risk to sponsor’s cash flows, calculating the cost of this “levered” sponsor equity as:
β_{levered} is a beta that reflects the additional risk of being subordinate to other stakeholders. Finance theory tells us how to make a levered beta from an asset beta:
Where:
T = the market value of tax equity
E = the market value of sponsor equity
Unfortunately, we now find ourselves in a somewhat sticky situation. This is not a publicly traded firm where we can just look up the market value of its securities. Our alternative is to estimate the values based on the cash flows each party receives, but the discount rates we need to calculate theses values apparently depend on the values themselves!
We can use an iterative approach to solve this problem. We start by creating preliminary estimates of the value of sponsor equity and tax equity in each period by discounting the cash flows they will subsequently receive at r_{asset}. This creates a certain ratio of T/E, which we can use to create a levered beta for sponsor equity and revised value estimates for each stakeholder. If we feed these revised value estimates back into our equations, the ratio of T/E changes slightly and results in a new estimates for market value. However, the before/after values for each stakeholder converge within a few iterations. Using this approach, we can estimate T/E, β_{levered}, and r_{levered} for each period. Figure 2 shows some examples from a few periods in our example project:
Figure 2: Changes in r_{levered} as Project Progresses

Inception 
Quarter 4 
Quarter 24 
PV_{total CF} 
$124M 
$81M 
$64M 
T 
$49M 
$16M 
$1M 
E 
$75M 
$65M 
$63M 
T/E 
0.67 
0.25 
0.02 
β_{levered} 
0.83 
0.63 
0.51 
r_{levered} 
7.87% 
6.63% 
5.92% 
Overall, the weighted average r_{levered} for our project turns out to be about 6.2%. This is higher than r_{asset} because the sponsor’s cash flows are to some degree subordinate to tax equity’s cash flows. However, the effect is relatively modest because T/E drops quickly as tax equity receives the ITC and benefits of accelerated depreciation in the first few years of the project. The overall β_{levered} turns out to be 0.55.
Interim Conclusions
Before we look at the cost of capital for a holding company that owns several projects like this, let’s look at what we have concluded so far (Figure 3):
Figure 3: Beta and Cost of Capital for Example Project Company
The cost of capital for the project company is 1.2%, reflecting the tax benefits that are only captured if the project has a tax equity investor. The cost of sponsor’s equity for this project is 6.2%. If we had similarlyfinanced projects with IRRs of 811% on the sponsor’s cash flows, we could conclude they were valueproducing for the sponsor.
Cost of Capital for Holding Companies
Now let’s estimate the cost of capital for a holding company that owns several projects like the one we just described. Let’s also assume this holding company has some debt.
In calculating the cost of capital for the project and for sponsor equity above, we used APV because of the shifting tax equitytoequity value over time. However, if our holding company is going to maintain a constant debttoequity ratio over time—issuing or calling debt or equity as necessary—then we can safely use a weighted average cost of capital (WACC):
(If the firm’s debttoequity ratio is not expected to remain constant, we would use the APV approach instead.)
Cost of Equity in Holding company
From our work before, we develop the formula for cost of equity in our holding company to be:
And
But what is the right value to use for β_{leveredholding}? First, we need a beta consistent with the volatility of cash flows of this asset (which consists of several project companies). Second, we need to adjust for the amount of leverage.
We used an asset beta of 0.5 for our project company, but beta averaged 0.55 for sponsor equity of that company because we considered tax equity to be a form of leverage. The fact that the holding company has cash flows from several project companies, however, means its overall volatility should be lower. Let’s assume for this post that the unlevered beta for the holding company should be 0.5, but the actual value would depend on the number and relative size of projects the holding company owns and on the correlation of their cash flows with one another.
Now we need to lever the beta. SolarCity LMC Series I LLC, an indirect subsidiary of SolarCity and the issuer of debt in its recent securitization transaction, issued $54M in debt against assets worth $88M, so it’s debttoequity ratio was 1.59. Let’s use that in our calculations. Adopting the same formula for levered beta we used before, we get:
Now we have all the pieces we need for the cost of levered equity of our holding company:
Cost of Debt
The debt in SolarCity’s recent securitization carried an interest rate of 4.80%. Though there are nuances here, let’s assume 4.8% as the cost of debt for our example holding company. (To be precisely correct, one would use a cost of debt that reflects both the promised rate and the historical default and recovery rates for BBBrated bonds. In practice the difference will be small.)
Weighted Average Cost of Capital
Using our formula for WACC_{h}:
Coincidentally, SolarCity has been using 6% as the discount rate for its retained value calculations in investor presentations.
Recall that the (1T) factor accounts for the tax deductibility of interest on the debt. If our holding company or its parent is not profitable (like SolarCity), it may not be able to use this benefit for quite some time. This effect would be relatively modest, however (WACC would be ~7%), and there may be mitigating factors. For example, SolarCity might have placed some assets in the securitized portfolio whose subsidies have already been monetized, resulting in lower effective leverage and lower cost of equity.
Summary: The Solar Cost of Capital
Finally, let’s look at our overall conclusions (Figure 4):
Figure 4: Beta and Cost of Capital for Example Project Company and Holding Company
In addition to the cost of project capital of 1.2% and sponsor’s cost of equity capital in the project of 6.2%, we now know the sponsor’s overall cost of capital is 6.0%. The relatively low cost of debt and the additional tax benefits received from using it each play a part in this reduction.
As we saw in our calculations throughout this post, a major determinant of the cost of equity is the expected volatility of the assets’ cash flows. The cost of debt is also a function of the expected risk in the cash flows. Therefore, the best path to reducing the cost of capital is to reduce actual or expected cash flow volatility from the assets. In solar, this may happen organically as investors gain more experience with the asset, but sponsors may be able to accelerate this by clearly presenting historical asset performance, diversifying the asset mix geographically or by customer type (commercial, government, residential), or even by including different types of assets in the portfolio (such as utilityscale wind, solar, or gas assets).
I would be happy to discuss the details of this analysis. Woodlawn would also be happy to perform custom analyses. Give me a call or send me an email.
Woodlawn would be happy to assist you with any questions about energy project finance. Please contact or Josh Lutton.
Leave a Reply