Corporate Finance

Estimating the cost of capital with the Brennan-Lally Capital Asset Pricing Model

Nicole Vignaroli Nicole Vignaroli
21 May 2021
7 min read

25 May 2021

The Discounted Cash Flow (DCF) under the Income Approach is a commonly used valuation method. The DCF method derives the value of an entity based on the future cash flows of the entity discounted back to a present value at an appropriate discount rate or weighted average cost of capital (WACC)[1].

The discount rate used to equate the future cash flows to their present value reflects the risk-adjusted rate of return demanded by a hypothetical investor for the enterprise being valued. Selecting an appropriate discount rate is a matter of professional judgement and takes into consideration relevant available market pricing data and the risks and circumstances specific to the enterprise being valued.

Typically, the discount rate should:

  • Be forward looking.

  • Reflect the opportunity cost of capital of investment.

  • Be market determined.

  • Reflect the risks associated with the investment.

In estimating the expected WACC, it is necessary to estimate the expected cost of equity capital and the expected cost of debt capital. WACC is typically derived as post-tax nominal and must be matched to the cash flows to which it is being applied. In typical cases, this is already a requirement of representing post-tax nominal estimates.

In practice, the cost of equity component of WACC is normally estimated based on a fundamental ground-up analysis using one of the available models for estimating the cost of capital, such as the Capital Asset Pricing Model (CAPM). The cost of debt component of WACC is usually estimated by analysing the appropriate yields on the company’s publicly traded bonds or bonds of similar comparable companies.

Since the definition of fair market value is premised on the estimated value that a knowledgeable willing buyer would attribute to the asset or entity, the selection of an appropriate discount rate also needs to consider that buyers incorporate other alternatives to the typical CAPM approach in estimating the cost of equity and the resulting WACC.

This article focuses on the assessment of an appropriate cost of equity using a theoretical aid which is commonly adopted in New Zealand, but not widely known or adopted in other markets, the simplified / modified version of the Brennan-Lally Capital Asset Pricing Model (Brennan-Lally CAPM)


The expected cost of equity capital cannot be directly observed and therefore must be estimated by some means. Several models for estimating the expected cost of equity capital exist, however, each model has its limitations.

Traditional CAPM approach

The cost of equity using the CAPM is summarised in the formula below:

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CAPM calculates the minimum rate of return that the company must earn on the equity-financed portion of its capital to leave the market price of its shares unchanged. The CAPM is the most widely accepted and used methodology for determining the cost of equity capital.

The CAPM assumes, amongst other things, that rational investors seek to hold efficient portfolios, being portfolios that are fully diversified. One of the major conclusions of the CAPM is that investors do not have regard to specific company risks (often referred to as unsystematic risk). However, there are several empirical studies that demonstrate that the investment market does not ignore specific company risks.

The standard CAPM is the most commonly employed world-wide and is used locally for the ‘capital charging’ / allocation regime for New Zealand government departments. However, the most widely used version in New Zealand is a tax-adjusted CAPM which recognises differential tax treatment for capital gains, dividends and interest.

Simplified / modified version of the Brennan-Lally CAPM

The simplified / modified version of the Brennan-Lally CAPM is a specific model that is commonly used by practitioners in New Zealand. It is viewed as the preferred method for determining an appropriate cost of equity capital in certain New Zealand regulated industries.

The first version of a tax-adjusted CAPM was provided by Brennan (1970), whilst Lally (1992), amongst others, adjusted it for dividend imputation. The impetus for adoption of the tax-adjusted CAPM would appear to have been the introduction of dividend imputation in New Zealand, although other aspects of the tax system, in particular, capital gains tax, would also have justified it. Both the standard CAPM and the tax-adjusted-CAPM versions assume internationally segregated capital markets. This assumption is particularly difficult to sustain in New Zealand’s case, and accordingly CAPM versions without this restriction are appealing.

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Table 1 compares the model inputs of CAPM and the Brennan-Lally CAPM:



Brennan-Lally CAPM

Risk-free rate
Yield on government bonds, no tax consideration
Yield on government bonds, after tax risk-free rate (investor tax rate)
Equity beta
Equity beta
Equity Market risk premium
Equity Market Return minus the risk-free rate
Tax adjusted EMRP (Equity Market Return minus the tax adjusted risk-free rate)

Table 1: Comparison of CAPM and Brennan-Lally CAPM

New Zealand adoption and limitations

The simplified version of the Brennan-Lally CAPM is the preferred method of the Commerce Commission in determining the cost of capital for regulated companies in New Zealand. The theory upon which CAPM is based has a number of assumptions. In practice, many of the parameters used in the model and their values cannot be directly observed and therefore proxies must be used, with the associated measurement uncertainties.

New Zealand, in particular, has few utility service providers that are listed, credit rated, have publicly traded bonds and operate stand alone or “pure play” businesses. Therefore, it is necessary to use publicly available information, recognising its limitations and adopt caution in drawing definitive conclusions from this data.

Since both Australia and the United States use the standard CAPM, the Commerce Commission’s mid-range estimate for the EMRP in the Brennan-Lally CAPM can be converted to the standard CAPM. As noted by Lally, an EMRP of 7% under the Brennan-Lally CAPM equates to an EMRP of around 5% for the standard CAPM. Therefore, for purposes of estimating an EMRP, converting an estimate based on the standard CAPM to an estimate based on the Brennan-Lally CAPM requires an addition of c. 2%.

The Brennan-Lally CAPM is an after-investor-tax version. There are theoretical and application issues related to the model. For example, the average personal tax rate of investors must be estimated. The taxes are assumed to be those that pertain to New Zealand investors, and on average across all investors. Furthermore, the model assumes that the New Zealand economy is closed to international investors.

The Brennan-Lally CAPM in practice

The cost of capital covers all relevant opportunity costs. It is considered to be a fair rate of return that can be used as the allowed rate of return for regulatory purposes, which in turn determines regulated firms’ prices. It also acts as a tool to balance interests of various stakeholders such as infrastructure owners and consumers. Setting the rate of return too high will result in consumers paying too much and a lower rate would result in the firm unable to attract sufficient capital to undertake efficient investment. The cost of capital can have a significant impact on the earnings of regulated businesses due to its role in the setting of regulated prices.

Commercial businesses/ entities, however, use cost of capital to assist in selecting the return maximising investments. Unlike regulatory cost of capital, there is no direct link between a competitive firm’s cost of capital and the prices it can charge in the market.


The Brennan-Lally CAPM is a specific model that is commonly used by practitioners in New Zealand and is viewed as the preferred method for determining an appropriate cost of equity capital in certain New Zealand regulated industries. Whilst there are theoretical and application issues related to the model, it is still relevant for application in the New Zealand market. However, users should use professional experience in its application, and have close regard to its limitations, the source of inputs being relied upon and differences in the model as compared to the traditional CAPM approach.

Findex Corporate Finance has deep experience in assessing complex and varied Valuation issues, financial derivative assessment and liquidity event advice. For assistance with your Valuation requirements, Transaction considerations and Financial Modelling needs, get in touch with our Valuations experts.

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Nicole Vignaroli
Author: Nicole Vignaroli | Senior Partner