# Why You May Want to Consider Cash-Adjusting CAPM Betas

Could holding too much cash lead to misestimating the firm’s value? Yes, it could.

The financial press and investing websites have recently put the spotlight on firms that have large cash balances. The primary example cited is Apple Inc. (e.g., here and here). As of 30 September 2017, Apple had USD 285 billion of cash and marketable securities on its balance sheet.

There are reasons why a company may want to hold a lot of cash. For example, cash gives firms a cushion during periods when cash flows are volatile, provides flexibility to make opportunistic investments, and allows firms the choice not to raise funds during disadvantageous periods. On the other hand, there are costs as well, which include the cost of carry (i.e., investing in cash generates a lower return than the investor’s cost of capital) and agency costs (i.e., managers may invest in negative NPV projects when they hold a high level of cash). Regardless of the potential motives for holding a large amount of cash, one thing that is certain is that Apple does not need USD 285 billion in cash to operate its business.

The surplus cash beyond what the company needs for its operations is known as excess cash. When conducting fundamental valuation, excess cash is considered a non-operating asset that is added to the value resulting from a discounted cash flow (DCF) analysis of the operations of a business. Therefore, the appropriate discount rate used in a DCF analysis should be a rate that reflects only the risk of the operations of the firm. However, the common approach of using betas obtained by regressing historical returns incorporates the level of excess cash during the estimation period. That is, when we calculate Apple’s beta using a regression, that beta is a mix of Apple’s operating asset beta and excess cash beta. This mix leads to an understatement of the firm’s beta used to calculate its cost of equity (COE). I’ll use Apple’s data using a valuation date of 31 December 2017 to illustrate the valuation impact of this understatement.

## Cost of Equity with Unadjusted Betas

The most common model used to estimate the COE is the capital asset pricing model (CAPM), which states:

Equation 1: *COE* = *Rf* + *B*_{L} (*Rm* - *Rf*)

where *Rf* is the risk-free rate, *B*_{L} is the levered beta of the firm, and (*Rm* - *Rf*) is the equity risk premium (ERP). For our illustration, we assume *Rf* equals 2.58% and ERP equals 6.50%. One way to estimate the levered beta is to use the beta obtained by regressing Apple’s weekly return on the weekly return of the market, which we will proxy with the SPDR S&P 500 ETF, over a two-year estimation period from January 2016 to December 2017. This results in *B*_{L} = 1.16. Applying the CAPM in Equation 1 results in an unadjusted COE equal to 10.1%.

## Cost of Equity with Cash-Adjusted Betas

To cash-adjust the beta, recall that a portfolio’s beta is the weighted-average of the beta of the assets in the portfolio. This relationship holds in the context of the firm’s asset beta. In the current context, the firm’s asset beta, which is also known as the unlevered beta, is the weighted-average of the operating asset beta and the excess cash beta. As such, we begin by unlevering the *B*_{L} calculated above to estimate Apple’s asset beta. Since Apple’s credit rating is an Aa, which Moody’s defines as *high quality* and *subject to very low credit risk*, we can assume for purposes of our analysis that Apple’s debt beta is equal to 0 and, consequently, we can use the Hamada formula. The Hamada formula calculates the unlevered beta (*B*_{U}) as follows:

Equation 2: *B*_{U} = *B*_{L} / (1 + (1 - *T*) *D*/*E*)

where *T* is the marginal tax rate and *D*/*E* is the average debt-to-equity ratio over the regression period used to estimate *B*_{L}. We assume the marginal tax rate equals 35%. The average debt-to-equity ratio for Apple over the two-year beta estimation period is 13.2%, which leads to *B*_{U} = 1.07.

Then, given the definition of a portfolio beta described above, we can represent the unlevered beta as follows:

Equation 3: *B*_{U} = *w*_{C} *B*_{C} + (1 - *w*_{C}) *B*_{A}

where *w*_{C} is the percentage of excess cash to firm value (i.e., the sum of the firm’s debt and equity), *B*_{C} is the excess cash beta, and *B*_{A} is the operating asset beta. We are interested in finding the value of *B*_{A} given all the other inputs to Equation 3, which we obtain as follows.

First, we determine the firm’s average excess-cash-to-firm-value ratio (*w*_{C}) over the two-year beta estimation period. As outsiders, it is difficult to determine how much cash a firm needs for operations. For example, one commonly cited rule of thumb is to estimate operating cash as 2% of revenues and then subtract that amount from the cash balance. However, for the purposes of our example, we will use the amount of long-term marketable securities Apple reports in its SEC filings as an alternative proxy. Apple states that long-term marketable securities have maturities that generally range from one to five years and, as such, placing the cash in long-term marketable securities suggests that Apple does not need the cash to fund its operations, at least in the short term. Using this assumption, we find *w*_{C} for Apple equal to 24.2% over the two-year beta estimation period.

Next, we turn to estimating the excess cash beta. Textbooks suggest that excess cash beta is equal to 0 or virtually 0. We perform a test of the reasonableness of this assertion. Since our estimate of excess cash is based on long-term marketable securities with maturities of one to five years, we estimate *B*_{C} using the beta of the Vanguard Short-Term Bond ETF, which has an average duration of 2.7 years. Similarly to how we estimated Apple’s levered beta, we regress the returns of the ETF on the return of the SPDR S&P 500 ETF using weekly returns over the period January 2016 to December 2017. We find that the beta is -0.04. In general, excess cash can also be invested in short-term instruments, so we can also test the zero-excess-cash beta assertion using short-term securities. Using the PIMCO Enhanced Short Maturity Active ETF and iShares Short Maturity Bond ETF as proxies, we find betas of -0.01 and 0.00, respectively. Given the above, it appears reasonable to assume that the excess cash beta is 0.

Applying *B*_{C} = 0, we find Apple’s operating asset beta (*B*_{A}) as follows:

Equation 4: *B*_{A} = *B*_{U} / (1 - *w*_{C}) = 1.17 / (1 - 24.2%) = 1.41.

We can then use Equation 2 to find *B*_{L}, which in this case is Apple’s re-levered beta. To avoid complications, we ignore any potential implications of the new corporate income tax rate of 21% that went into effect on 1 January 2018 (link) in the re-levering process and assume the marginal tax rate remains the same at 35%.

In our illustration, we assume that Apple’s historical D/E is a reasonable proxy for its target D/E. However, we should subtract the excess cash from the equity in the D/E ratio because, if we add the excess cash to the DCF value we calculate, then the capital structure of the operating assets we are valuing in the DCF should not include the amount of excess cash. This has the effect of increasing the firm’s leverage for purposes of calculating the COE. The average cash-adjusted debt-to-equity ratio is 18.3% (compared to the unadjusted debt-to-equity ratio of 13.2%) and the Apple re-levered beta equals 1.58. Using Equation 1 and the same risk-free rate of 2.58% and ERP of 6.5%, we calculate a cash-adjusted COE of 12.8%.

## Illustration of Potential Valuation Impact

To understand whether such changes are meaningful, we should tie our illustration to some form of valuation impact. To calculate equity value using a DCF analysis, we typically (1) discount the free cash flows to the firm (FCFF) by the weighted-average cost of capital (WACC), (2) subtract debt, and (3) add excess cash. Therefore, as a first step, we need an estimate of the WACC and FCFF.

The WACC is the blended rate of the after-tax cost of debt and cost of equity. Assuming a pre-tax cost of debt of 3.0%, which is the yield on an index of Aa bonds, and a tax rate of 35% results in an after-tax cost of debt of 1.95%. Assuming the historical average leverage ratios are a good proxy for Apple’s long-term leverage, the unadjusted debt-to-capital equals 11.7% and the cash-adjusted debt-to-capital ratio (i.e., debt plus equity less excess cash) equals 15.4%. Note that the increased leverage has an offsetting effect (i.e., decreases WACC) because the cash adjustment puts greater weight on the cost of debt, which is lower than the cost of equity. This leads to an unadjusted WACC of 9.2% and a cash-adjusted WACC of 11.1%.

Projections of FCFF are more challenging to perform and require a complicated mix of facts, inputs, and assumptions. Purely for illustrative purposes, I borrow the 2018–2022 FCFF projections from here and also use the 10x terminal multiple the author uses. These projections yield a DCF value of operations as of 31 December 2017 of USD 747 million using the unadjusted WACC and USD 692 million using the cash-adjusted WACC.

To get to equity value, we subtract USD 116 million of debt and add USD 195 million in excess cash. The cash-adjusted equity value is USD 771 million. By contrast, the unadjusted equity value is USD 826 million, which is 7% higher.

There are two issues that are worth noting with the unadjusted equity value calculation. First, the overvaluation is in part due to double counting of the benefits of holding excess cash. The unadjusted equity value adds back excess cash to the enterprise value when we already benefit from a lower unadjusted WACC due to the inclusion of excess cash when calculating the beta. Second, instead of adding back only excess cash, it is common to find analysts adding back the entire cash balance. Since the entire cash balance is larger than the excess cash balance, doing so would lead to an even larger overvaluation.

## About the Author

Clifford S. Ang, CFA, is a vice president at Compass Lexecon, where he specializes in the valuation of businesses and hard-to-value assets primarily in the context of litigation. He is also the author of the financial modeling textbook *Analyzing Financial Data** and Implementing Financial Models Using R*, which is published by Springer (link here and here), and teaches courses on bond and equity valuation at DataCamp (link here and here). Additional information can be found on www.cliffordang.com or on his LinkedIn page.