For the risk adjustment of expected cash flows, the certainty equivalent cash flows replace the risky cash flows with risk-free cashflow. The certainty equivalent is, of course, lower than the uncertain cash flow and the bigger the risk, the higher the downward adjustment. If this adjustment is made, it is also necessary to use the risk-free rate as the discount rate since the cash flows are now risk-free.

De facto, it is extraordinarily difficult to assess the probability of distress and adjust the expected cash flows, hence. Not only do we need to estimate the probability of distress each year, but we also have to keep track of the cumulative likelihood of distress as well. This is because a firm that becomes distressed in year three loses its cash flows not just in that year but also in all subsequent years.

We assume that even in distress, the firm will be able to receive the present value of expected cash flows from its assets as proceeds from the sale.

This assumption implies that the firm has the bargaining power to demand fair market values for its assets. Additionally, it can not only do this with assets in place (investments made and products already produced) but also with growth assets (products it may have been able to produce in the future). However, firms in distress do not have the power to demand such values.

In summary, distress will not have a material impact on the value if any of the following three conditions hold:

- There is no possibility of distress because of the firm’s size, its standing, or there is a governmental guarantee.
- Firms with profitable investments have easy access to capital markets in order to raise equity or debt capital to sustain through bad times. This ensures that firms are never forced into a distress sale.
- The expected cash flows fully incorporate the likelihood of distress and the discount rate is adjusted for the higher risk associated with distress. As well, we assume that firms receive sale proceeds in the event of a distress sale that are equal to the present value of expected cash flows if the firm was a going concern.

However, it is likely that at least one of the three conditions do not hold. There are respectively sound arguments for that. First of all, even large, publicly-traded firms must fear the possibility of financial distress. Kahl (2001) has shown that 151 publicly traded firms in the US between 1980 and 1983 did experience financial distress. Secondly, the investment propensity has, however, risen again in recent years. Shown by McKinsey & Company, the global private equity deal volume has increased in the past decade from $0.3 trillion in 2009 by 366.67 % to $1.4 trillion in 2018. Finally, both input parameters, expected cash flows and discount rates, do not adequately consider the possibility of financial distress, as shown in the next section.

## How can financial distress correctly be considered in DCF valuation?

The following section will introduce the usage of the DCF model for the valuation process of distressed firms in practice and lead on with a framework on how to sufficiently consider financial distress.

Gilson, Hotchkiss, and Ruback (2000) analyze the market value of 63 firms that have filed for bankruptcy in the United States, have emerged from their bankruptcy as public firms, are listed on one of the world’s largest stock indices (NYSE, AMEX, or Nasdaq) and have two years of cash flow projections. They then compare these market values with their estimates for the firm values derived through a DCF valuation. Their DCF model, however, differs slightly from the previously introduced DCF models. Instead of using either Dividends, Flow to Equity or Free Cash Flow, they use Capital Cash Flows as their cash flow input, which is calculated as follows:

CCF=NI+cash flow adjustments+cash and noncash interest

Where CCF is the Capital Cash Flows and NI is the Net Income. This is due to the reason that the CCF is discounted at the rate of an all-equity firm with the same risk as a leveraged firm. Since the leverage is likely to change over time, it is easier to use the CCF, wherefore, the discount rate does not have to be adapted to such changes. Nevertheless, the CCF approach results in the same PV as the FCF discounted by the WACC.

As the discount rate, they use the unlevered cost of equity, consisting of the risk-free rate, which equals the long-term Treasury bond yield for the month of the PV date, the market risk premium, which they have calculated at 7.4 % and an unlevered beta of 0.35, obtained

The results of their study show that the valuation error in the DCF method is tremendous. Defined as the ratio of estimated value to actual value (i.e., (Estimated value)⁄(Market value)), it ranges from 17.6 % to 259 %. As well, only 25 % of the estimated values are within a range of 15 % of the actual market values. These extreme deviations cannot be solely due to lack of information or strategic biases in the cash flows, as they state. But rather because the distress was not fully incorporated in the valuation process.

As now found out, financial distress has an impact on the two relevant input parameters in DCF valuation, the expected cash flows and the appropriate discount rate. In consequence, both parameters can be modified in the DCF model to reflect the effects of financial distress. The second approach to fully incorporate financial distress is to deal with financial distress separately. Both methods are introduced in a framework by Damodaran (2006) and will be further assessed in this section.

## Modification of the DCF model

### Adjust future cash flows

First of all, the expected cash flows must be estimated correctly, meaning that the probability of financial distress must be included. Damodaran (2006) gives a short introduction on how to do so, which will be depicted in the following section. In order to reflect the full extent of financial distress, every possible scenario with a different likelihood of financial distress would have to be considered when calculating the expected cash flow. This must be done every year, when future cash flows occur, since every future cash flow and the probability of financial distress may change from year to year. He gives the formula as follows:

〖Expected cash flow〗_t=∑_(j=1)^(j=n)▒〖π_jt*〖Cash flow〗_jt 〗

Where πjt is the probability of scenario j in period t and Cash flowjt is the certain cash flow in scenario j in period t. The sum of all scenarios then gives the expected cash flow for that period.

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However, it is highly difficult to consider every possible scenario. Therefore, the formula is simplified towards only considering two scenarios. These are the going concern and the distress scenario. In the going concern scenario, expected growth rates and cash flows, which are estimated under the assumption the firm will survive, are used. IN contrast, in the distress scenario, the assumption is made that the firm is liquidated. The formula then looks like this:

〖Expected cash flow〗_t=π_(Going concern,t)*(〖Cash flow〗_(Going concern,t) )+

(1-π_(Going concern,t) )*(〖Cash flow〗_(Distress,t))

Where πGoing concern, t is the cumulative probability that the firm will continue to operate in period t. The probabilities for the distress scenario will have to be calculated subsequently for every year. Hence, we obtain:

〖Cumulative probability of survival〗_t=π_t=∏_(n=1)^(n=t)▒〖(1-π_(Distress,n))〗

Where πDistress,n is the probability of the firm becoming distressed in period t. To put this into context, a firm with the probability of distress of 30 % in period one and a probability of distress of 20 % in period two, would have a cumulative probability of surviving of:

Cumulative probability of survival over 2 periods = (1 - 0.3) * (1 - 0.2) = 0.56 or 56 %

Adjusting the future cash flows to the probability of distress is similar to the prior introduced method of the certainty equivalent cash flows. However, in this case, cash flows are not adjusted by fully cutting out the potential of risk, but rather by aiming to incorporate these risks of financial distress.

### Adjust the discount rate

The second adjustment that can be made is to estimate the discount rate correctly. Usually, the cost of equity is received from using the beta of the firm and the cost of debt by using the interest rates of bonds issued by this firm. However, there is one major problem for each discount rate.

In the case of the equity discount rate, the firm’s beta is estimated by a regression analysis of the historical stock-price data over a long period of time, often between two to five years. Nevertheless, the distress of the firm’s financial situation might only occur over a concise period. Thus, the firm’s beta will not fully consider the actual financial risk of the company. To obtain a more reasonable cost of equity, there are two approaches:

Adjust the CAPM betas for distress: Often used in the case of private companies, the approach for estimating the company’s beta is to look at the levered betas of comparable firms, that are similar in size, operations, and industry. By calculating the weighted average of levered betas, a proxy for the industry average levered beta can be obtained. This proxy then has to be unlevered by using the leverage of the comparable firms. Finally, this unlevered industry average is then re-levered with the firm’s leverage. Since distressed firms often have an extraordinary high leverage, this will lead to a high levered beta as well, which considers the financial distress situation more properly. The following shows the formula for calculating the levered beta:

β_L=β_U*(1+(1-T)*L)

Where β_L is the levered beta, β_U is the unlevered beta, T is the tax rate, and L is the firm’s leverage.

Since a distressed firm does not get any tax advantages, the levered beta rises even more. With a much higher beta, the cost of equity increases and in consequence, the PV of expected cash flows is lower.

Use distress factor models: Since the fundamental CAPM formula already accounts for the systematic risk in the cost of equity, it can be extended by a distress factor to as well amount for distress risk. This would increase the cost of equity and accordingly lower the PV of expected cash flows.

The problem concerning the cost of debt is that it is solely based on promised cash flows and not on expected cash flows. This is due to the reason that in DCF valuation, the going concern assumption is made, which is why future cash flows are assumed to occur definitely. The interest rates of corporate bonds, which depict the cost of debt, are based upon these promised cash flows, whereby the yield to maturity of corporate bonds of financially distressed companies is extraordinarily high. A solution to this problem is to base the cost of debt on the firm’s bond rating. These are ratings given to bonds by private credit rating agencies, the three leading agencies being Fitch Ratings Inc., Moody’s Investors Service, and Standard & Poor’s, indicating the credit quality of the bonds. The ratings are based on the issuer’s ability to pay for bonds interest expenses and on its financial health. This solution still leads to a very high cost of debt, nonetheless lower than the yield to maturity in the case of financial distress.

Now that both, cost of equity and cost of debt, have been adjusted to the possibility of financial distress, the cost of capital, consisting of them both, must be adjusted as well. For that, the weights of respectively equity and debt must be estimated. In the initial period, the current debt to total capital ratio (i.e., Debt⁄(Total Capital)) is a reasonable selection. For distressed firms, this ratio is usually tremendously high. For every future period, the weights of equity and debt must be forecasted again, since the financial situation of the firm is likely to change with improvements in profitability. Consequently, the debt ratio is expected to shift towards lower, more reasonable levels.