Excerpt

## Contents

**List of Abbreviations**

**List of Symbols**

**List of Tables**

**1 Introduction**

**2 Valuation of loss carryforwards**

2.1 Fundamentals of business valuation

2.2 Literature review

**3 DCF valuation methods**

3.1 The WACC method

3.2 The APV method

3.3 The Flow-to-Equity method

**4 Example case**

4.1 Assumptions and simplifications

4.2 The indirect method

4.2.1 The WACC method

4.2.2 The APV method

4.2.3 The Flow-to-Equity method

4.3 The direct method

4.3.1 The WACC method

4.3.2 The APV method

4.3.3 The Flow-to-Equity method

4.4 Interpretation of the results

**5 Conclusion**

**References**

## List of Abbreviations

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## List of Symbols

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## List of Tables

1 Pro Forma Income Statement for Company 1, 2019-2024

2 Free Cash Flow Forecast for Company 1

3 Pro Forma Income Statement for Company 2,2019-2024

4 Free Cash Flow Forecast for Company 2

5 Indirect Method: WACC (Company 1)

6 Indirect Method: WACC (Company 2)

7 Indirect Method: Unlevered Value (Company 1)

8 Indirect Method: Levered Value according to APV Method (Com pany 1)

9 Indirect Method: Unlevered Value (Company 2)

10 Indirect Method: Levered Value according to APV Method (Com pany 2)

11 Indirect Method: Flow-to-Equity (Company 1)

12 Indirect Method: Flow-to-Equity (Company 2)

13 Direct Method: WACC

14 Direct Method: APV

15 Direct Method: Flow-to-Equity

## 1 Introduction

If a company wants to acquire another business or if investors want to buy shares of a publicly traded entity, it is important to determine the intrinsic value of this company. By doing this, investors can determine a maximum price they are willing to pay, so that the investment creates financial value for them. There are different methods business analysts can apply for company valuations. This thesis concentrates on the Discounted Cash Flow (DCF) analysis. More specifically, it is worked with the Weighted-average Cost of Capital (WACC) method, the Adjusted Present Value (APV) method, and the Flow-to-Equity method . In addition, the focus is on tax loss carryforwards and the problem of how to incorporate the valuation of them into a DCF framework . If a company had losses in the past, it can carry these losses forward to reduce taxable income in future periods. Thus, using loss carryforwards in future periods increases net income in these periods, because less taxes must be paid. Since applying the DCF method discounts future free cash flows and not future net incomes, it may prove difficult to include loss carryforwards in the DCF analysis. Generally, two approaches are accepted for valuing loss carryforwards. One can either indirectly or directly determine the value of loss carryforwards. The indirect approach would be to compute the value of an identical firm with and without a loss carryforward and then to subtract the difference between these two firm values (Piehler and Schwetzler, 2010, pp. 94-95). One issue arising hereby is which discount rate to use for the business valuation. Especially since in the periods where taxable income is reduced to zero, the interest tax shield is not applicable. The difference between the firm value of the company with a loss carryforward and the identical company without one, can be interpreted as the value of the loss carryforward. However, the increase in firm’s value is not necessarily distributable to equity investors, since it could also be coming from an increase in debt capital and not only from an increase in equity value. Therefore, the question remains if the increase in entity value or the increase in equity value is relevant for determining the value of the loss carryforward, when the indirect method is applied. The direct method requires discounting the future tax savings that are caused by the loss carryforward (Piehler and Schwetzler, 2010, p. 95). Here too the issue needs to be addressed, which discount rate to use for the valuation.

The thesis starts by explaining the fundamentals of business valuation and how the three DCF methods work. After that, a literature review is presented. The purpose of the literature review is to show the strategies others have developed to value loss carryforwards correctly.

To show how to incorporate the valuation of loss carryforwards into a DCF framework, an example case was designed that involves two identical companies. Both of them would have the exact same expected stream of future free cash flows, however, one of them has a tax loss carryforward. Cost of capital for the businesses is given and is the same for both companies. The WACC method, the APV method, and the Flow-to-Equity method are applied and combined with the direct, as well as, the indirect method. When the results of the direct method are compared with the results of the indirect method for each one of the three DCF methods, it should be possible to draw a conclusion of which of these approaches works, and gives a correct solution, and which one does not.

The purpose of this bachelor thesis is to solve the problems mentioned above. This is why the example case ignores specific tax laws that prohibit the unrestricted application of loss carryforwards in future periods. This makes it easier to only focus on the problems that are addressed and to not go beyond the constraints of this thesis.

## 2 Valuation of loss carryforwards

### 2.1 Fundamentals of business valuation

The DCF analysis considers the time value of money. This concept states that money received today is worth more than money received in the future because of the opportunity cost of capital (Nürnberg, 1972, p. 655). Money received today can be invested earlier and thus a positive rate of return can be earned sooner. The discount rate used in the DCF analysis is the rate of return investors can expect from the best (meaning highest rate of return) alternative investment with similar risk characteristics (Titman and Martin, 2011, p. 98). With the DCF analysis one can compute present values of a stream of cash flows. The present value can be interpreted as the value added in the current period from the stream of cash flows earned in the future (Ross et al., 2016, p. 274). The cash flows that are discounted in a DCF valuation are after-tax cash flows. This means that the tax expense has been subtracted. The DCF valuation generally assumes that the tax expense can be computed by multiplying taxable income by the negative tax rate. If taxable income is positive, the tax expense will be a negative amount. However, if taxable income is negative, the tax expense will be a positive amount. A positive tax expense can be interpreted as money received from tax authorities. This implies that in the DCF framework it is assumed that there is an immediate loss compensation from the government (Das Wirtschaftslexikon, n.d.). If, for example, the tax rate is thirty-five percent and a company has a negative taxable income of €100, their tax expense is equal to €35.

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Hence, the government pays the business €35 as immediate loss compensation. In most countries there is no such policy. In the United States, Germany, and most other countries, companies can carry back and carry forward losses to reduce their taxable income in other periods. So, instead of receiving money from the government in periods with negative pretax cash flows, companies can use their tax loss to pay less in taxes in periods with a positive pretax cash flow.

The cash flows that are discounted when applying the DCF analysis are called free cash flows. This is because they are distributed to the investors of the company and not needed by the company for investments in working capital or fixed assets (Ross et al., 2016, p. 34). For the business to remain a going concern, it needs to reinvest parts of the cash that is generated by the assets of the company into new assets. All the rest is assumed to be available to equity and debt investors. To calculate free cash flow (Berk and DeMarzo, 2017, pp. 322-323), one can start by adjusting net income. The first step in doing so, is to determine unlevered net income, which is equal to net income assuming the firm is only equity financed. This is done by adding after-tax interest expense. Next, one must add back depreciation, since it is a non-cash expense. To finally receive free cash flow of the firm, increases in net working capital and capital expenditures must be subtracted as well. Net working capital is the difference between current assets and current liabilities (Ross et al., 2016, p. 22). If the business has increased net working capital during the period, it means that more current assets have been acquired, or that current liabilities have been paid back, or both. So, if net working capital has increased, cash outflows have occurred that were not recorded as an expense in the income statement. Capital expenditures are also cash outflows not reported as an expense (Berk and DeMarzo, 2017, p. 273).

If the three DCF methods addressed in this thesis are being applied, there must be a differentiation between entity value and equity value (Ballwieser and Hachmeister, 2016, p. 137). The WACC method and the APV method determine the value of the entire entity, whereas the Flow-to-Equity method computes only the value of a firm’s equity. The future free cash flows to equity investors are discounted when this method is used (Berk and DeMarzo, 2017, p. 684). If a firm is fully equity financed, entity value and equity value would be alike. But with the inclusion of debt capital, entity value equals equity value plus the market value of debt capital (Streitferdt, 2004, p. 675).

### 2.2 Literature review

The purpose of the literature review is to show the strategies that are presented in the literature on how to value loss carryforwards accurately. Piehler and Schwetzler state that company value is influenced by the ability of a business to generate future free cash flows for its shareholders. Since loss carryforwards reduce future tax payments and hence increase future free cash flows, their impact on company value is positive. Piehler and Schwetzler mention that there are two general approaches in valuing loss carryforwards (Piehler and Schwetzler, 2010, p. 61). One can determine their value indirectly or directly. The indirect approach is to compute the value of the loss carryforward as the difference between the enterprise value of the same company with and without a loss carryforward. For the direct approach, one must determine the present value of future tax savings, which is the value of the loss carryforward. The transferability of loss carryforwards in the scenario of mergers and acquisitions is very limited (Meitner and Streitferdt, 2011, p. 79). This is why an acquiring company might attribute a smaller value to the loss carryforward of a company it intends to acquire than the seller of this company. Situations like this show, why the precise assessment of loss carryforwards is important.

In practice, the direct valuation of loss carryforwards is often simplified. One approach is to multiply the nominal value of the loss carryforward with a fixed tax rate. This method is not theoretically sound and leads to inaccurate values, since the value of a loss carryforward depends on the amount of taxable income in future periods, which is not considered by this method (Meitner and Streitferdt, 2011, p. 87). Another practical solution is to discount expected future tax savings induced by the loss carryforward with the cost of equity capital of the business. This is in line with Popp. He suggests using the company’s cost of capital for determining the entity value of a firm with a loss carryforward as well as for the separate valuation of a loss carryforward (Popp, 1997, p. 211). His approach is based on a judicial decision by the OLG Düsseldorf (Higher Regional Court of Düsseldorf), which stated that using a loss carryforward to save taxes has the same risk characteristics as the operational activities of the business (OLG Düsseldorf, Decision of April 11, 1988, p. 1111). Meitner and Streitferdt however argue that this method generally leads to incorrect results, because in the case of uncertainty, the company’s cost of capital and risk-adequate discount rates for the expected future tax savings do not correspond (Meitner and Streitferdt, 2011, p. 87). The risk characteristics of future tax savings are not the same as the risk characteristics of future tax bases (Meitner and Streitferdt, 2011, p. 89). This is due to a downward and an upward limit of the tax savings for each period. The upward limit is the nominal value of the unused loss carryforward at the beginning of the period multiplied by the tax rate. The downward limit is zero. The tax base, however, can take any value in future periods. The upward limit of the tax savings for each period is dependent on the development of the tax base in previous periods. Therefore, the tax savings caused by a loss carryforward are path dependent. None of the practical solutions considers this sufficiently (Meitner and Streitferdt, 2011, p. 89). The application of the company’s cost of capital as the discount rate for future tax savings underestimates the value of the loss carryforward (Piehler and Schwetzler, 2010, p. 96). Thus, since loss carryforwards influence the risk characteristics of future free cash flows of the business and hence also its cost of capital and cost of equity capital, the value of the loss carryforward is needed beforehand when conducting a business valuation, so that the risk-adequate discount rates can be determined (Meitner and Streitferdt, 2011, p. 83). This is why computing the value of a loss carryforward as the difference between two company values is redundant and has no advantage over calculating it separately (Streitferdt, 2004, p. 675).

Another way to value loss carryforwards, is to treat the tax savings from a loss carryforward as an option (Piehler and Schwetzler, 2010, p. 68). If the loss can only be carried forward for one period, it is like a European call option with a cap (Piehler and Schwetzler, 2010, p. 67). The cap is the amount of the loss carryforward that is available at the beginning of the period. The underlying asset is the tax base, and the strike price is zero. This valuation method however becomes very complex if more than just one future period is considered (Piehler and Schwetzler, 2010, p. 77).

To factor in the path-dependency of loss carryforwards, Piehler and Schwetzler suggest using a binomial tree, to forecast the tax base (Piehler and Schwetzler, 2010, p. 74). To solve for the value of the loss carryforward, one must recursively solve the binomial tree. If the loss carryforward can be used for more than two periods, simulation models must be used that calculate trajectories for the tax base (Piehler and Schwetzler, 2010, p. 79). It is suggested to use Monte-Carlo simulations for future tax bases, especially since the path dependency of future tax savings requires multiple scenarios with different development paths for future tax bases (Meitner and Streitferdt, 2011, p. 90; Piehler and Schwetzler, 2010, p. 95). Meitner and Streitferdt define Earnings before Interest and Taxes (EBIT) as the tax base and forecast future EBIT using the risk-neutral probability distribution. The stochastic process they recommend for determining the risk-neutral probability distribution, is the arithmetic Brownian motion. The risk-adequate discount rate for the risk-neutral expected value of an uncertain future payment is the risk-free interest rate (Meitner and Streitferdt, 2011, p. 91).

Since the purpose of this thesis is to solve the problem of valuing loss carryforwards with the help of standard DCF methods, it is important to disregard the path dependency of future tax savings and to assume that future tax savings and future tax bases have the same risk characteristics, so that the company’s cost of capital can be used as the discount rate. This is a very simplifying assumption (Streitferdt, 2004, p. 679). However, since net income needs to be forecasted to project future free cash flows to determine the tax expense, it seems reasonable that also the settlement of the loss carryforward can be predicted. Following the rationale of the DCF analysis, one should assume that a business uses its loss carryforward as early as possible and reduces the forecasted taxable income by as much as possible for as long as possible.

With loss carryforwards there are two different tax effects. One is that loss carryforwards include a tax advantage that is independent from the financing. The other one is that loss carryforwards might influence the tax advantage of debt financing (Streitferdt, 2004, pp. 677-678). The reason for the second effect is that interest expense might not be tax deductible, since the loss carryforward reduces taxable income to zero. To forecast these tax effects of loss carryforwards correctly, the company valuer must project how the loss carryforward will be used in future periods. As it is mentioned above, this does not pose an additional challenge to the valuation process. Even if a business does not have a loss carryforward, future taxable income must be predicted to compute future free cash flows. If future taxable income is known, it can be projected how the loss carryforward will be used in the future (Streitferdt, 2004, p. 678).

Piehler and Schwetzler also write about the factors that influence the value of a loss carryforward (Piehler and Schwetzler, 2010, p. 95). A greater tax base has a positive impact on the value of a loss carryforward, because the tax savings can occur earlier on and thus have a greater present value. And if the lifetime of the loss carryforward is restricted, it becomes more probable with a larger tax base that the loss carryforward can be fully used in time. Also, the greater the nominal value of a loss carryforward is, the greater is its contribution to enterprise value, since less taxes must be paid in the future. The length of the lifetime of a loss carryforward correlates positively with its value as well, since it becomes more probable that the loss carryforward can be used completely before it becomes invalid. The higher the level of indebtedness of a company is, the lower the value is of its loss carryforward. This is because the higher the debt level of a business is, the larger are its future interest payments. They are subtracted from the tax base before the loss carryforward is. And the smaller the tax base is, the longer it takes until the loss carryforward is used. According to the reasoning of the DCF method, tax savings that appear later in time have a smaller present value than tax savings that appear earlier in time (Meitner and Streitferdt, 2011, p. 84). However, if the returns from the additional assets financed by debt capital are greater than interest payments, the impact on the value of the loss carryforward is positive (Piehler and Schwetzler, 2010, p. 87).

## 3 DCF valuation methods

### 3.1 The WACC method

The WACC method is a DCF analysis that can be applied for a levered firm. It assumes when determining the cash flows that the business is fully equity financed, but then incorporates the impact debt financing has in the discount rate (Ballwieser and Hachmeister, 2016, pp. 138-139). To determine the WACC of a levered firm, it is necessary to know its capital structure. The cost of equity capital and the cost of debt capital of a business differ. Equity capital usually bears higher costs, since equity investors demand a higher rate of return than debt investors do (Berk and DeMarzo, 2017, p. 530). The reason for this is that equity investments are considered riskier. This is due to the fact that if a business becomes insolvent, debt investors have a higher priority in getting their money back. Equity investors are more likely to lose all their invested capital in the case of bankruptcy. If a business increases leverage, one might think that the cost of capital of the entire business decreases, since the proportion of debt capital increases. However, Modgliani and Miller’s first proposition states that a company cannot change its value due to changes in its capital structure (Berk and DeMarzo, 2017, p. 525; Ross et al., 2008, p. 429). One reason is that equity cost of capital increases, if leverage increases, which is what Modigliani and Miller’s second proposition declares (Berk and DeMarzo, 2017, p. 531; Ross et al., 2008, p. 431). Increased leverage leads to more payment obligations for the business and thus greater risk for equity investors that the business might become unable to meet its payment obligations. If the capital structure of a corporation is known, one can compute its WACC, which is the weighted average of the equity cost of capital and the debt cost of capital (Ross et al., 2008, p. 491). It also incorporates the tax advantage of debt capital, which is that interest payments are tax deductible, whereas dividend payments are not. This is called the interest tax shield. The WACC can be calculated as:

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**[...]**

- Quote paper
- Ruben Kuhnle (Author), 2019, Valuation of loss carryforwards in the context of business valuation, Munich, GRIN Verlag, https://www.grin.com/document/512988

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