Switch Option to Shut Down Example

Problem Framing

In this post I want to give a simple example of a switch option to shut down operations. Project management can decide each year whether to continue production or shut down operations in this year. If operations is shut down, management can generate cost savings by reducing fixed costs. If considered production continues, the project can generate additional revenues and contribution cash flows.
The project lifetime is 10 years, the WACC of the market contribution cash flows is 10.0% and constant over time. The contribution cash flows are shown in the graph below. The default (or risk) free rate is 5.0%. The switches between the mode of operation to the mode of shut down require costs in both directions. Switch costs, contribution cash flows and savings are shown in the table. Savings and switch costs increase with an inflation rate of 1.5% per year.

Swith Option to Shut Down Valuation

We want to give answers to the following questions: What is the value of this option to switch between the two modes? When do we have to switch between operation and shut down to get the maximum value added to the project?

DCF analysis provides a present value of the market contribution cash flows of 461 million EUR. A Monte-Carlo-Simulation provides a project volatility of 0.30. We want to analyze this switch option with the binomial approach of Cox-Ross-Rubinstein. As time periods we take one time step per year, so that you can read the figures in the lattice properly. For higher accuracy we could take smaller time periods anytime.

Below you can have look at the two binomial lattices. The first value at each node is the value of the underlying (market contribution cash flows). The second value is the value of the underlying including the switch option value. In the third line you can see whether you have to take the option and switch to the other mode or not. “Sw” means to switch to the other mode, “go” means to stay in the mode.

Binomial tree of the project’s active operation mode
Binomial tree of the project’s shut down mode

Beginning the project with the mode of operation (production), the value of the project including the option is 513 MEUR. That is 52 MEUR higher than the value of the project without any option (461 MEUR). Hence the option adds a value of 52 MEUR to the project, the ROV (real option value) is 52 MEUR. That is also the maximum that project management should invest in having the option. If you start the project with the shut down mode, the value added is only 33 million EUR.

The value added of 52 million EUR means that the NPV of the classical DCF analysis may convert from negative to positive because of this additional value. That could lead to a reconsidering of the project decision. The ENPV (expanded NPV) is the NPV of the project plus the value of the switch option. The savings of the shut down mode must be separate outgoing cash flows of the DCF analysis. They have to be discounted with the default free discount rate of 5.0%, because the savings are part of the project’s fixed costs. That is consistent to the component cash flow procedure (CCFP) approach. Investment and fixed costs cash flows have to be discounted with the default (or risk) free discount rate and not with the WACC of the market contribution cash flows.

In the binomial lattices you can also see what you have to do in which situation in the 10 years. Depending on the economic development, you should stay in the mode or switch to the other mode. This is a practical guideline for project management.

Additional Remarks

I constructed the event tree of the project’s contribution cash flows out of a Monte-Carlo-Simulation. Of course you can also create the nodes of the event trees by calculating the time values of the outstanding contribution cash flows explicitly. Discussion with management and marketing can provide the required cash flows and probabilities of the event tree. Analytical valuation methods like Black-Scholes-Merton cannot provide any solution for option types like this.

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Option to Choose Example

Problem Framing

In this post I want to give a simple example of a choose option valuation. The considered project lasts 10 years, the WACC of the contribution (market) cash flows is 10.0% and constant over time. The contribution cash flows are shown in the graph below. Let the risk free rate be 5.0%. The project provides 3 options: 1) Option to expand with an investment of 100 kEUR (increasing with an inflation rate of 2% per year). The contribution cash flows would be increased by 20%, if managements invests in the expansion. 2) Option to abandon the project with a salvage value of 100 kEUR (increasing with an inflation rate of 2% per year) and 3) Option to contract with a savings of 200 kEUR (increasing with an inflation rate of 2% per year) and a contraction factor of 0.9. DCF analysis provides a present value of the market contribution cash flows of 1 million EUR. A Monte-Carlo-Simulation shows a project volatility of 0.30. We analyze this choose option with the binomial approach of Cox-Ross-Rubinstein. As time periods we take two time steps per year, so that you can read the figures in the lattice properly. For higher accuracy we could take smaller time periods anytime.

Choose Option Valuation

We want to give answers to the following questions: What is the value of this option to choose? When do we have to take which option to get the maximum value added for the project?

We take the binomial approach from Cox-Ross-Rubinstein to solve that issue. Following you can have look at the binomial lattice. The first value of each node is the value of the underlying (market contribution cash flows). The sevond value is the value of the options at this node. In the third line you can see whether you have to take an option and which option you have to take. “exp” means to invest in the expansion of the project, “go” means to take no option at this node and “con” means to invest in the contraction of the project.

The total value of the three options is 137 kEUR. That is the maximum investment that should be done for the three options in sum. The option to abandon is not taken in any node. That means that you should not invest in this abandonment option. In the first year you should not take any option, let the project evolve. In the second year there might be the first opportunities to take the expansion option. In the following years the expansion option is a good opportunity in case of positive cash flow development. Your project controlling should have a look at the cash flow development and go the right path through the lattice over time. In the first six years the contraction option provides no addition value to the project. But in the last three years of the project the contraction option becomes more important.

Note that this choose option adds a value of 137 kEUR to the project. That means that the NPV of the classical DCF analysis can convert from negative to positive because of the additional value. That could lead to a reconsidering of the project decision. The ENPV (expandedNPV) is the NPV of the project plus the value of the choose option.

Additional Remarks

I constructed the event tree from the project’s contribution cash flow volatility out of a Monte-Carlo-Simulations. Of course you can also create the nodes of the event trees by calculating the time values of the outstanding contribution cash flows explicitly. Discussion with management and marketing can provide the required cash flows and probabilities of the event tree.

This option to choose combines the three options of expansion, contraction and abandonment. This example also shows that the value of various options is not the sum of its individual options. Although the option to abandon has an option value by itself, it contributes no additional value to the option to choose, because it is not required in any node. Analytical valuation methods like Black-Scholes-Merton cannot provide exact solutions for such interdependent options.

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Option to Switch Example

Problem Framing

In this post I want to give a simple example of a swich option valuation. The considered project lasts 10 years, the WACC of the contribution (market) cash flows is 10.0% and constant over time. The contribution cash flows are shown in the graph below. Let the risk free rate be 5.0%. The project provides 2 operation modes (possibilities), one with technology A and the other with technology B. A Monte-Carlo-Simulation of technology A shows a project’s contribution cash flow volatility of 0.30. The corresponding Monte-Carlo-Simuation of technology B provides a project’s contribution cash flow volatility of 0.15. We analyze this switch option with a binomial approach. As time periods we choose one time step per year, so that you can read the figures in the lattices. For higher accuracy we could take smaller time periods anytime. The present value of the project market contribution cash flows is 1 million USD. Switch costs from technology A to B start with 145 kUSD, from technology B to A start with 80 KUSD. These costs increase with an inflation rate of 2.0%.

Switch Option Valuation

We want to give answers to the following questions: What is the value of this option to switch between technology A and technology B? How much can we invest in this flexibility keeping a positive added value to the project? And when do I have to switch between the 2 technologies to get the maximum value added?

We take the binomial approach from Cox-Ross-Rubinstein to solve that issue. Following you can have look at the binomial lattices for both technologies. The first value of each node is the value of the underlying (market contribution cash flows), the sevond value is the value of the switch option at the corresponding node. In the third line you can see whether you have to switch to the other technology or not (“sw” means to switch, “go” means to stay in the technology).

Binomial tree of switch option for technology A
Binomial tree of switch option for technology B

The value of the switch option starting with technology A is 21 kUSD. Starting with technology B the switch option value is 157 kUSD. If the investment for the switch option flexibility is below these option values, you should do the investment. If you can choose the starting technology, you should start with B. This results in a higher value added, the corresponding investments not taken into account. In the first year you have to make no switch in any case. In the second year it depends on the cash flow development, if you start with technology A. Switch in the bad case to technology B and stay in technology A in case of positive development. Starting with technology B you should stay there and make no switch, independent of the cash flow development. In the third year you should switch to technology A in the best cash flow development. Analyzing the event/option tree through time in this way provides a guideline for what to do in which year, depending on the cash flow development.

Note that this switch option adds a value of 157 kEUR to the project. That means that the NPV of the classical DCF analysis can convert from negative to positive because of this additional value. That could lead to a reconsidering of the project decision. The ENPV (expanded NPV) is the NPV of the project plus the value of the switch option.

Additional Remarks

I constructed the event tree from the project’s contribution cash flow volatilities out of Monte-Carlo-Simulations. Of course you can also create the nodes of the event trees by calculating the time values of the outstanding contribution cash flows explicitly. Discussion with management and marketing can provide the required cash flows and probabilities of the event tree.

This switch option valuation approach can be applied to many problems with different operation possibilities. Switch options are compound options with path-dependency. They are a good examples that real options can be more complicated than financial options. Analytical valuation methods like Black-Scholes-Merton cannot give you a solutions for problems like that.

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Replication Portfolio in Binomial Model

In this post I a want to give a short derivation of the replication portfolio and the risk neutral probabilities in the binomial model from Cox-Ross-Rubinstein. Let V be the value of the underlying asset in t_0. In a project or investment this might be the present value of the project’s contribution (market related) cash flows. The positive development of V at time t_1, V^+, occurs with probability p, the negative development with value V^- in t_1 with probability 1-p. The twin security of the underlying in the open market takes a similar notation S, S^+, S^-,p. We consider an option with option value E in t_0 that leads to an option value of E^+ in the upper state V^+ and to an option value of E^- in the lower state V^-. As result we are searching the option value E at time t=0.

Next we replicate the option value in t_1 by a portfolio of n shares of twin security S partly financed by borrowings of amount B at the risk-free rate r. The values of the upper and lower state in t_1 are E^+=nS^+-\left(1+r\right)B and E^-=nS^--\left(1+r\right)B.

In efficient markets there exist no profitable arbitarge opportunities. Therefore the outcome of the option value E in t=1 must be the same in the upper and in the lower state. Setting E^+-nS^+=E^--nS^- we get:

    \[n=\frac{E^+-E^-}{S^+-S^-}\]


Replacing n in the previous equations we obtain the value borrowed at the risk-free rate r:

    \[B=\frac{1}{1+r}\frac{{E^+S^--E}^-S^+}{S^+-S^-}\]


The law of one price tells us that the value of assets that lead to the same cash flows must be the same. That means that the value of the option at time t_0 must be the same as the value of the portfolio at time t_0. Therefore we can set E=nS-B. With that we calculate the value of the option in t_0:

    \[E=\frac{\left(\frac{S\left(1+r\right)-S^-}{S^+-S^-}\right)E^++\left(1-\frac{S\left(1+r\right)-S^-}{S^+-S^-}\right)E^-}{1+r}\]


We create a new variable p^\prime to simplify the previous expression.

    \[p^\prime=\frac{S\left(1+r\right)-S^-}{S^+-S^-}\]


Hence we obtain:

    \[E=\frac{p\prime E^++\left(1-p\prime\right)E^-}{1+r}\]



p^\prime can be interpreted as probability for E^+, 1-p^\prime for E^-. p^\prime and 1-p^\prime are known as risk-neutral probabilities. Note that the value of the option does not explicitly involve the actual probabilities p and 1-p of the underlying. Instead, it is expressed in terms of risk-neutral probabilities. They allow to discount the expected future values at the risk-free rate.

Discounting at the risk-free rate is the main difference between decision tree analysis (DTA) and contingent claim analysis (CCA) or real options analysis (ROA). DTA does not take into account that the risk of the cash flow streams changes when you consider options and opportunities. ROA implements this issue correctly.

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WACC, Return Rates & Betas with Debt

Joachim Kuczynski, 02 April 2021

In this post I want to summarize some interesting results concerning equity return rates , betas and WACC of a levered company. Regarding the market value balance sheet of a firm we can state that the value of the unlevered firm VU plus the present value of the tax shield VTS must be the same as the sum of levered equity E and debt D:

    \[VU+VTS=E+D\]


Further the rates of return on each side of the balance sheet are the weighted average of the component rates of return:

    \[r_A\frac{VU}{VU+VTS}+r_{TS}\frac{VTS}{VU+VTS}=r_E\frac{E}{E+D}+r_D\frac{D}{E+D}\]


Substituting VU in the rate of return expression we get a general form of the equity return rate:

    \[r_E=r_A+\left(r_A-r_D\right)\frac{D}{E}-\left(r_A-r_{TS}\right)\frac{VTS}{E}\]


Consequently the general form of CAPM beta is given by:

    \[\beta_E=\beta_A+\left(\beta_A-\beta_D\right)\frac{D}{E}-\left(\beta_A-\beta_{TS}\right)\frac{VTS}{E}\]


The WACC is defined as the weighted average of equity and debt return rates including tax shield at corporate income tax rate T_C. If the tax shield savings are proportional to the taxes paid (see WACC with Tax Shield), the WACC is given by:

    \[WACC=r_E\frac{E}{E+D}+r_D\left(1-T_C\right)\frac{D}{E+D}\]


Substituting the equity return rate we get a general form of the WACC:

    \[WACC=r_A\left(1-\frac{VTS}{V}\right)-r_DT_C\frac{D}{V}+r_{TS}\frac{VTS}{V}\]


r_A, r_D, r_{TS} are the return rates of the unlevered asset, debt and tax shield. V and VTS are the values of the levered firm and the tax shield. D is the amount of debt, V is the value of the levered firm, namely the sum of equity and debt.

Modigliani and Miller: Constant debt value
If the firm keeps its dept value D constant, there are no specific market risks concerning the tax shield. Therefore we can set the tax shield discount rate r_{TS} equal to the debt discount rate, r_D. The tax shield present value with constant debt D is:

    \[VTS=\sum_{j=1}^{\infty}{DT_C\left(\frac{1}{1+r_D}\right)}^j=\frac{DT_C}{r_D}\]


Hence we get simplified expressions for equity return, equity beta and WACC:

    \[r_E=r_A+\left(r_A-r_D\right)\frac{D}{E}\left(1-T_C\right)\]


    \[\beta_E=\beta_A+\left(\beta_A-\beta_D\right)\frac{D}{E}\left(1-T_C\right)\]


    \[WACC=r_A\left(1-T_C\frac{D}{E+D}\right)\]

Assuming that debt interest rate does not depend on the market return rate (CAPM) we can set \beta_D=0. Hence we get the well-known Hamada equation for levered beta:

    \[\beta_E=\beta_A\left(1+\frac{D}{E}\left(1-T_C\right)\right)\]


It is important to realize that Hamada’s equation is only valid if the value of debt is kept constant over time.

Harris and Pringle: Constant leverage ratio
Constant leverage ratio means that debt value is proportional to the value of the unlevered firm. According to Harris and Pringle that results in r_{TS}=r_A.

    \[r_E=r_A+\left(r_A-r_D\right)\frac{D}{E}\]


    \[\beta_E=\beta_A+\left(\beta_A-\beta_D\right)\frac{D}{E}\]


    \[WACC=r_A-r_DT_C\frac{D}{E+D}\]


But we have to take care. Miles and Ezzell, Arzac and Glosten have shown that you have a tax shield discount rate of r_D in the first period, and of r_A in the following periods to have a constant leverage ratio over time. The premise of r_{TS}=r_A does not hold.

Miles and Ezzell
With a perpetuity growing rate g of debt and discounting in the first period with r_D instead of r_A we obtain:

    \[{VTS}^{ME}=\frac{Dr_DT_C\left(1+r_A\right)}{\left(r_A-g\right)\left(1+r_D\right)}\]

Harris and Pringle
Taking the formula of Miles and Ezzell and setting r_TS equal to r_A in the first period, we get the a simplified expression for VTS:

    \[{VTS}^{HP}=\frac{Dr_DT_C}{\left(r_A-g\right)}\]

General debt ratio
If the amount of leverage is flexible and not constant or growing with a constant growth rate over time, the previous formulas do not work. In this case you have to use the APV method, in which you calculate the tax shield in each time period seperately.

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Baldwin Rate of Return | MIRR

Baldwin rate definition

The modified internal rate of return (MIRR), or Baldwin rate of return respectively, is an advancement of the internal rate of return (IRR). But also the MIRR can be misleading and can generate false investment decisions. The MIRR is defined as:

    \[MIRR=\sqrt[n]{\frac{\text{FV(contribution cash flows,WACC)}}{\text{PV(invest cash flows, financing rate)}}}-1\]

FV means the final value at the last considered period, PV stands for the present value.

Pitfalls of the Badwin rate

These points have to be considered carefully when applying the MIRR:

  • Cash flows in different countries, with different currencies, equity betas, tax rates, capital structure, etc. should be evaluated with specific risk-adjusted discount rates. In MIRR the project is profitable, if the rate of return is higher than the required WACC. But which WACC do we mean in projects with various differing cash flows ? No diversification of cash flows can be taken into account in MIRR. But that is crucial in evaluating international projects.
  • You need premises about the reinvestment rate of the contribution cash flows that affect the profitability of the project. These premises are not required in the (e)NPV concept. Hence you add an additional element of uncertainty in your calculation when using the MIRR, without any need.
  • Reinvesting contribution cash flows (numerator of the root) with the risk adjusted WACC means that the return of the project increases when the project risks and WACC increases. That cannot be true. In pinciple you should not use key figures that require assumptions about reinvestment return rates. You are evaluating a certain project and not of other unknown investment sources. In general you can discount all cash flows with its appropriate discount rate and capitalize it to the last period.
  • Does capitalizing (or rediscounting) a cash flow with a risk-adjusted discount rate to a future period make sense in general? I do not think so. To rediscount cash flows with a risk adjusted discount rate including a risk premium means that you are increasing the risk of the project. The project does not remain the same, because its risk increases. Only taking a riskless discount rate for reinvestments would not increase the risk of the project. The MIRR comes from a classical perspective with no risk adjustment of the discount rates. If you are using risk-adjusted discount rates, you are mixing two concepts that do not fit.
  • An additional positive cash flow must improve the profitability of the project. If you add an additional, small cash flow in an additional period n+1, the Baldwin rate can decrease. This is because the number of periods increases and the value of the root decreases. Cases that lead to wrong results are not acceptable for decision key figure.
  • If you have e.g. an after sales market with small positive cash flows, the Baldwin rate decreases by considering these cash flows in your calculation. This is because the number of periods increases and the n-th root decreases. Thus an after sales market cannot be implemented in your calculation.
  • You have to define clearly, which cash flow is in the numerator and which is in the denominator of the root. There is no clear and logic distinction. Thus you can find different definitions in literature. Anyway avoid to take balance sheet definitions of “investment”. Note that besides investments also fixed costs and leasing payments have to be discounted with a default free discount rate in general.
  • You cannot compare mutual exclusive investment projects, if the investments or the project periods are different.
  • You can also not evaluate investment projects with negative value contribution to the firm. But anyway such projects exist and have to be decided.
  • All cash flows should be considered as expected value of a probability distributions. The expected value of the Baldwin rate is not the Baldwin rate of the expected values of the cash flows.

Conclusion

The (e)NPV concept is much better than the MIRR or Baldwin Rate of Return. The (e)NPV does not have all the pitfalls mentioned above. Further you can also evaluate and compare value-loosing investment alternatives and do not need any premises about reinvestment rates. There are only disadvantage of the MIRR / Baldwin rate compared to the (e)NPV, try to avoid the application of MIRR / Baldwin rate.

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Operating Leverage

Operating leverage is the sensitivity of an asset’s value on the market development caused by the operational cost structure, fixed and variable costs. The asset can be a company, a project or another economic unit. A production facility with high fixed costs is said to have high operating leverage. High operating leverage means a high asset beta caused by high fixed costs. The cash flows of an asset mainly consists of revenues, fixed and variable expenses:

cash flow = revenues – fixed expenses – variable expenses

Costs are variable if they depend on the output rate. Fixed costs do not depend on the output rate. The present value (PV) of the asset is the present value of its cash flows. Present values are linear, we obtain for the asset’s PV:

PV(asset) = PV(revenues) – PV(fixed expenses) – PV(variable expenses)

Rearranging leads us to:

PV(revenues) = PV(fixed expenses) + PV(variable expenses) + PV(asset)

Those who receive the fixed expenses are like debtholders in the project. They get fixed payments. Those who receive the net cash flows of the asset are like shareholders. They get whatever is left after payment of the fixed expenses. Now we analyze how the beta of the asset is related to the betas of revenues and expenses. The beta of PV(revenue) is a weighted average of the betas of its component parts:

    \[\beta_{revenue}=\beta_{\text{fixed exp.}}\frac{\text{PV(fixed exp.)}}{\text{PV(revenue)}}+\]


    \[+\beta_{\text{var. exp.}}\frac{\text{PV(var. exp.)}}{\text{PV(revenue)}}+\beta_{\text{asset}}\frac{\text{PV(asset)}}{\text{PV(revenue)}}\]

The fixed expense beta is close to zero, because the fixed expenses do not depend on the market development. The receivers of the fixed expenses get a fixed stream of cash flows however the market develops. That means \beta_{\text{fixed exp.}} = 0. The betas of revenues and variable expenses are more or less the same, because they are both related to the output. Therefore we can substitute \beta_{\text{revenue}} for \beta_\text{var.exp.}.

    \[\beta_{\text{asset}}=\beta_{\text{revenue}}\frac{\text{PV(revenue)-PV(var.exp.)}}{\text{PV(asset)}}\]


Setting PV(revenue) – PV(var.exp.) = PV(asset) + PV(fixed exp.) we obtain:

    \[\beta_{\text{asset}}=\beta_{\text{revenue}}\left[ 1 + \frac{\text{PV(fixed exp.)}}{\text{PV(asset)}}\right]\]

This is the relationship of asset beta to the beta of turnover. The asset beta increases with increasing fixed costs. As an accounting measure we define the degree of operating leverage (DOL) as:

    \[\text{DOL}= 1 + \frac{\text{fixed exp.}}{\text{profits}}\]

The degree of operating leverage measures the change in profits when revenues change.

Valuing the equity beta is a standard issue in DCF analysis. In many cases you take an industry segment beta and adjust it to your company or project. The adjustment of the industry beta also includes the adjustment of operating leverage. We assume that \beta_{\text{revenue}} is the same for all companies in the industry segment. \beta_{\text{revenue}} is the beta of the segment without operating leverage. The \beta_{\text{asset}}^{\text{ind. segm.}} is the average asset beta of the industry segment, which has an average ratio of fixed expenses to profits. \beta_{\text{asset}}^{\text{ind. segm.}} is provided by public databases.

For detailed information see: Brealey/Myers/Allen: Principles of Corporate Finance, 13th edition, p. 238, McGraw Hill Education, 2020)


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After-Tax Discount Rate

In this post I want do derive the after-tax discount rate from the before-tax discount rate. “Before tax” means that the tax shield is not considered in the discount rate. It does not mean that the tax expenses (without tax shield) are not considered in the free cash flow. The tax expenses (without tax shield) are a part of the free cash flow in the before-tax and in the after-tax discount rate. For further information have a look at my other post WACC with Tax Shield. Abbreviations:

r … before-tax discount rate
r^{*} … after-tax discount rate
L … rate of debt to sum of equity E and debt D, L=D/(E+D)
r_D … debt interest rate
r_E … equity interest rate
t … marginal corporate tax rate

We assume that the values of r_D, r_E and L are known. Then the before-tax discount rate is:

    \[r=\left( 1-L \right)r_{E}+Lr_D\]


Rearranging the above to solve for r_{E} we have:

    \[r_{E}=\frac{r-Lr_D}{1-L}\]


The after-tax discount rate at a constant leverage rate is:

    \[r^{*}=\left( 1-L \right)r_{E}+L\left( 1-t \right)r_D\]


This is the famous equation most financial analysts might know. The factor “-t” comes from the tax shield and decreases the discount rate. Hence the discount rate after taxes is lower than the return rate before taxes. But you have to take care. This after-tax formula is only valid if the leverage rate L remains constant. Additionally it assumes that the total amount of tax expenses can be deducted by tax shield. If these two premises are not true, the previous formula does not work and you have to an analyze the topic with the adjusted present value (APV) approach. For a general view see this post. By substituting r_{E} we get:

    \[r^{*}= r -Ltr_D\]


This formula can be useful, because you do not have to know the equity return rate to calculate the after-tax return rate. But have in mind that this is only valid, if the leverage ratio is constant and the total tax shield amount can really be deducted from the tax expenses.

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Pitfalls of DCF Analysis

Correctly appraising capital projects with DCF analysis methods requires knowledge, practice and acute awareness of potentially serious pitfalls. I want to point out some common errors in project appraisal and suggest ways of avoiding them. For many people DCF analysis seems to be quite easy but it is not for complex projects. Here are some crucial issues from my point of view:

  • Decision focus: The calculation is focused on making the right decision concerning a project or an investment. That can be different from a calculation including all expenditures of the project or investment, e.g. sunk costs. For further comments concering this topic see Incremental Free Cash Flows.
  • Point of view: It has to be defined clearly from which perspective you are doing the decision and calculation. For example, the calculation can be different from the view of a business area and from the view of the overall company. The right perspective determines the relevant incremental cash flows.
  • Investment: Define clearly what you mean when talking about “investment”. Avoid the balance sheet view, look at investment as initial expenditures reqired for later contribution cash flows. In my point of view the term “investment” is best defined as commitments of resources made in the hope of realizing benefits that are expected to occur over a reasonably long period of time in the future.
  • Cash flows: A clear view of cash flow is important, avoid views from accounting and cost accounting, e.g. depreciation. And take into account tax effects.
  • Incremental cash flows: The correct definition of incremental cash flow is crucial. It is the difference between the relevant expected after-tax cash flows associated with two mutually exclusive scenarios: (1) the project goes ahead, and (2) the project does not go ahead (zero scenario). Sunk costs must not considered. For further comments see Incremental Free Cash Flows.
  • Comparing scenarios: Alway be aware of having a relative sight between the cash flow scenarios. Sometimes it is not so easy to define what would happen in the future without the project (zero scenario).
  • Risk-adjusted discount rates: Risk adjustment of discount rates has to be done for all (!) cash flows of the investment project that have significant risk differences: Fixed costs, investment expenses, one time expenses and payments, expenses for working capital, leasing, tax shields and contribution cash flows (turnover and variable costs) in various markets. For more infos concerning risk adjusted discount rates see Component Cash Flow Procedure.
  • Key figures: The only key figure that is valid for all types of projects and investment decision is the famous NPV. All other well-known figures like IRR, Baldwin rate, … are leading to false decisions in some cases. NPV also allows to build the bridge to financial calculation approaches like option valuation. Payback and liquidity requirements have to be considered carefully additionally to NPV.
  • Expected versus most likely cash flows: Quite often analysts take most likely cash flows. The right way is to consider the expected value of the cash flows.
  • Limited capacity: Do not forget internal capacity limitation when regarding market figures. Limited capacity has also to be considered when constructing the event tree in real options analysis. Besides that the temporal project value development with contribution cash flow’s WACC has to be ensured in the binomial tree.
  • Hurlde rates: Avoid hurlde rates for project decisions, because the can also lead to false decisions. Especially when you take one hurdle rate for different projects.
  • Cash flow forecasting: Forecasts are often untruthful. Try to verify and countermeasure cash flows from different sources.
  • Inflation: Be careful considering inflation. In multinational project it might influence the foreign currency location’s required return. You can also consider a relationship between inflation rate and expected future exchange rates according to the purchasing power parity (PPP).
  • Real and nominal discount rates and cash flows: The procedure should be consistent for cash flows and discount rates. Usually we take nominal values for the calculation.
  • Real Options: A DCF analysis should always be linked to a real options analysis. The more flexibility is in the project the more important is a real options analysis. Risk adds value to real options.
  • Precise cash flow timing: The influence of timing intervals can be significant. You can choose smaller time intervals in crucial time periods to increase accuracy.

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Option to Wait

This is a simple example of an option to wait. We consider a 15 year project which requires an investment of 105 M€, that can be done anytime. Arbitrage Pricing Theory provides a yearly risk-adjusted capital discount rate (WACC) of 15%. Investment and internal risk cash flows are discounted by the risk-free rate. We assume for all years equal free net cash flow present values of 100/15 M€. Classical incremental cash flow analysis provides a present value of the market-related net cash flows of 100 M€. That means that the classic NPV of the project is -5 M€. Because of the negative NPV management should reject the project.

But management has an option to wait. It can wait with the decision and invest only if the market development is profitable. For sure the company loses revenues because of the delayed investment, but on the other hand management gets more information about market development. The question is: What is the value of this option to wait and how long should management wait with that investment decision? Can the project become profitable?

Monte-Carlo-Simulation of the project provides a project volatility of 30%. The risk-free rate is 5%. Next we are performing a real option analysis (ROA) of the waiting option with the binomial approach regarding 15 time steps, one for each year.

Real option analysis provides a project value of 21 M€. That means that the value added by the waiting option is 26 M€. Because the project value with waiting option is positive we should not reject the project any more. Management should go on with the project. Including the option in the project valuation leads to the opposite management decision. And besides the waiting option there might be additional options like the option to abandon or the option to expand/contract. They would bring additional value to the project.

Real option analysis also provides the information that there should be no investment done before the second year. Dependent from the market development management can decide when to invest according to the time value of the expected free cash flows.

In this example we assumed yearly cash flows that results in a decrease of the expected future cash flows. This corresponds to paying dividends at financial securities. Considering options in the lifetime of a project requires binomial valuation with leakage. If you assume relative leakage you get a recombining tree, with absolute leakage values you get a non-recombining binomial tree.

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