## 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.

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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