# 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).