A wind park operator is considering a 5 M€ project that will boost the park's capacity by 10MW. Additionally, there will be an added yearly operation and maintenance cost of 20 €/kW for the next decade. The efficiency of this technology, which is standard for wind energy, stands at 30% (a capacity factor of 0.3). The electricity price follows Geometric Brownian motion (GBM) process with μ=0.04 and σ=0.30, and with an initial electricity price 30 €/MWh.

TASK 1

Calculate the project's worth using the Net Present Value (NPV) method. Use the average price expected over the next 10 years as a static electricity price estimation. When calculating NPV, factor in a discount rate of 9.5% to mirror the owner's risk preference.

Hint: Intermediate result: electricity price=36.9 €/MWh. 

Mind the unit conversions during calculating. How would you interpret the results? Should this project be exercised or rejected according to NPV criterion?

TASK 2

Suppose next that the operator has a staged investment option. Initially, investor can invest 1 M€. After a year, the investor can defer the decision to either continue by investing a reduced subsequent 4M€ investment cost or abandon the project, avoiding the 4 M€ cost. Note that in the case of a deferred investment, the time horizon we consider is the deferred year + the lifetime of the project (it means 11 years). For your calculations, use a risk-free interest rate of 5% for overall discounting for simplicity. Determine the value of the deferred option. And how does the value of the option changes when the price volatility changes? 

Hint: Use a time step of 0.25 year (n=4) when constructing the binomial tree to balance between computational effort and accuracy.

TASK 3

Try to interpret the results obtained from TASK 1 and TASK 2. Engage in a discussion on the methodology, the setup of this question, or any other related topic of your choosing. Feel free to share your insights or perspectives.