The following assignment deals with the construction of a 500 MW offshore wind f

Question

The following assignment deals with the construction of a 500 MW offshore wind farm. Following the decision to construct the wind farm, it will take 4 years for the design, construction, purchase, production and construction of the turbines until they can go into operation. The time when the turbines begin operation is referred to as time 0, and the costs for the previous 4 years have been:

year -4: 200 million DKK

year -3: 500 million DKK

year -2: 1,500 million DKK

year -1: 2,000 million DKK

After year 20, it is expected to no longer be profitable to operate the turbines, therefore they must be removed at an expected cost of 500 million DKK. The cost of operating and maintaining the turbines is estimated to be 800 million DKK/year for years 1-20. Energy production from the turbines, of course, depends on the wind speed, which can always vary. Based on detailed measurements of wind velocity in that location, it is estimated that the wind farm should produce 2,300,000 MWh annually. However, the uptime of the turbines is assumed to be only 95%, and it is further assumed that there is a loss of electricity in the cables and substations, so net production is only 2,000,000 MWh/year. Investment amounts are attributable to the beginning of the years, while receipts are attributable to the end of the years. A discount rate of 10% per year is used.

Find the following:

Part I:

1 What is the capital value of the investments in the four years before the turbines are put into operation, calculated at time 0?

2. If the electricity price is assumed to be constant over the 20 years, what should it be, at a minimum, for the investment in the offshore wind farm to be profitable? For onshore wind turbines, it is most likely - as above - that the life span is 20 years. However, evidence suggests that wind turbines have a longer life span at sea due to lower turbulence in the wind over the ocean.

3. If life expectancy increases from 20 to 25 years, what should the minimum electricity

price be for the investment in the offshore wind farm to be profitable?

For the following question, life expectancy is assumed to be 20 years, but after 20 years, a major repair and technological upgrading of the turbines will be made, extending the life span by 10 years. The assumptions for question 1 are assumed to be valid, including the expectation of costing 500 million DKK for the turbines to be removed after termination of operation. However, the price of electricity in years 21-30 is expected to be only 0.50 DKK/kWh.

4. If an investment of 1,000 million DKK after 20 years will make it possible to increase the life of the turbines to 30 years, would such an investment be profitable?

Part II:

Simulate the effect of uptime of the turbines (assumed initially 95%) on the NPV (use 95% confidence interval). In your simulation assume this factor follows a uniform distribution Uniform[85%-98%].

Part III:

Perform a sensitivity analysis on the production rate 2,000,000 MWh/year over the NPV.

Explanation / Answer

Values @Millions in DKK Question 1 Present value(@year 0) of capital investments (a) Year (b) Investment ( c ) Present Value@ 10% (d) Present Value = (b)*( c ) year -4 200 1.4641 292.82 year -3 500 1.331 665.5 year -2 1500 1.21 1815 year -1 2000 1.1 2200 4973.32 Assuming x is the rate per MWH                      PVF is the present value factor                      PVAF is the present value annuity factor Question 2 when termination costs are not considered when termination costs are considered (2*(x)-800)*pvaf(10%,20y) = 4973.32 (2*(x)-800)*pvaf(10%,20y) - 500*pvf(10%,20y) = 4973.32 (2x-800)*8.5136=4973.32 (2x-800)*8.5136 - 500*0.1486=4973.32 2x=(4973.32/8.5136) + 800 2x=(4973.32+74.32/8.5136) + 800 2x = 1384.162 2x = 1392.891 x = 692.0809 x = 696.4457 Minimum Price of electricity shall be 692.08 DKK / MWH Over next 20 years Minimum Price of electricity shall be 696.45 DKK / MWH Over next 20 years Question 3 when life expectancy is 25years, (2*(x)-800)*pvaf(10%,25y) - 500*pvf(10%,25y) = 4973.32 (2x-800)*9.077 - 500*0.0923=4973.32 2x=(4973.32+(500*0.0923)/9.077) + 800 2x = 1352.988 x = 676.4939 Minimum Price of electricity shall be 676.49 DKK / MWH Over next 25 years Question 4 Rate per KWH 0.5 DKK Hence rate per MWH = 0.50*1000 = 500 DKK Revenue per annum = 2 million MWH * 500DKK = 1000 Million DKK Expense per annum = 800 million DKK Net Revenue per annum = 1000 Million DKK - 800 Million DKK = 200 Million DKK Present value of 10 years 200Million DKK After 20 years =200*pvaf(10%, 10y) - 1000 =(200*6.1446)-1000 228.92 Present value of 10 years 200Million DKK at year 0 = 228.92*pvf(10%,20y) 34.017512 NPV Is Positive, Hence investment of 1000 Million DKK After 20 years is profitable

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