Title: Problem Set 4

Page 1

Please indicate if the following statements are true or false:

Question 1.1

Q: A typical project in the energy sector will start with a negative cash flow
A: true

Question 1.2

Q: A positive cash flow means that a project is generating revenue
A: true

Question 1.3

Q: We need to discount the future cash flow if we want to convert them to present day monetary values
A: true

Question 1.4

Q: With a discount rate of 20%, 1 franc would be 0.4 franc in 5 years
A: false
If wrong: Answer: 1 * 1.2^5. We move cash flow forward in time and not backward, so we must compound it and not discount it.

Indicate if the following statements regarding the social discount rate are true or false.

Question 2.1

Q: A high social discount rate implies that consumption and costs of future generations are valued more than current consumption and costs.
A: false

Question 2.2

Q: The reason that some policymakers are disinterested in implementing climate policy instruments is the low social discount rate, which means that any future benefits of climate policy are not worth making today.
A: false

Question 3

Q: Which of these could be reasons to discount future costs and benefits (select whichever is applicable)?
- An investment made today implies that one would not be able to invest in any other alternative.
- The value of money declines over time, as incomes increase.
- Consumers tend to be impatient, and need to be compensated for receiving or making payments in the future.
- All of the above. (correct)

Page 2

Question 4

Q: Consider a policy that makes it cheaper for utility-scale solar PV producers to borrow for setting up a power plant. How would this policy affect the net present value (NPV) of this power plant, ceteris paribus?
- It will increase it (correct)
- It will decrease it
- It will stay the same
- Difficult to say

Question 5

- Please complete the two formulas used to calculate the private and social net present value.
- \({CF}_t\)
- \(I\)
- \({NPV}_p\)
- \({B}_t\)
- \({C}_t\)
- \({r}_s\)
- \({NPV}_s\)
Q: NPV_p
A: \({NPV}_p\)
Q: NPV_s
A: \({NPV}_s\)
Q: CF
A: \({CF}_t\)
Q: B
A: \({B}_t\)
Q: C
A: \({C}_t\)
Q: I
A: \(I\)

Question 6

- A firm is evaluating different options for projects involving building a power plant. Which of the available options generates net gains to the company?
- Project A has a NPV = -$24,000 and Project B has a NPV=-$20,000.

Both projects have a cost of capital of 22%, Project A has an IRR r= 20% and Project B has an IRR r= 25%.

Project A has a NPV = $39,000 and Project B has a NPV=-$20,000.

Both projects have a cost of capital of 18%, Project A has an IRR r= 20% and Project B has an IRR r= 25%.
- Project A
- Both
- None
- Project B
Q: = 20% and Project B has an IRR r
Q: =
Q: none
A: None
Q: a
A: Project A
Q: both
A: Both
Q: b
A: Project B

Question 7

Q: What describes the internal rate of return r* (IRR)?
- r* is the interest rate that an investor has to pay to finance his project.
- r* is the discount rate that maximizes the net present value (NPV) of a project.
- r* is the discount rate that makes the net present value (NPV) of a project zero. (correct)

Page 3

A company has an opportunity to make an investment of 500 million CHF into a hydro power plant or 200 million CHF into a gas fired power plant. The construction time is 2 years for both plants. It is assumed the investment costs can be divided evenly over the construction period. The company’s cost of capital is 12%. It further expects an after tax net cash flow for the two projects for the first five years of operation as shown below:

Question 8

Q: For the following calculations, assume that the construction of both plants would start simultaneously in time period 0 and that the reference year is the first year of the construction.

Calculate the net present value (NPV) of the two projects starting from today until the end of the displayed operation period:
- NPV of gas fired power plant is -14.9 million CHF
- NPV of gas fired power plant is 14.9 million CHF (correct)
- NPV of gas fired power plant is 114.9 million CHF
- NPV of hydro power plant is 15 million CHF
- NPV of hydro power plant is -30.0 million CHF (correct)
- NPV of hydro power plant is 0 CHF

Question 9

Q: Given the information above, calculate the internal rate of return (IRR) of the two projects.
- The hydro power plant has an IRR of around 8.8%
- The hydro power plant has an IRR of around 9.9 % (correct)
- The hydro power plant has an IRR of around 7.7 %
- The gas power plant has an IRR of around 14.6 % (correct)
- The gas power plant has an IRR of around 6.7 %
- The gas power plant has an IRR of around 10.3 %

Question 10

Q: The gas and hydro power plants have a far longer life time than just five years. Would your preference for one of the projects change if you take into account the whole life time of the plants of 20 years after construction? Assume that the cash flows of the sixth year of operation onwards are equal to the cash flows of the fifth year.
- NPV of gas plant becomes ca. 262 million CHF and the NPV of the hydro plant ca. 222 million CHF. The gas plant is now preferable.
- NPV of gas plant becomes ca. 262 million CHF and the NPV of the hydro plant ca. 482 million CHF. The hydro plant is now preferable. (correct)

Question 11

Q: Given your calculations, in which time horizon is each project preferable given its NPV (assuming that the cash flows of the sixth year of operation onwards are equal to the cash flows of the fifth year)?
- The gas plant is preferable up to a time horizon of 14 years. From the 15th year the hydro plant has a higher NPV.
- The gas plant is preferable up to a time horizon of 21 years. From the 22nd year the hydro plant has a higher NPV.
- The gas plant is preferable up to a time horizon of 7 years. From the 8th year the hydro plant has a higher NPV. (correct)

Page 4

Question 12

Q: Levelized cost can best be compared to:
- Marginal cost
- Total cost
- Fixed cost
- Average cost (correct)

Question 13

Q: How is the levelized cost of energy (LCOE) of a given technology defined?
- LCOE = Total Life Cycle Energy Cost / Total Lifetime Energy Production
- LCOE = Total Life Cycle Capital Cost / Total Lifetime Energy Production
- LCOE = Total Life Cycle Energy and Capital Cost / Total Lifetime Energy Production (correct)

Question 14

Q: Which is the correct ranking for the external costs of different energy technologies in the EU (ranging from highest to lowest) with regards to CO2 emissions?
- PV > gas > coal
- PV > coal > gas
- Coal > gas > PV (correct)
- Gas > coal > PV

Page 5

Question 15

Q: Based on estimates from the IEA, what is the LCOE of new nuclear energy supplies entering service in 2027?
- 90-100 USD per MWh
- 100-130 USD per MWh
- 130-260 USD per MWh (correct)

Question 16

Q: Consider another policy that increases waste management costs for nuclear energy producers. What is the impact of this policy in the relative LCOE of nuclear energy, compared to other technologies, ceteris paribus?
- Difficult to say
- It stays the same
- It decreases it
- It increases it (correct)

Question 17

Q: A owner of a single family house installs a solar panel for the production of electridcity on the roof. The total costs for the solar panel is 20'000 CHF (installation in time period 0). The maintanence cost is 200 CHF per year starting in the year after the installation. The life cycle of the investment is 20 years after the year of installation. The average annual production is 5'000 kWh starting in the year of the installation. Further, the government grants an initial subsidy of 5'000 CHF for the installation of the panels. Assuming a discount rate of 5%, calculate the levelized cost of energy LCOE of this scenario (real values, assume no inflation).
- LCOE is 0.26 CHF / kWh (correct)
- LCOE is 0.32 CHF / kWh
- LCOE is 0.20 CHF / kWh

Page 6

Question 18

Q: Please, select the correct one-factor learning curve equation.

\(C_t\): Cost of unit production at time t

\(C_0\): Average unit production cost at time t=0

\(CP_t\): Cumulative output produced up to time t

\(a\): Elasticity of learning

\(e_t\): Stochastic term
- \(C_t = C_0 C P_{t}^a e_t\) (correct)
- \(C_t = C_0 + C P_{t}^a e_t\)
- \(C_t = \frac{C P_{t}^a e_t}{C_0} \)
- \(C_t = C_0 - C P_{t}^a e_t\)

Question 19

Q: Please, select the correct two-factors learning curve equation.

\(C_t\): Cost of unit production at time t

\(C_0\): Average unit production cost at time t=0

\(CP_t\): Cumulative output produced up to time t

\(a\): Elasticity of learning

\(R_t\): Knowledge stock up to time t

\(b\): Elasticity of learning-by-researching

\(e_t\): Stochastic term
- \(C_t = C_0 C P_{t}^a R_{t}^b e_t\) (correct)
- \(C_t = C_0 - C P_{t}^a R_{t}^b e_t\)
- \(C_t = C_0 +C P_{t}^a R_{t}^b e_t\)
- \(C_t = \frac{C P_{t}^a R_{t}^b e_t}{C_0} \)

Page 7

Please indicate if the following statements concerning the learning curve are true or false.

Question 20.1

Q: The two-factor learning curve shows the relationship between research spending and profit.
A: false

Question 20.2

Q: The two-factor learning curve shows the impact of learning-by-doing and learning-by-researching.
A: true

Question 20.3

Q: The two-factor learning curve involves plotting a relationship between unit production costs and cumulative output, and cumulative research spending.
A: true

Question 20.4

Q: The one-factor learning curve shows the relationship between the production costs of one unit of output using a certain technology and the cumulative output of that technology.
A: true

Question 21

Q: Consider a one-factor learning curve in a simple economy, in which increasing the cumulative quantity of solar PV based electricity produced by 1%, leads to a decline in costs by 0.5%. Assume that the initial cost of producing 1 kWh of energy is CHF 0.20, and the current cost of production is CHF 0.10. Ignoring any stochastic disturbances, what is the cumulative solar PV installed capacity between these two time periods in this economy?
- ¼ kWh
- 8 kWh
- 4 kWh (correct)
- ½ kWh

Page 8

- Drag and drop the descriptions of the flow chart for a cost benefit analysis in the right places.
- Compare discounted benefits and costs for all alternatives
- Choose appropriate discount rate
- Evaluate the benefits

(state in monetary terms)
- Identify benefits:

1. Primary

2. Secondary

3. Intangibles
- Evaluate the costs

(state in monetary terms)
- Selection of projects to be evaluated
- Identify costs:

1. Primary

2. Secondary

3. Intangibles
Q: compare
A: Compare discounted benefits and costs for all alternatives
Q: identify
A: Identify benefits: 1. Primary 2. Secondary 3. Intangibles; Identify costs: 1. Primary 2. Secondary 3. Intangibles
Q: select
A: Selection of projects to be evaluated
Q: choose
A: Choose appropriate discount rate
Q: identify
A: Identify benefits: 1. Primary 2. Secondary 3. Intangibles; Identify costs: 1. Primary 2. Secondary 3. Intangibles
Q: evaluate
A: Evaluate the costs (state in monetary terms); Evaluate the benefits (state in monetary terms)
Q: evaluate
A: Evaluate the costs (state in monetary terms); Evaluate the benefits (state in monetary terms)