Energy Systems Analysis
Problem Set 1
This problem is designed to help you explore the valuation of investment projects, and compare projects using several alternative criteria. Use Microsoft Excel to perform the calculations.
1. Your firm has an investment opportunity ("Project A") that you have been asked to consider, and report to your boss whether the company should move forward or not. The project would require an up-front investment of $800,000, and would generate annual revenues of $100,000. Assume that there would be no operating costs - the only cost is the initial investment. Assume a project lifetime of 20 years.
a. Make a spreadsheet in Excel for valuing this project. [HINT: put all numbers in 1,000s in the spreadsheet to avoid extra zeros].
b. Calculate the NPV at three different discount rates: 8%, 10%, and 12%.
c. If your boss tells you that in general, alternative projects are getting around 10%, should you recommend going ahead with this project (based only on the information provided here)? Why or why not?
2. Consider a second, alternative project ("Project B"). This project requires only $8000, and generates $2000 per year for 20 years, with no operating costs. Assume a discount rate of 10% for this question.
a. Make a spreadsheet in Excel for this project on separate worksheet. [HINT: use "copy/paste worksheet" command to copy the project from Q1 and then modify].
b. Calculate the NPV of this project at a discount rate of 10%, and compare to the NPV of Project A. Which project would you recommend based on NPV?
c. Calculate the Benefit-Cost Ratio for both Project A and Project B and compare. Which project would you recommend for your company based on the Benefit-Cost Ratio criterion?
d. Calculate the Internal Rate of Return (IRR) for both Projects A and B, and compare. [HINT: Use the "IRR()" function in Excel, do not use trial-and-error). Which project would recommend based on IRR?
e. Given your answers to b) - d) above, what would be your overall recommendation to your boss, and why?
3. You've been asked to consider yet a third investment ("Project C"). This project also requires an initial investment of $800,000, and also has a 20-year lifetime. This project will receive annual revenues of $250,000, but have annual operating costs of $145,000.
a. Assuming a 10% discount rate, calculate the NPV of this project, and compare to Project A. Which project is better in terms of the NPV criterion?
b. Calculate the Benefit-Cost ratio, and compare to Project A. Which is better in terms of this criterion?
c. What would be your overall recommendation and why?
4. For your internship at the U.S. Environmental Protection Agency, you've been asked to help calculate the economic benefits of a climate change policy. Assume that this requires a one-time investment of $1 Billion immediately. No benefits are produced for the first 100 years. In years 101-200, there is an annual benefit of $100 Million.
a. Calculate the NPV of this policy for discount rates of:
i. 0%
ii. 1%
iii. 2%
iv. 3%
b. Most economists have concluded that an appropriate social discount rate for public projects is in the range of 3% to 7%. Based on that assumption, could EPA justify this policy? Why or why not?
c. Discuss any factors that may not be adequately considered in performing this analysis using a non-zero (e.g., 2% or 3%) discount rate.
d. Discuss any concerns about performing this valuation using a discount rate of zero.