Peter J Wilcoxen > PAI 723 Economics for Public Decisions

Exercise 9

Due Wednesday 12/1.

Fuel cells are an alternative to batteries for powering electric vehicles. They are very efficient and produce little pollution, but at the moment they are very expensive to produce. Making them less expensive will take a lot of research and will not pay off for a decade or more. This exercise asks you to use present value calculations to evaluate a potential investment fuel cell research.

Imagine you are the manager of a company in the energy industry. Suppose you know that for a $100 million investment today you could develop a fuel cell technology that you could license to auto companies for $10 million per year forever starting in 10 years. Until then, it would earn nothing (the scientists are still working on it in the lab). For simplicity, assume you would have no costs apart from the initial $100 million.

To raise the $100 million, however, you would have to issue a bond (just as corporations or government agencies do). A bond is basically a legally enforceable IOU: in exchange for money today, your company agrees to make specified payments in the future. In this case, suppose you could raise $100 million today by issuing a bond promising to pay $7 million per year until year 10, at which time you would pay an additional $7 million plus the original $100 million.

Using a spreadsheet program, determine whether it would be a good idea to go ahead with the project if the interest rate were 5%. That is, would it be profitable to borrow the money and make the investment? What is the present value of the project? How would the PV and your decision be affected if the interest rate were 4% or 6% instead? Turn in a your spreadsheet for the 5% case. Make sure there's enough text and documentation that it will be clear how you arrived at your results when the sheet is printed.

To eliminate ambiguities about the timing of payments, here's how to set things up. The investment would cost $100 million in year 0 (today) and would produce $10 million of income per year with the first payment in year 11. The bond would raise $100 million in year 0, would cost you $7 million in years 1-9, and would cost $107 million in year 10 (7+100).

Also, the point of this exercise is to help you learn exactly how present value calculations are done. As a result, please build the worksheet using the fundamental present value formulas from class rather than Excel's built-in present value functions like PV.


Please submit your spreadsheet on Blackboard. If you use a program other than Excel, please save and submit it in XLS or XLSX format. If that's a problem, please send me a note.

Additional Information

FAQ: Do we need to worry about cash-flow constraints?
You might be concerned about how the firm would be able to pay $7 million of interest each year before the project begins paying off (that is, that the firm might be constrained by its cash flow). In this problem, you don't need to worry about that: you can assume that the firm has enough revenue from its other activities to pay the interest as long as the overall project is worthwhile.
Present Value Formulas
Summary of the key formulas.
Other Resources on Present Value
Additional information and example problems
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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 11/17/2021