Sample Exam Problems

PACE Bonds

Property Assessed Clean Energy (PACE) bonds are recent innovation some states have adopted to help home owners finance energy efficiency improvements. Roughly speaking, a PACE bond allows a home owner to avoid borrowing for up-front capital costs. Instead, those costs are paid by the home owner’s municipality and the home owner repays the city through a higher property tax. This question explores how they work.

Suppose a home owner is considering installing a residential photovoltaic (PV) system. The system would have an AC capacity of 3.1 kW, and would cost $4 per watt to build. It would last 30 years and would have a capacity factor of 17% (typical for PV in NYS). Every kWh generated by the system would allow the home owner to avoid paying $0.145 (average price in NYS) to buy that electricity from the grid. The system is expected to last 30 years and you may assume it has no annual costs—the only cost is the up-front capital. The home owner can borrow or lend at an interest rate of 10%.

  1. Please compute the net present value of the system to the home owner. Assuming that her only interest is in avoiding electricity costs (no other environmental motivation), would she go ahead with it?

Now consider the system from the city government’s point of view. Suppose that the system would provide $45 per year in external benefits (avoided damages from conventional electricity generation). Also suppose that the city has a good credit rating and can borrow or lend at 2%.

  1. Including both the private benefits and the externality, what is the NPV of the system from the city’s perspective?
  2. Now suppose the city considers offering the homeowner PACE bond financing with the following characteristics. The city would pay the entire construction cost of the system, in exchange for which the homeowner would pay an extra $570 in property taxes every year for 30 years. What is the NPV of the PACE payments to the city? Does it cover the construction cost? Including the environmental benefits as well, what is the NPV to the city?
  3. If the project goes ahead, what is the net effect on the homeowner’s annual costs including both energy savings and PACE repayments? What is the NPV to the homeowner? Is it a good idea from the homeowner’s perspective to proceed?
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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 05/01/2018