Suppose that the installed cost of a commercial solar hot water heating system is $ and the annual fuel cost saving is $ Assume counter factually that fuel cost savings accrue as a single sum at the end of each year. The cost of the solar system is incurred at the end of year or the very beginning of year The system lasts for years, after which time, its value is zero.

a What is the net present value of the investment at At

b As an alternative to Net Present Value, we can annualize the cost of the solar system and compare this figure with annual fuel cost savings. What is the annualized cost of the solar system at At

c What is the net annualized value annualized benefits minus annualized costs of the solar system at At Note: If you now derive the present value of net annualized values, the answer should be the same as your answer in Part a

d Go back to the fuel cost assumptions in part a and b We know that there are important social benefits to fuel oil displacement in the form of reduced CO

SOX, and NOX emissions. What level of annual air quality benefit measured in

$ terms, to be subtracted from fuel costs would be necessary to make the solar

system break even at At

Hint: the answer can be found in Part b

e Suppose we determine that the annual social cost of the fossil fuel the solar system displaces is of its market price. We place a tax on fossil fuel. Is the

solar system competitive now that we have internalized the social damage in the

fuel oil at At Look at Part d

NPV at ; NPV at

Annualized cost at ; Annualized Costs at

Net annualized value at Net annualized value at

Check: PV of annualized value at PV at

Needed environmental damage savings for system to pay off at

At

Is system now competitive at At