Problem 1

Suppose that the installed cost of a commercial solar hot water heating system is $15,000 and the

annual fuel cost saving is $1,000. 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 0

(or the very beginning of year1). The system lasts for 25 years, after which time, its value is

zero.

(a) What is the net present value of the investment at 10%? At 5%?

(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 10%? At 5%?

(c) What is the net annualized value (annualized cost minus annualized benefits) of the solar

system at 10? At 5%? 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 CO2,

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 10%? At 5%?

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 50% of its market price. We place a 50% tax on fossil fuel. Is the

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

fuel oil at 10%? At 5%. (Look at Part d).