Suppose that the installed cost of a commercial solar hot water heating system is $25,000 and the annual fuel cost saving is $1,500. 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 year 1). The system lasts for 30 years, after which time, its value is zero.
a. What is the net present value of the investment at 12%? At 6%?
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 12%? At 6%?
What is the net annualized value (annualized benefit minus annualized cost) of the solar system at 12%? At 6%?
c. Suppose fuel cost savings escalate at the rate of interest, i.e. FCS1=1500 (1+R); FCS2=1500 (1+R)2. Now what is the net present value of the solar system at a 12% interest rate?
d. Go back to the fuel cost assumptions in part (a) and (b). We know that there are important social benefits to fossil fuel savings in form of reduced CO@, SOX, and NOX emissions. Measuring these benefits in dollar terms, what would their value have to be (adding this value to the original fuel savings benefit) for the solar system to break even at 12%? At 6%?
e. Suppose we determine that the annual social cost of the fossil fuel the solar system displaces is 40% of its market price. We place a 40% tax on fossil fuel, increasing the value of fuel savings to the private investor by 1.4 Is the solar system competitive (now that we have internalized the social damage in the fuel oil at 12%? at 6%?)