You are a hyperbolic discounter. In fact your discount rate between year t and year t+1 is given by .05/(1+t) for t=0(today), 1 (next year), 2, 3, … This means the discount rate between today and a year from now is .05. The discount rate between a year from now and two years from now is .025 and so on.
You are considering an investment in energy conservation (solar panels on your roof) that has a lifetime of 5 years. It will cost you $130 to install (these are very inexpensive panels…) and will reap benefits in terms of energy saved of $10 in year 1, $20 in year 2, $30 in year 3, $40 in year 4 and $50 in year 5
a. Calculate your discount factors for each of the next 5 years
b. What is the net present value of the energy savings?
c. Is the installation a good investment for you?
d. Would the installation be a good investment if your discount rate were a constant 5% over the 5 years?