Question

Your energy bill is expected to be $250 next month (month 1) and is expected to grow at 0.50% per month for the foreseeable future (aka forever), after your utility provider ran into financial trouble. You read recently that installing solar panels on your roof will reduce your energy bill by 20% (so month 1 would be $200) and decrease the growth of the bill to 0.30% per month for the foreseeable future. Assuming this is true, that you plan to stay in the house for the foreseeable future, and that the applicable discount rate is 9% per year, from a pure financial perspective what is the most you’d be willing to pay today to have solar panels installed immediately? Assume the panels could be installed quickly and the cost savings would start in month 1.

Answer 1

The maximum amount that should be paid from a financial perspective is equal to the total present value of the monthly savings in the perpetual energy bills discounted at the applicable discount rate

Expected First Bill = $ 200, Growth Rate = 0.3 % per month, Discount Rate = 9 % per annum or (9/12) = 0.75 % per month

PV of Solar = PVs = 200 / (0.0075 - 0.003) = $ 44444.44

Expected First Bill = $ 250, Growth Rate = 0.5 % and Discount Rate = 0.75 %

PV of Non-Solar = 250 / (0.0075-0.005) = $ 100000

PV of Cost Savings = (100000 - 44444.44) = $ 55555.56

Maximum Amount Payable for the Solar Panel = PV of Cost Savings = $ 55555.56