Your energy bill is expected to be $200 next month (month 1) and is expected to

Question

Your energy bill is expected to be $200 next month (month 1) and is expected to grow at 0.5% per month for the foreseeable future (aka forever). You read recently that installing solar panels on your roof will reduce your energy bill by 25% (so month 1 would be $150) and decrease the growth of the bill to 0.25% 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 12% per year, from a pure financial perspective what is the most you’d pay today to have solar panels installed immediately? Assume the panels could be installed quickly and the cost savings would start in month 1.

Explanation / Answer

OLD DECISION EXPECTED BILL= $200 growth=   g 0.50% DISOCUNT RATE= r 12% PV OF Growing Perpetuity= EXPECTED Cash flow /(r-g) $200*(1+.005)/(.12-.005) = $ 1,747.83 NEW DECISION EXPECTED BILL= $150 growth=   g 0.25% DISOCUNT RATE= r 12% PV OF Growing Perpetuity= EXPECTED Cash flow /(r-g) $150*(1-.0025)/(.12+.0025) = $ 1,221.43 CONCLUSION- From a pure financial perspective,$1221.43 is the most I’d pay today to have solar panels installed immediately instead of Old electricity method, BY this I can save = $ 526.4($1747.83- $ 1221.43)

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