Payback Period Example #2
Lt. Dave Rajakovich has 1200 ft2 of roof in his home in Pittsburgh, PA (HDD = 6,000). He is considering upgrading the insulation from R-16 to R-22. The estimate from the contractor was 775.Hishomeisheatedwithnaturalgas.Lastyear,theaveragepricehepaidfornaturalgaswas9.86/MCF. Assuming an AFUE of 86%, how long will it take Dave to recover his investment?
Ok, this is 5.11. Here Dave has a house, and he is trying to improve the insulation and the contractor comes up with an estimate of $775. He is using natural gas to heat the home, and we are trying to calculate how long will it take Dave to recover his investment? And this is a typical problem that uses an equation for payback period. Equal to Ci, cost of insulation, times R1 times R2 times efficiency divided by cost of energy times again R2 minus R1, this is the final R-value minus the initial R-value times HDD times 24.
Payback = Ci × R1 × R2 × ECe × [R2 - R1] × HDD × 24
Do we have all the pieces of information for this formula?
Cost of insulation: Cost of insulation should be in dollars per square foot. So Dave has got an estimate of $775 to cover an area of 1200 square foot. Roof area happens to be 1200 ft2. To cover this area with insulation it costs 775,sowecancalculatethecostperft.Thishappenstobe0.65 per ft2. That’s what we want, per ft2.
Do we know R1? Yes we know, R1 is equal to 16, R2 is equal to 22 and the furnace efficiency, E, is equal to 0.86. And we also know HDD. HDD is 6,000, and we know 24 hours.
$7751,200 ft2 = $0.65 / ft2R1 = 16R2 = 22E = 0.86HDD = 6,000
Only thing here is we need to calculate the cost, Ce, cost of energy. And we are paying here, or Dave is paying 9.86perMCF.Remember,MCFisbasicallyonemillionBTUs.Sothepricewouldbe9.86 per million BTUs. So this will be equal to 0.00000986.
Ce = $9.86 / MCF = 9.86 / 1,000,000 BTUs = 0.00000986
And if we plug this into this number here, into this formula here, 0.65 times 16 times 22 times 0.86 and divided by this is 0.00000986 and R2 – R1 happens to be 6 and 6,000 is the degree days and 24. This should come out to be, I guess 23 years roughly. This is kind of a long time period to recover the investment.
=0.65 × 16 × 22 × 0.86$0.00 00986 × 6 × 6,000 × 24Payback Period = 23 years