### In Texas Suburbs Conserving Energy Isn't The Only Thing That Doesn't Come Easy

In an October 20th article of the WSJ entitled, "In Texas Suburbs, Conserving Energy Doesn't Come Easy", the tradeoffs of trying to conserve energy were presented. In the discussion, one property owner anticipated that the additional $17,000 he spent on his home for energy efficient features would save $64 a month. He figured that the savings would pay off the cost in about 22 years. Since one of the other enjoyments of life we have besides reading the WSJ is teaching finance, we thought we ought to shed some light on this calculation.

The homeowner has taken his $17,000 initial cost and divided it by his anticipated monthly savings of $64. This yields a payoff of about 266 months which divided by 12 give us approximately 22 years. However, as we like to point out to our students, what happened to the opportunity cost of his initial investment? Or in others words money has time value. For instance, if we assume the owner took out a 30 year mortgage with rates of about 5.7% a year, then his initial $17,000 investment would be costing an additional $98.67 on his 30 year monthly mortgage payment. So at that interest rate the $64 a month savings evaporates. Indeed we find that at the 5.7% annual interest rate, if the $64 a month savings is anticipated to run on forever, (known as a perpetuity), then it is worth about $13,474. Not quite the $17,000 we need to justify the inital investment.

But not to worry. One thing we can be sure of in finance as with life is that the future brings with it a host of possible outcomes. So if the $64 savings the homeowner generates through time increases at say a rate of 0.2% a month or about 2.4% year, then the initial $17,000 will be paid off in about 40 years. Given the recent increases in the cost of energy, this investment in energy efficiency will more than likely pay for itself. Unless of course some unforeseen innovation makes the current energy market obsolete. But that is another story.

The homeowner has taken his $17,000 initial cost and divided it by his anticipated monthly savings of $64. This yields a payoff of about 266 months which divided by 12 give us approximately 22 years. However, as we like to point out to our students, what happened to the opportunity cost of his initial investment? Or in others words money has time value. For instance, if we assume the owner took out a 30 year mortgage with rates of about 5.7% a year, then his initial $17,000 investment would be costing an additional $98.67 on his 30 year monthly mortgage payment. So at that interest rate the $64 a month savings evaporates. Indeed we find that at the 5.7% annual interest rate, if the $64 a month savings is anticipated to run on forever, (known as a perpetuity), then it is worth about $13,474. Not quite the $17,000 we need to justify the inital investment.

But not to worry. One thing we can be sure of in finance as with life is that the future brings with it a host of possible outcomes. So if the $64 savings the homeowner generates through time increases at say a rate of 0.2% a month or about 2.4% year, then the initial $17,000 will be paid off in about 40 years. Given the recent increases in the cost of energy, this investment in energy efficiency will more than likely pay for itself. Unless of course some unforeseen innovation makes the current energy market obsolete. But that is another story.