This week I worked on a project with one of my Microsoft peers and I helped him install some energy usage monitoring equipment in his house.  Without being specific about the solution, I must say it is pretty cool.  As a result of installing this and then running around his house flipping electrical devices on and off to see how they impacted the data being returned, we started talking about cost efficiency of various options.

Notice I use the phrase, cost efficiency.  While I try to be green wherever I can, sometimes it just doesn’t make financial sense, and it definitely isn’t easy (check out the song Bein' Green).  Often the information to figure this out is really hard to find.  As a result of this I broke out Excel and spent several hours working on some numbers.  Herein lies the story of the analysis as to whether or not LED lights make sense.  I share this so that others can use what I learned or replicate the methodology to make more cost efficient purchases.  Also this methodology will also work for other replacements, say refrigerator or AC unit.

With any analysis, we make certain assumptions and require inputs and outputs to estimate the impact.  These are discussed below.

ASSUMPTIONS:

• While there is definitely an energy difference in the whole process of mining raw materials through manufacturing to putting the product on the shelves, the analysis assumes those energy costs are factored into the price of the bulb.  Additionally, it doesn’t cover incidentals like fuel costs to get the bulb from the store to the house.  Thus, in an effort to simplify the analysis, this only looks at the costs of the bulbs and electricity.
• Today’s prices are fixed, the price of energy and light bulbs will not change over the course of the duration of the analysis.  Though this does not represent reality, the results can easily be adjusted.  Increases in energy prices, decreases in LED bulb costs, and increases in incandescent bulb costs, will increase savings and decrease the break even point.

INPUTS:

• The cost, estimated service time (usage dependent life time), and wattage of the energy efficient option (LED/CFL).
• The cost, estimated service time, and wattage of the comparison option (incandescent bulbs).
• The energy cost.  In charge per Kilo-Watt Hour (KWH).
• The hours of use per month.
• The Cost Of Capital.

OUTPUTS:

• The time to break even on the investment.
• The total savings over the life of the investment.

Definition – Cost Of Capital:  In the context of this discussion, this means the interest rate that could be earned with using the money elsewhere.  This essentially affects how long it takes to break even and how much savings you end up with when the bulb finally wears out.  Two examples, let’s say you have 100 dollars today to spend and the LED bulb costs \$80 more than the incandescent:

• Option 1 – You can either buy the incandescent light bulb or invest in a savings account that earns 10% interest.  If you spend the \$80 difference on the LED today, you are costing yourself the ability to earn 10% interest on the money.  This means you are losing \$8 per year of income.  This sort of means you are “borrowing” the money at 10% until you break even, and then you start earning 10% on what you save from that point forward.
• Option 2 – You have no intention of saving the money.  This essentially means that you have an interest rate of 0%.  At the end of the life of the bulb all we are measuring is how much more cash you had in your pocket to spend as a result of buying the LED today.

Sample Data For Inputs (These numbers come from my favorite big box home supplies retailer website):

• LED Bulbs cost \$60 plus tax, about \$65, use 12 watts and last 50,000 hours.  (For the numbers, I looked PAR-30 floods, as this is what we happened to be comparing)
• Incandescent bulbs cost \$8 plus tax, about \$8.50, use 75 watts and last 2,000 hours.
• These bulbs are in the home office which gets a lot of use, to the tune of 12 hours or so a day, 22 or so days a month.  This is a total of 264 hours per month.
• The cost of electricity is about \$0.11 per KWH in this area.  This includes the distribution and usage charges.

To illuminate the math behind how much we get charged for the energy to use the light, let me show how it is worked out.  The energy cost of an LED bulb used for 1 hour at 12 watts (converted to 0.012 KW) at \$0.11 per KWH costs \$0.00132 (1 hr. * 0.012 KW * \$0.11 per KWH = \$0.00132).  If the bulb is used for 100 hours a month, that means that it costs \$0.132 per month to use.  For the incandescent bulb, just replace the 0.012 KW with 0.075 KW for the incandescent bulb.  This results in a \$0.00693 savings per hour of use (\$0.00825 per KWH incandescent - \$0.00132 per KWH LED).

Other considerations:

The longer service time of the LED light means that if an incandescent bulb will be used instead, the incandescent bulb will have to be replaced multiple times over the life of the LED.  The math:  50,000 hours of life out of the LED divided by 2,000 hours of life out of the incandescent.  This results in the incandescent bulb being replaced 25 times (50,000 hrs / 2,000 hrs = 25).  This would cost \$212 in incandescent bulbs over the 50,000 hours of use (\$147 in total savings).  The question is also where you would break even which is \$65 for the LED divided by \$8.50 per incandescent, which is 7.64 changes of the light bulb (\$65 / \$8.50 = 7.64 changes).

Note:  Time has a significant impact on whether or not the investment pays off.

• 10 hours of use per month:
• That would take 1528 months or 127 years to break even on the bulb purchase alone.  (2000 hours * 7.64 bulbs / 10 hours)
• That would take 5,000 months to use up the LED or 417 years to realize the totals savings.
• 730 hours of use per month (365 days / 12 months * 24 hours = 730 hours per month average) – on all the time.  Just replace the number of hours of use in the previous equations to do the math here.
• That would take 21 months or less then 2 years.
• The total life of the LED would be about 69 months, or less than 6 years to realize the savings.

Combining all of this (read as “Plugging the data into Excel”):

We’ll assume that this is in the home office and the light is used 12 hours a day, 22 days a month (264 hours).

Option 1 – Cost of Capital is 10%

• Break-even point = 1.75 years
• Total savings at end of life of the LED bulb = \$1,005
• Total lifetime of the LED bulb = 15.8 years

Option 2 – Cost of Capital is 0%

• Break-even point = 1.6 years
• Total savings at end of life of the LED bulb = \$484
• Total lifetime of the LED bulb = 15.8 years

Q.  Why does it take longer to break even with a higher capital cost, but you save more over the same period?

A.  This is the power of compound interest.  This is another topic.

So all this math is really fun, but what does this mean?

Let’s start with the amount of usage of the bulb.  Due to the cost of energy, the greater the difference in the wattage AND the more you use the bulb, the greater the impact on savings and pay off.  Check out this picture.

Using the same numbers as Option 1:

As can be seen from the above chart, there is a really steep curve on breaking even.  Furthermore, if the bulb is used less than about 43 hours a month, the purchase of it will never break even.  Also, from the picture, we can see that in order to break-even in a reasonable time frame (let’s say 5 years), the bulb needs to be used at least about 100 hours per month (about 3.5 hours per day, every day).

Using the same numbers as Option 2:

As we saw in the math, if you don’t save the money, you break even a lot faster (steeper curve), though the break even times in low usage are ridiculously long (who’s going to use a bulb for 400 years?).  This means that in order to break even in the same 5 year time frame, you need to use the light about 80 hours a month (2.75 hours per day, every day).

In the longer term (How much does this actually save me?):

As we can see, payback times are significantly impacted by the usage.  This also leads to an impact on the savings from using an LED bulb over the lifetime of the bulb.  We will have 4 scenarios we will look at here:

 Usage Cost Of Capital 1 280 hours per month (Home Office estimate) 0% 2 280 hours per month 10% 3 730 hours per month (Light is on all the time) 0% 4 730 hours per month 10%

Note:  Where the red (dashed) line crosses the blue is the estimated lifetime of the bulb.  The blue line predictions to the right of that intersection are what would happen if you keep up with the same savings strategy.

Scenario 1 – LED lasts 15 years and saves \$479 over the course of the 15 years:

Scenario 2 – LED lasts 15 years and saves \$944 over the course of the 15 years:

Scenario 3 – LED lasts 5 years and saves \$432 over the course of the 5 years:

Scenario 4 – LED lasts 5 years and saves \$537 over the course of the 5 years:

Note:

Summary:

• LEDs don’t pay off for infrequently used lights, ever.
• Regardless of your cost of capital, given current costs, it appears that the lights need to be used about 80 to 100 hours in order to break even in a reasonable time frame.  Reasonable to the author is 5 years.
• The more the light remains on, the more money LEDs save over time.
• Narrowing of price differences in LED and incandescent bulbs and increases in energy prices will accomplish the following three cases:
• Increase the savings over time.
• Reduce the break-even point for purchase time frames.
• Make LED replacements for low usage lights, less than 80 to 100 hours, viable.

The spreadsheet all this work was done in is attached to this post so that others can play with the numbers as well.