n: The number of bulbs being replaced with LED light bulbs. Example: 100.

cb: The cost of a normal bulb. Example: $1.00.

cl: The cost of an LED light bulb. Example: $50.00.

ib: The initial investment for replacing all bulbs with normal bulbs. Example: n * cb = $100.

il: The initial investment for replacing all bulbs with LED light bulbs. Example: n * cl = $5,000.

lb: The lifespan of a normal bulb. Example: 1,000 hours.

ll: The lifespan of an LED light bulb. Example: 50,000 hours.

t: The amount of time your lights are running. Example: 40 hours/week.

wb: The wattage of a normal bulb. Example: 60 watts.

wl: The wattage of an LED light bulb. Example: 6 watts.

e: The cost of electricity. Example: $0.14 kilowatt hours.

s: The total savings. Example: Solve for s!

So, now to refine our variables. We already know that:

ib = n * cb = $100

il = n * cl = $5,000

Next, we need to know how many times we will have to replace our normal bulbs (r), using the equation:

r = ll / lb = 50

The total cost of replacements is:

cr = (r - 1) * cb * n = $4,900.

We use r - 1 because the first "replacement" is considered in the initial investment. Next, we need the cost to keep the bulbs running for one year:

eb = (wb / 1000) * e * t * 52 = 17.47

el = (wl / 1000) * e * t * 52 = 1.75

Next, the total savings per bulb per year:

s = eb - el = 15.72

Or for all the LED light bulbs:

st = s * n = $1,572

How many years will we be seeing these savings before having to reinvest? Well, how many years does the bulb last?

y = ll / (t * 52) = 24.04

Making the total savings over the lifespan of the LED light bulbs:

sf = (st * y) + cr + ib - il = $37,790.88.

Note that that's not even counting the cost of labor to replace the bulbs. Of course, you might run the bulbs for longer, which won't change your actual savings, but will change how much you save per year. Using the above numbers, you would save a bit over $1500/year, so the bulbs would pay for themselves in a little more than three years, and be turning ROI every year thereafter. If you run your LED light bulbs 80 hours a week, it becomes somewhat under two years. If your lights are on 24/7, LED light bulbs can easily pay for themselves in the first year.