To determine the payback time and return on investment (ROI) for switching a yellow incandescent traffic light to a yellow LED traffic light, we will break down the calculation as follows:
Key Assumptions:
We will assume the following for both incandescent and LED traffic lights:
Incandescent Bulb:
- Power Consumption: 135 watts (common for yellow incandescent traffic lights).
- Lifespan: 8,000 hours.
- Cost per bulb: $5.
- Operating Hours: 24 hours per day, 365 days a year.
- Electricity Rate: $0.12 per kWh (kilowatt-hour).
- Annual Energy Cost (Incandescent): $141.91 (as calculated previously).
- Maintenance Cost per Replacement: $55 (includes labor and the cost of the bulb).
LED:
- Power Consumption: 10 watts (standard for a yellow LED traffic light).
- Lifespan: 50,000 hours.
- Cost of LED Module: $100.
- Operating Hours: 24 hours per day, 365 days a year.
- Annual Energy Cost (LED): $10.51 (as calculated previously).
- Maintenance Cost for LED: $0 (LEDs last 50,000 hours and require no replacement in this time).
Step 1: Annual Savings
Energy Savings:
The annual energy cost savings when switching from an incandescent yellow traffic light to an LED yellow traffic light can be calculated as:Annual Energy Cost (Incandescent)−Annual Energy Cost (LED)=141.91 $−10.51 $=131.40 $\text{Annual Energy Cost (Incandescent)} – \text{Annual Energy Cost (LED)} = 141.91 \, \text{\$} – 10.51 \, \text{\$} = 131.40 \, \text{\$}Annual Energy Cost (Incandescent)−Annual Energy Cost (LED)=141.91$−10.51$=131.40$
Maintenance Savings:
Since the incandescent bulb needs to be replaced 6.25 times over the 50,000-hour lifespan of the LED (at a cost of $55 per replacement), the total maintenance savings over 50,000 hours is:6.25 replacements×55 $ per replacement=343.75 $ over the LED lifespan6.25 \, \text{replacements} \times 55 \, \text{\$ per replacement} = 343.75 \, \text{\$ over the LED lifespan}6.25replacements×55$ per replacement=343.75$ over the LED lifespan
Amortized annually (50,000 hours = 5.7 years), the maintenance savings per year is:343.75 $50,000 hours×8,760 hours/year=60.19 $/year\frac{343.75 \, \text{\$}}{50,000 \, \text{hours}} \times 8,760 \, \text{hours/year} = 60.19 \, \text{\$/year}50,000hours343.75$​×8,760hours/year=60.19$/year
Total Annual Savings:
The total savings, combining both energy and maintenance, is:131.40 $ (energy savings)+60.19 $ (maintenance savings)=191.59 $ total savings per year131.40 \, \text{\$ (energy savings)} + 60.19 \, \text{\$ (maintenance savings)} = 191.59 \, \text{\$ total savings per year}131.40$ (energy savings)+60.19$ (maintenance savings)=191.59$ total savings per year
Step 2: Payback Period
The payback period is the time it takes to recover the initial investment in the LED through annual savings. The initial investment for the LED is $100.Payback Period=Initial InvestmentAnnual Savings=100 $191.59 $ per year≈0.52 years\text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Savings}} = \frac{100 \, \text{\$}}{191.59 \, \text{\$ per year}} \approx 0.52 \, \text{years}Payback Period=Annual SavingsInitial Investment​=191.59$ per year100$​≈0.52years
This means the payback period for switching to a yellow LED traffic light is approximately 6 months.
Step 3: Return on Investment (ROI)
The ROI is calculated based on the total savings over the lifetime of the LED (50,000 hours) compared to the initial investment.
- Total Savings Over the LED’s Lifetime:
- The total savings (energy + maintenance) over 50,000 hours is approximately $1,065 (as previously calculated).
- Initial Investment: $100
The ROI is calculated as:ROI=Total Savings Over the LED’s Lifetime−Initial InvestmentInitial Investment×100\text{ROI} = \frac{\text{Total Savings Over the LED’s Lifetime} – \text{Initial Investment}}{\text{Initial Investment}} \times 100ROI=Initial InvestmentTotal Savings Over the LED’s Lifetime−Initial Investment​×100 ROI=1,065 $−100 $100 $×100=965%\text{ROI} = \frac{1,065 \, \text{\$} – 100 \, \text{\$}}{100 \, \text{\$}} \times 100 = 965\%ROI=100$1,065$−100$​×100=965%
Summary:
- Payback Period: Approximately 0.52 years (or 6 months).
- Return on Investment (ROI): Approximately 965% over the LED’s lifetime.
These calculations show that switching from an incandescent yellow traffic light to an LED results in a very fast payback time (around 6 months) and an exceptionally high return on investment, making it a highly cost-effective and energy-efficient solution.
