Question

30 number, 100W incandescent lamps are used for exterior lighting and it is being recommended to replace with 25 number 20 W CFL or 15 number 20 W fluorescent Tube light. Determine the payback period for each of the two recommended, by using following information. i) Cost of one incandescent lamp Rs.10/- ii) Cost of one CFL Rs.80/- and iii) Cost of one fluorescent tube Rs.140/-. Assume cost per unit is Rs 4/- and working hours 10 per day.

Answer 1

To determine the payback period for each lighting replacement option, we'll follow these steps:

1. **Calculate the total power consumption and cost for each option:**

   **Incandescent Lamps:**
   - Total power = 30 lamps × 100W = 3000W or 3 kW.
   - Daily energy consumption = 3 kW × 10 hours = 30 kWh.
   - Daily cost = 30 kWh × Rs. 4/- = Rs. 120/-.

   **CFLs:**
   - Total power = 25 lamps × 20W = 500W or 0.5 kW.
   - Daily energy consumption = 0.5 kW × 10 hours = 5 kWh.
   - Daily cost = 5 kWh × Rs. 4/- = Rs. 20/-.

   **Fluorescent Tube Lights:**
   - Total power = 15 tubes × 20W = 300W or 0.3 kW.
   - Daily energy consumption = 0.3 kW × 10 hours = 3 kWh.
   - Daily cost = 3 kWh × Rs. 4/- = Rs. 12/-.

2. **Calculate the initial cost of replacing each type of lighting:**

   **CFL Replacement:**
   - Cost = 25 CFLs × Rs. 80/- = Rs. 2000/-.

   **Fluorescent Tube Replacement:**
   - Cost = 15 tubes × Rs. 140/- = Rs. 2100/-.

3. **Calculate the savings per day for each replacement option:**

   **CFL Replacement:**
   - Daily savings = Daily cost of incandescent lamps - Daily cost of CFLs
   - Daily savings = Rs. 120/- - Rs. 20/- = Rs. 100/-.

   **Fluorescent Tube Replacement:**
   - Daily savings = Daily cost of incandescent lamps - Daily cost of fluorescent tubes
   - Daily savings = Rs. 120/- - Rs. 12/- = Rs. 108/-.

4. **Calculate the payback period:**

   **CFL Replacement:**
   - Payback period = Initial cost / Daily savings
   - Payback period = Rs. 2000/- / Rs. 100/- = 20 days.

   **Fluorescent Tube Replacement:**
   - Payback period = Initial cost / Daily savings
   - Payback period = Rs. 2100/- / Rs. 108/- ≈ 19.44 days.

**Summary:**
- **CFL Replacement:** Payback period is 20 days.
- **Fluorescent Tube Replacement:** Payback period is approximately 19.44 days.

Answer 2

To determine the payback period for each of the two recommended replacements, follow these steps:

### 1. Calculate the Total Energy Consumption

**Incandescent Lamps:**
- Number of lamps: 30
- Power rating per lamp: 100W
- Total power consumption: \( 30 \text{ lamps} \times 100 \text{ W} = 3000 \text{ W} \) or \( 3 \text{ kW} \)
- Daily energy consumption: \( 3 \text{ kW} \times 10 \text{ hours} = 30 \text{ kWh} \)

**CFLs:**
- Number of CFLs: 25
- Power rating per CFL: 20W
- Total power consumption: \( 25 \text{ CFLs} \times 20 \text{ W} = 500 \text{ W} \) or \( 0.5 \text{ kW} \)
- Daily energy consumption: \( 0.5 \text{ kW} \times 10 \text{ hours} = 5 \text{ kWh} \)

**Fluorescent Tube Lights:**
- Number of tubes: 15
- Power rating per tube: 20W
- Total power consumption: \( 15 \text{ tubes} \times 20 \text{ W} = 300 \text{ W} \) or \( 0.3 \text{ kW} \)
- Daily energy consumption: \( 0.3 \text{ kW} \times 10 \text{ hours} = 3 \text{ kWh} \)

### 2. Calculate the Daily Energy Cost

Cost per unit (kWh) is Rs. 4/-.

**Incandescent Lamps:**
- Daily energy cost: \( 30 \text{ kWh} \times 4 \text{ Rs/kWh} = 120 \text{ Rs} \)

**CFLs:**
- Daily energy cost: \( 5 \text{ kWh} \times 4 \text{ Rs/kWh} = 20 \text{ Rs} \)

**Fluorescent Tube Lights:**
- Daily energy cost: \( 3 \text{ kWh} \times 4 \text{ Rs/kWh} = 12 \text{ Rs} \)

### 3. Calculate the Total Initial Costs

**Incandescent Lamps:**
- Cost of 30 lamps: \( 30 \text{ lamps} \times 10 \text{ Rs/lamp} = 300 \text{ Rs} \)

**CFLs:**
- Cost of 25 CFLs: \( 25 \text{ CFLs} \times 80 \text{ Rs/CFL} = 2000 \text{ Rs} \)

**Fluorescent Tube Lights:**
- Cost of 15 tubes: \( 15 \text{ tubes} \times 140 \text{ Rs/tube} = 2100 \text{ Rs} \)

### 4. Calculate the Payback Period

Payback period is the time required to recoup the initial investment through the savings in energy costs.

**Savings for CFLs:**
- Daily saving: \( 120 \text{ Rs} - 20 \text{ Rs} = 100 \text{ Rs} \)
- Initial cost difference: \( 2000 \text{ Rs} - 300 \text{ Rs} = 1700 \text{ Rs} \)
- Payback period: \( \frac{1700 \text{ Rs}}{100 \text{ Rs/day}} = 17 \text{ days} \)

**Savings for Fluorescent Tube Lights:**
- Daily saving: \( 120 \text{ Rs} - 12 \text{ Rs} = 108 \text{ Rs} \)
- Initial cost difference: \( 2100 \text{ Rs} - 300 \text{ Rs} = 1800 \text{ Rs} \)
- Payback period: \( \frac{1800 \text{ Rs}}{108 \text{ Rs/day}} = 16.67 \text{ days} \)

### Summary
- **Payback period for replacing with CFLs:** 17 days
- **Payback period for replacing with Fluorescent Tube Lights:** 16.67 days

Both options offer a quick payback period, with fluorescent tube lights being slightly more cost-effective in terms of payback time.