Give step-by-step solution with explanation and final answer:
Your municipality charges households R3.20 per kWh for any usage above 500 kWh. Suppose, by installing a solar geyser at an initial price of R16 000 you will save approximately up to 450kWh of electrical energy per month.
2.1. Calculate the payback period (in months) of the solar geyser.
(5)
2.2. Analyse how the breakeven period will be affected by an increase in the price of electricity, if the Energy Regulator (NERSA) approves a 13% average increase in electricity tariffs for the 2026/2027 financial year. {5}
Question:
Give step-by-step solution with explanation and final answer:
Your municipality charges households R3.20 per kWh for any usage above 500 kWh. Suppose, by installing a solar geyser at an initial price of R16 000 you will save approximately up to 450kWh of electrical energy per month.
2.1. Calculate the payback period (in months) of the solar geyser.
(5)
2.2. Analyse how the breakeven period will be affected by an increase in the price of electricity, if the Energy Regulator (NERSA) approves a 13% average increase in electricity tariffs for the 2026/2027 financial year. {5}
This is AI generated Response.
Asked by: ravi
Created at: 2025-08-14 18:26:09
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Let's solve each part step by step:
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**2.1. Calculate the payback period (in months) of the solar geyser.**
**Given:**
- Initial cost of solar geyser = **R16 000**
- Savings in electricity per month = **450 kWh**
- Tariff for usage above 500 kWh = **R3.20 per kWh**
**Monthly Savings Calculation:**
Monthly savings = Energy saved × Price per kWh
Monthly savings = 450 kWh × R3.20/kWh
Monthly savings = **R1,440**
**Payback Period (in months) Calculation:**
Payback period = Initial cost / Monthly savings
Payback period = R16,000 / R1,440
Payback period ≈ **11.11 months**
**Final Answer for 2.1:**
> The payback period of the solar geyser is **approximately 11.1 months**.
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**2.2. Analyse how the breakeven period will be affected by an increase in the price of electricity, if NERSA approves a 13% average increase in electricity tariffs for the 2026/2027 financial year.**
**New Tariff Calculation:**
Old tariff = R3.20/kWh
Increase = 13%
New tariff = R3.20 × (1 + 0.13)
New tariff = R3.20 × 1.13
New tariff = **R3.616/kWh**
**New Monthly Savings Calculation:**
Monthly savings = Energy saved × New price per kWh
Monthly savings = 450 kWh × R3.616
Monthly savings = **R1,627.20**
**New Payback Period Calculation:**
Payback period = R16,000 / R1,627.20
Payback period ≈ **9.83 months**
**Analysis:**
- With the electricity price increase, the monthly savings will **increase** because each kWh saved is now worth more money.
- As a result, the payback period will be **shorter** because the initial investment is recovered faster with higher monthly savings.
**Final Answer for 2.2:**
> If the electricity tariff increases by 13%, the monthly savings from the solar geyser will increase, reducing the payback period to about **9.8 months**. This means the breakeven period will be **shorter** than before the tariff increase because the value of the energy saved each month is greater. Any further increases in electricity tariffs will continue to decrease the breakeven period for the solar geyser investment.
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**Summary Table:**
| Scenario | Monthly Savings | Payback Period (months) |
|------------------------------|----------------|------------------------|
| Original Tariff (R3.20/kWh) | R1,440 | 11.1 |
| With 13% Increase (R3.62/kWh)| R1,627.20 | 9.8 |
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