To calculate the Net Present Value (NPV) of both Project A and Project B, we follow these steps:

Step 1: Determine the Net Cash Flows for Each Year

Project A:

• Initial Investment: R4,800,000 + R300,000 (installation) = R5,100,000
• Annual Cash Inflows: R3,100,000
• Annual Cash Outflows: Starting at R1,300,000 in Year 1 and increasing by R100,000 each subsequent year.

Net Cash Flows:

• Year 1: R3,100,000 - R1,300,000 = R1,800,000
• Year 2: R3,100,000 - R1,400,000 = R1,700,000
• Year 3: R3,100,000 - R1,500,000 = R1,600,000
• Year 4: R3,100,000 - R1,600,000 = R1,500,000
• Year 5: R3,100,000 - R1,700,000 = R1,400,000
• Residual Value at the end of Year 5: R300,000

Project B:

• Initial Investment: R5,100,000
• Annual Cash Inflows: R3,100,000
• Annual Cash Outflows: R1,500,000 each year.

Net Cash Flows:

• Year 1 to Year 5: R3,100,000 - R1,500,000 = R1,600,000 (constant for all years)
• No residual value for Project B.

Step 2: Determine the Present Value Factor for Each Year

Using the minimum rate of return (discount rate) of 14%, we use the present value (PV) factors for each year. Given that we are using four-decimal PV tables, here are the PV factors:

• Year 1: PV factor = 0.8772
• Year 2: PV factor = 0.7695
• Year 3: PV factor = 0.6749
• Year 4: PV factor = 0.5921
• Year 5: PV factor = 0.5194

Step 3: Calculate the Present Value of Each Year’s Net Cash Flow

Project A:

$\text{NPV}_{\text{Year 1}} = R1,800,000 \times 0.8772 = R1,578,960$ $\text{NPV}_{\text{Year 2}} = R1,700,000 \times 0.7695 = R1,308,150$ $\text{NPV}_{\text{Year 3}} = R1,600,000 \times 0.6749 = R1,079,840$ $\text{NPV}_{\text{Year 4}} = R1,500,000 \times 0.5921 = R888,150$ $\text{NPV}_{\text{Year 5}} = R1,400,000 \times 0.5194 = R727,160$ $\text{NPV of Residual Value} = R300,000 \times 0.5194 = R155,820$

Total NPV of Cash Inflows:

$\text{Total NPV} = R1,578,960 + R1,308,150 + R1,079,840 + R888,150 + R727,160 + R155,820 = R5,738,080$

NPV of Project A:

$\text{NPV} = R5,738,080 - R5,100,000 = **R638,080**$

Project B:

$\text{NPV}_{\text{Year 1}} = R1,600,000 \times 0.8772 = R1,403,520$ $\text{NPV}_{\text{Year 2}} = R1,600,000 \times 0.7695 = R1,231,200$ $\text{NPV}_{\text{Year 3}} = R1,600,000 \times 0.6749 = R1,079,840$ $\text{NPV}_{\text{Year 4}} = R1,600,000 \times 0.5921 = R947,360$ $\text{NPV}_{\text{Year 5}} = R1,600,000 \times 0.5194 = R831,040$

Total NPV of Cash Inflows:

$\text{Total NPV} = R1,403,520 + R1,231,200 + R1,079,840 + R947,360 + R831,040 = R5,492,960$

NPV of Project B:

$\text{NPV} = R5,492,960 - R5,100,000 = **R392,960**$

Step 4: Conclusion

• NPV of Project A: R638,080
• NPV of Project B: R392,960

Project A has a higher NPV compared to Project B, making it the more financially attractive option according to the NPV method.

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Do you have any further questions or would you like more details? Here are some related questions you might consider:

1. What is the Internal Rate of Return (IRR) for each project?
2. How does the inclusion of residual value in Project A affect its NPV?
3. What would be the NPV of Project B if the cash inflows increased by 5%?
4. How does changing the minimum rate of return to 12% affect the NPV of both projects?
5. Which project would be more favorable if both had the same initial investment cost?

Tip: The NPV method is preferred in capital budgeting because it accounts for the time value of money and provides a direct measure of how much value will be added to the firm by undertaking the project.