To calculate the Internal Rate of Return (IRR) for Project B, we first need to follow the general steps for determining IRR through net present value (NPV) calculations at two different discount rates, 17% and 18%. The IRR is the rate at which the NPV equals zero. Since we're given cash flows and costs, we will start by calculating the NPVs at both discount rates.

Step 1: Identify the relevant cash flows for Project B

• Initial cost: R5,100,000 (including R400,000 for installation).
• Annual cash inflows: R3,100,000 per year for 5 years.
• Annual cash outflows: R1,500,000 per year for 5 years.
• Net annual cash flows (inflows - outflows):
  $3,100,000 - 1,500,000 = R1,600,000$ per year.
• Depreciation: Depreciation is not a cash flow and won't affect the NPV calculation.

Therefore, we are working with annual net cash flows of R1,600,000 for 5 years.

Step 2: Calculate NPVs at 17% and 18%

NPV Formula

The formula for NPV is:

$NPV = -\text{Initial Cost} + \sum_{t=1}^{5} \frac{\text{Net Cash Flow}}{(1 + r)^t}$

where:

• $\text{Initial Cost} = R5,100,000$
• $\text{Net Cash Flow} = R1,600,000$ (constant for 5 years)
• $r = \text{discount rate}$ (either 17% or 18%)

NPV at 17%

We substitute $r = 0.17$:

$NPV_{17\%} = -5,100,000 + \left( \frac{1,600,000}{(1 + 0.17)^1} + \frac{1,600,000}{(1 + 0.17)^2} + \frac{1,600,000}{(1 + 0.17)^3} + \frac{1,600,000}{(1 + 0.17)^4} + \frac{1,600,000}{(1 + 0.17)^5} \right)$

Let's compute this step-by-step.

NPV at 18%

Similarly, we substitute $r = 0.18$:

$NPV_{18\%} = -5,100,000 + \left( \frac{1,600,000}{(1 + 0.18)^1} + \frac{1,600,000}{(1 + 0.18)^2} + \frac{1,600,000}{(1 + 0.18)^3} + \frac{1,600,000}{(1 + 0.18)^4} + \frac{1,600,000}{(1 + 0.18)^5} \right)$

I'll now calculate both NPVs and proceed to determine the IRR.The calculated NPVs are as follows:

• NPV at 17%: R18,953.86
• NPV at 18%: -R96,526.37

Step 3: Determine the IRR

We can now use the interpolation formula to estimate the IRR between the two discount rates:

$\text{IRR} = r_1 + \frac{\text{NPV}_1}{\text{NPV}_1 - \text{NPV}_2} \times (r_2 - r_1)$

where:

• $r_1 = 17\%$, $\text{NPV}_1 = 18,953.86$
• $r_2 = 18\%$, $\text{NPV}_2 = -96,526.37$

I'll now calculate the IRR using this formula.The Internal Rate of Return (IRR) for Project B is approximately 17.16%.

Summary of results:

• NPV at 17%: R18,953.86
• NPV at 18%: -R96,526.37
• IRR: 17.16%

If you have any questions or need further clarification, feel free to ask!

Here are 5 related questions you could explore:

1. How would the IRR change if the cash inflows or outflows were different?
2. What does a positive NPV at 17% suggest about Project B?
3. How would a longer project duration (e.g., 10 years) affect the IRR calculation?
4. What is the impact of depreciation on the project's financial evaluation?
5. How does the IRR compare to other project evaluation methods like payback period or ROI?

Tip: The IRR is a good measure to compare projects, but it’s always important to consider the NPV as well, especially when deciding between different discount rates.