The directors of Hybrid Ltd intend expanding the company and they have the choice of investing in one of  two projects at the start of 2025 viz. Project A or Project B. Each project is expected to have a five-year life, with only Project A having a residual/scrap value of R300 000. The annual cash inflows from each project are estimated at R3 100 000. The company desires a minimum rate of return of 14%. 
Project A is anticipated to cost R4 800 000 excluding R300 000 for installation. The annual cash outflows  are estimated to be R1 300 000 for year one. These cash outflows are expected to increase by R100 000  per year thereafter. Depreciation is estimated to be R960 000 per year. 
Project B cost is expected to cost R5 100 000 including R400 000 for installation. The annual cash outflows  are estimated to be R1 500 000. Depreciation is estimated to be R1 020 000 per year. Calculate Internal Rate of Return of Project B (expressed to two decimal places ) using discount rates of 17% and 18% only. Your answer must include two net present value calculations and the determination of the IRR.

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.

The directors of Hybrid Ltd intend expanding the company and they have the choice of investing in one of two projects at the start of 2025 viz. Project A or Project B. Each project is expected to have a five-year life, with only Project A having a residual/scrap value of R300 000. The annual cash inflows from each project are estimated at R3 100 000. The company desires a minimum rate of return of 14%. Project A is anticipated to cost R4 800 000 excluding R300 000 for installation. The annual cash outflows are estimated to be R1 300 000 for year one. These cash outflows are expected to increase by R100 000 per year thereafter. Depreciation is estimated to be R960 000 per year. Project B cost is expected to cost R5 100 000 including R400 000 for installation. The annual cash outflows are estimated to be R1 500 000. Depreciation is estimated to be R1 020 000 per year. Calculate Internal Rate of Return of Project B (expressed to two decimal places) using discount rates of 17% and 18% only. Your answer must include two net present value calculations and the determination of the IRR.

Learn how to calculate the Internal Rate of Return (IRR) for Project B by computing the Net Present Values (NPV) at 17% and 18%. This finance problem includes step-by-step calculations of NPV, followed by interpolation to determine the IRR, and is ideal for students or professionals in finance or accounting.

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