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. Refer to the investment opportunities for 2025 and calculate the following. Ignore taxes. Use only the four decimals present value tables that appear after question 2.3. 2.2 Net Present Value of both projects

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.

---

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.

Learn how to calculate the Net Present Value (NPV) for Project A and Project B in capital budgeting. Understand the financial attractiveness of each project based on cash inflows, outflows, and residual values. Includes detailed step-by-step calculations using a minimum rate of return of 14%.

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