Facman Facilities Management considers investing R50 000 in a project that will result in equal incomes of R23 000 for three years. The firm’s cost of capital is 15%. By using a Net Present Value calculation, determine whether the firm should invest in the project.

To determine whether Facman Facilities Management should invest in the project, we can calculate the **Net Present Value (NPV)** of the project. The NPV is calculated by discounting the future cash flows (incomes) back to their present value using the firm's cost of capital and then subtracting the initial investment.

### Formula for NPV:

\[
\text{NPV} = \sum \left(\frac{R_t}{(1 + r)^t}\right) - C_0
\]

Where:
- \( R_t \) = Cash inflow at time \( t \) (R23,000 in this case)
- \( r \) = Discount rate (15% or 0.15)
- \( t \) = Time period (in years)
- \( C_0 \) = Initial investment (R50,000)

### Step-by-Step Calculation:

1. **Year 1:**
   \[
   \text{PV}_1 = \frac{23,000}{(1 + 0.15)^1} = \frac{23,000}{1.15} \approx 20,000
   \]

2. **Year 2:**
   \[
   \text{PV}_2 = \frac{23,000}{(1 + 0.15)^2} = \frac{23,000}{1.3225} \approx 17,388
   \]

3. **Year 3:**
   \[
   \text{PV}_3 = \frac{23,000}{(1 + 0.15)^3} = \frac{23,000}{1.5209} \approx 15,118
   \]

4. **Total Present Value of Cash Inflows:**
   \[
   \text{Total PV} = 20,000 + 17,388 + 15,118 \approx 52,506
   \]

5. **NPV Calculation:**
   \[
   \text{NPV} = 52,506 - 50,000 = 2,506
   \]

### Conclusion:

The NPV is R2,506. Since the NPV is positive, Facman Facilities Management should invest in the project because it will add value to the firm.

Would you like to dive deeper into any specific part of this calculation? Here are some related questions:

1. How does changing the discount rate affect the NPV?
2. What if the cash flows were not equal over the three years?
3. How would you calculate the NPV if the project lasted longer than three years?
4. What are the limitations of using NPV in investment decisions?
5. Can NPV be used to compare multiple projects? If so, how?

**Tip:** When comparing multiple projects using NPV, choose the project with the highest positive NPV, as it indicates the greatest potential to increase the firm's value.

Learn how to calculate the Net Present Value (NPV) for Facman Facilities Management's investment decision involving R50,000 initial investment and equal R23,000 incomes over three years at a 15% cost of capital. Determine if the project should be invested in based on the NPV calculation.

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