determine if the net present value of options 2 and 3

Let's calculate the Net Present Value (NPV) for Options 2 and 3.

### **Option 2: Sell the Know-How for a Single Payment of R4 Million**

- **Payment Received:** R4 million at the end of December 20X4.

Since this is a single payment received immediately, the NPV calculation is straightforward:

\[
\text{NPV}_{\text{Option 2}} = \frac{R4,000,000}{(1 + 0.12)^0} = R4,000,000
\]

### **Option 3: Sell the Know-How for a Royalty of R10 per Unit**

For Option 3, the NPV will be calculated based on the royalties received each year. We will discount these royalties back to the present value using the WACC of 12%.

#### **Royalty Revenue Per Year:**
\[
\text{Royalty Revenue}_t = \text{Number Sold}_t \times R10
\]

#### **Discounting the Cash Flows:**
The NPV for Option 3 is calculated as the sum of the discounted royalty revenues over the five years.

**Year 20X5:**
\[
\text{Royalty Revenue}_{20X5} = 100,000 \times R10 = R1,000,000
\]
\[
\text{Discounted Cash Flow}_{20X5} = \frac{R1,000,000}{(1 + 0.12)^1} = R892,857.14
\]

**Year 20X6:**
\[
\text{Royalty Revenue}_{20X6} = 100,000 \times R10 = R1,000,000
\]
\[
\text{Discounted Cash Flow}_{20X6} = \frac{R1,000,000}{(1 + 0.12)^2} = R797,193.88
\]

**Year 20X7:**
\[
\text{Royalty Revenue}_{20X7} = 100,000 \times R10 = R1,000,000
\]
\[
\text{Discounted Cash Flow}_{20X7} = \frac{R1,000,000}{(1 + 0.12)^3} = R711,776.68
\]

**Year 20X8:**
\[
\text{Royalty Revenue}_{20X8} = 80,000 \times R10 = R800,000
\]
\[
\text{Discounted Cash Flow}_{20X8} = \frac{R800,000}{(1 + 0.12)^4} = R508,932.97
\]

**Year 20X9:**
\[
\text{Royalty Revenue}_{20X9} = 80,000 \times R10 = R800,000
\]
\[
\text{Discounted Cash Flow}_{20X9} = \frac{R800,000}{(1 + 0.12)^5} = R454,405.32
\]

### **Total NPV for Option 3:**
\[
\text{NPV}_{\text{Option 3}} = R892,857.14 + R797,193.88 + R711,776.68 + R508,932.97 + R454,405.32 = R3,365,165.99
\]

### **Conclusion:**

- **Option 2:** NPV = **R4,000,000**
- **Option 3:** NPV = **R3,365,165.99**

Since the NPV of Option 2 is higher than that of Option 3, Option 2 (selling the know-how for a single payment of R4 million) is the more financially advantageous choice.

Would you like to dive deeper into these results, or do you have any other questions?

---

### **Further Exploration Questions:**
1. How would changes in the WACC affect the NPVs of Options 2 and 3?
2. What would be the impact of taxation on the NPVs calculated?
3. How sensitive is the NPV to changes in the sales volume for Option 3?
4. What is the break-even sales volume for Option 3 to equal the NPV of Option 2?
5. How would inflation affect the cash flows and NPVs?
6. What are the risks associated with Option 3 compared to Option 2?
7. If the company had alternative uses for the R4 million, how would that affect the decision?
8. How does the time value of money influence the preference between the lump sum in Option 2 and the royalties in Option 3?

### **Tip:**  
When dealing with mutually exclusive projects, always compare the NPVs or other financial metrics to determine the best option under different scenarios.

Learn how to calculate the Net Present Value (NPV) for Options 2 and 3 using discounted cash flow (DCF) analysis. Option 2 involves a lump-sum payment, while Option 3 includes royalty payments. Understand the financial implications and make informed decisions.

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