 Eva bought the Angel Face Boutique for R120 000. Her estimated cash inflows for the next five years are R15 000, R28 000, R42 000, R35 000 and R40 000.

If the NPV equals R4 500, then the cost of capital is


a.
7,92%.


b.
8,78%.


c.
10,27%.


d.
25,70%.

To determine the cost of capital (rate of return) that results in a Net Present Value (NPV) of R4,500, we need to use the NPV formula:

\[
NPV = \sum \left( \dfrac{C_t}{(1 + r)^t} \right) - C_0
\]

Where:
- \( NPV \) is the Net Present Value,
- \( C_t \) are the cash inflows at time \( t \),
- \( C_0 \) is the initial investment,
- \( r \) is the discount rate (cost of capital),
- \( t \) is the time period.

### Given:
- \( NPV = R4,500 \),
- \( C_0 = R120,000 \),
- Cash inflows over 5 years: \( R15,000, R28,000, R42,000, R35,000, R40,000 \),
- We need to solve for \( r \).

The equation will look like this:
\[
4500 = \left( \dfrac{15000}{(1 + r)^1} + \dfrac{28000}{(1 + r)^2} + \dfrac{42000}{(1 + r)^3} + \dfrac{35000}{(1 + r)^4} + \dfrac{40000}{(1 + r)^5} \right) - 120000
\]

Let me solve for \( r \) using numerical methods.The cost of capital that results in a Net Present Value of R4,500 is approximately **7.92%**, which corresponds to option **a**.

Would you like further details on the calculation or any related concepts?

Here are 5 related questions to expand the topic:
1. How is the NPV affected by changes in the cost of capital?
2. What is the importance of NPV in capital budgeting?
3. How do you calculate the Internal Rate of Return (IRR)?
4. What are the differences between NPV and Payback Period?
5. How would inflation affect the future cash inflows?

**Tip**: The cost of capital is often used as a discount rate for NPV, representing the expected return required by investors.

Eva bought the Angel Face Boutique for R120 000. Her estimated cash inflows for the next five years are R15 000, R28 000, R42 000, R35 000, and R40 000. If the NPV equals R4 500, then the cost of capital is:
a. 7,92%.
b. 8,78%.
c. 10,27%.
d. 25,70%.

This problem involves calculating the cost of capital using the Net Present Value (NPV) formula. Eva purchased a business for R120 000, and the cash inflows over five years are given. Using the NPV formula and solving for the discount rate, we find the cost of capital to be 7.92%. Suitable for finance students or anyone learning business valuation.

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