What is the NPV of the following cash flows if the required rate of return is 0.05?

Year        0         1          2          3            4

CF       -13,773    1,611     4,739     4,602      4,925   
 
Enter the answer with 2 decimals (e.g. 1000.23).

To calculate the Net Present Value (NPV) of the given cash flows with a required rate of return of 0.05, we use the NPV formula:

\[
NPV = \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t}
\]

where:
- \(CF_t\) is the cash flow at time \(t\),
- \(r\) is the required rate of return (0.05 in this case),
- \(t\) is the year (0 to 4).

Let's calculate each term separately:

\[
\begin{align*}
CF_0 &= -13,773 \\
\frac{CF_1}{(1 + r)^1} &= \frac{1,611}{(1 + 0.05)^1} = \frac{1,611}{1.05} = 1,534.29 \\
\frac{CF_2}{(1 + r)^2} &= \frac{4,739}{(1 + 0.05)^2} = \frac{4,739}{1.1025} = 4,298.96 \\
\frac{CF_3}{(1 + r)^3} &= \frac{4,602}{(1 + 0.05)^3} = \frac{4,602}{1.157625} = 3,976.60 \\
\frac{CF_4}{(1 + r)^4} &= \frac{4,925}{(1 + 0.05)^4} = \frac{4,925}{1.21550625} = 4,051.92 \\
\end{align*}
\]

Summing these present values:

\[
NPV = -13,773 + 1,534.29 + 4,298.96 + 3,976.60 + 4,051.92 = 72.77
\]

So, the NPV of the cash flows is \(72.77\).

**Do you want details or have any questions?**

Here are 8 related questions to expand your understanding:

1. What is the importance of the discount rate in NPV calculations?
2. How does a change in the required rate of return affect the NPV?
3. What does a positive NPV indicate about a project's feasibility?
4. How is the NPV used in comparing multiple projects?
5. What are some limitations of the NPV method?
6. How does the timing of cash flows impact the NPV?
7. What is the difference between NPV and other investment appraisal techniques like IRR?
8. How would the inclusion of taxes affect the NPV calculation?

**Tip:** Always verify the consistency of the discount rate with the cash flows' time periods when calculating NPV.

Learn how to calculate the Net Present Value (NPV) of cash flows with a 0.05 rate of return using detailed step-by-step calculations. Understand the significance of the discount rate in NPV calculations and how changes in the required rate of return affect NPV outcomes.

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