ABC Corp. is analyzing a project that is expected to increase after-tax cash flows by $8.50 million per year for 5 years. They spent $1 million last year on consulting fees and need to spend $17.40 million in equipment today. What is the net present value of the project, if the required return is 6.60%? Ignore the impact of taxes and depreciation.

Question 4Answer

a.

$13,683,659

b.

$16,828,147

c.

$17,828,147

d.

$3,405,329

e.

$18,828,147

To calculate the Net Present Value (NPV) of the project, we need to account for the cash inflows and outflows, applying the appropriate discount factor for each period.

### Given Information:
- **Annual cash inflows**: $8.50 million per year for 5 years.
- **Initial outlay (equipment cost)**: $17.40 million today.
- **Sunk cost (consulting fees)**: $1 million (already spent, so it's irrelevant to the NPV calculation).
- **Required return (discount rate)**: 6.60% per year.
- **Number of years**: 5 years.

### Formula for NPV:
\[
NPV = \sum \left( \frac{{C_t}}{{(1 + r)^t}} \right) - C_0
\]
Where:
- $C_t$ is the cash inflow in year $t$,
- $r$ is the required return (6.60%),
- $C_0$ is the initial investment (equipment cost).

### Steps:

1. **Discount the annual cash flows**:
   The cash inflow of $8.50 million occurs at the end of each year for 5 years. The present value of each inflow is calculated using the formula for the present value of an annuity:
   \[
   PV = C \times \left( \frac{{1 - (1 + r)^{-n}}}{r} \right)
   \]
   Where:
   - $C$ is the annual cash inflow ($8.50 million),
   - $r$ is the required return (6.60% or 0.066),
   - $n$ is the number of years (5 years).

2. **Subtract the initial investment**:
   The initial investment of $17.40 million is subtracted from the total present value of the cash inflows.

Let's now calculate the NPV.

#### Step 1: Present value of annual cash flows
\[
PV_{\text{inflows}} = 8.50 \times \left( \frac{{1 - (1 + 0.066)^{-5}}}{0.066} \right)
\]
\[
PV_{\text{inflows}} = 8.50 \times \left( \frac{{1 - (1.066)^{-5}}}{0.066} \right)
\]
\[
PV_{\text{inflows}} = 8.50 \times \left( \frac{{1 - 0.744}}{0.066} \right)
\]
\[
PV_{\text{inflows}} = 8.50 \times \left( \frac{{0.256}}{0.066} \right)
\]
\[
PV_{\text{inflows}} = 8.50 \times 3.878
\]
\[
PV_{\text{inflows}} \approx 32.96 \text{ million}
\]

#### Step 2: Calculate NPV
Now, subtract the initial investment of $17.40 million:
\[
NPV = 32.96 - 17.40 = 15.56 \text{ million}
\]

So, the Net Present Value of the project is approximately **$15.56 million**.

### Answer:
The closest match to this result is **option b: $16,828,147**.

Would you like more details on the calculation, or do you have any other questions?

### Related Questions:
1. How would the NPV change if the required return were higher or lower than 6.60%?
2. What is the effect of adding taxes or depreciation on the NPV?
3. How does the time value of money impact project evaluation?
4. What is the difference between NPV and internal rate of return (IRR)?
5. How can you determine the sensitivity of NPV to changes in cash flows?

**Tip:** Always exclude sunk costs (like the consulting fees) when calculating NPV, as they are costs that have already been incurred and cannot be recovered.

ABC Corp. is analyzing a project that is expected to increase after-tax cash flows by $8.50 million per year for 5 years. They spent $1 million last year on consulting fees and need to spend $17.40 million in equipment today. What is the net present value of the project, if the required return is 6.60%? Ignore the impact of taxes and depreciation.

Learn how to calculate the net present value (NPV) for a project, including annual cash inflows of $8.50 million for 5 years and an initial equipment investment of $17.40 million. This detailed solution uses the NPV formula and discounted cash flow principles to determine the project's value. Suitable for high school students and finance learners.

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