Your firm is considering buying a new machine. Here are the facts:  the machine costs $94,350. Over the next 15 years (the life of the machine), the machine will generate annual revenues of $33,422.5. The annual cost of the goods sold (COGS) is $6,919.5 per year and other costs; selling, general, and administrative expenses (GS&A) are $2,586.6 per year. Depreciation on the machine is straight-line over 15 years (that is: $6,290 per year). At the end of 15 years, the machine’s salvage value (or terminal value) is zero. If the firm’s tax rate is 21.05% and the firm’s discount rate for projects of this kind is 14.54%, what is NPV for this project?

To calculate the Net Present Value (NPV) of the project, we need to break down the problem into several steps and then sum up the cash flows for each year. Here is the procedure:

### 1. **Calculate Annual Cash Flow before Taxes (EBIT)**
EBIT (Earnings Before Interest and Taxes) can be calculated by subtracting COGS, GS&A expenses, and depreciation from the revenue.

\[
\text{EBIT} = \text{Revenue} - \text{COGS} - \text{GS\&A} - \text{Depreciation}
\]

Given the following values:
- **Revenue:** \$33,422.5 per year
- **COGS:** \$6,919.5 per year
- **GS&A:** \$2,586.6 per year
- **Depreciation:** \$6,290 per year

\[
\text{EBIT} = 33,422.5 - 6,919.5 - 2,586.6 - 6,290 = 17,626.4 \, \text{per year}
\]

### 2. **Calculate After-Tax Cash Flow**
After-tax cash flow is calculated by applying the tax rate to EBIT, and then adding back the depreciation (since depreciation is a non-cash expense).

\[
\text{After-tax EBIT} = \text{EBIT} \times (1 - \text{Tax Rate})
\]
\[
\text{After-tax Cash Flow} = \text{After-tax EBIT} + \text{Depreciation}
\]

- Tax rate = 21.05%

\[
\text{After-tax EBIT} = 17,626.4 \times (1 - 0.2105) = 13,904.96
\]

Now, add back the depreciation:

\[
\text{After-tax Cash Flow} = 13,904.96 + 6,290 = 20,194.96 \, \text{per year}
\]

### 3. **Calculate Net Present Value (NPV)**
The NPV is the present value of the after-tax cash flows over the life of the machine, minus the initial cost. Since the cash flows are constant, we can use the formula for the present value of an annuity:

\[
\text{NPV} = \left( \frac{\text{Cash Flow}}{\text{Discount Rate}} \times \left(1 - \frac{1}{(1 + \text{Discount Rate})^{15}}\right) \right) - \text{Initial Investment}
\]

Where:
- Cash Flow = \$20,194.96
- Discount Rate = 14.54% (0.1454)
- Number of years = 15
- Initial Investment = \$94,350

Let's calculate this:

\[
\text{NPV} = 20,194.96 \times \left( \frac{1 - \frac{1}{(1 + 0.1454)^{15}}}{0.1454} \right) - 94,350
\]

Now let's calculate it step-by-step.The Net Present Value (NPV) of the project is approximately **\$26,415.64**. 

This positive NPV suggests that purchasing the machine is a profitable investment for the firm, as it generates value above the initial cost when discounted at the firm's required rate of return.

Would you like to explore more details or have any questions? Here are some related questions:

1. How does changing the discount rate affect the NPV?
2. What is the breakeven point for this investment?
3. How does depreciation impact cash flows over time?
4. Can a different tax rate change the investment decision?
5. How do we compute the internal rate of return (IRR) for this project?

**Tip:** A positive NPV typically indicates a good investment opportunity if the firm wants to maximize shareholder wealth.

Your firm is considering buying a new machine. Here are the facts: the machine costs $94,350. Over the next 15 years (the life of the machine), the machine will generate annual revenues of $33,422.5. The annual cost of the goods sold (COGS) is $6,919.5 per year and other costs; selling, general, and administrative expenses (GS&A) are $2,586.6 per year. Depreciation on the machine is straight-line over 15 years (that is: $6,290 per year). At the end of 15 years, the machine’s salvage value (or terminal value) is zero. If the firm’s tax rate is 21.05% and the firm’s discount rate for projects of this kind is 14.54%, what is NPV for this project?

Calculate the Net Present Value (NPV) of a machine purchase with a 15-year lifespan, straight-line depreciation, annual revenue of $33,422.5, COGS of $6,919.5, and GS&A expenses of $2,586.6. The firm's tax rate is 21.05% with a discount rate of 14.54%. Learn how to compute the NPV step-by-step using EBIT, after-tax cash flow, and the present value of cash flows over time.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation