Jasper Metals is considering installing a new molding machine which is expected to produce operating cash flows of $70,500 per year for 9 years. At the beginning of the project, inventory will decrease by $29,600, accounts receivables will increase by $27,800, and accounts payable will increase by $20,100. At the end of the project, net working capital will return to the level it was prior to undertaking the new project. The initial cost of the molding machine is $300,000. The equipment will be depreciated straight-line to a zero book value over the life of the project. The equipment will be salvaged at the end of the project creating an aftertax cash flow of $82,000. What is the net present value of this project given a required return of 11.7 percent?
		$124,067
		$131,797
		$136,741
		$141,597
		$118,672


To determine the net present value (NPV) of this project, we will break it down into key components: initial investment, operating cash flows, terminal cash flow (which includes salvage value and changes in working capital), and discounting all of these cash flows to the present value using the required return of 11.7%.

### 1. **Initial Investment**
The initial outlay includes the cost of the machine and changes in net working capital (NWC). The changes in NWC at the beginning of the project are:
- **Decrease in inventory:** $ +29,600 $
- **Increase in accounts receivable:** $ -27,800 $
- **Increase in accounts payable:** $ +20,100 $

Thus, the change in NWC is:
\[
\Delta NWC = 29,600 - 27,800 + 20,100 = +21,900
\]
Since an increase in net working capital is treated as a cash inflow, the total initial investment will be:
\[
\text{Initial Investment} = 300,000 - 21,900 = 278,100
\]

### 2. **Operating Cash Flows**
The operating cash flows are provided as $ 70,500 $ per year for 9 years. Since the equipment is depreciated straight-line to zero over 9 years, the annual depreciation is:
\[
\text{Annual Depreciation} = \frac{300,000}{9} = 33,333.33
\]

However, since we are provided with the operating cash flows directly (after accounting for depreciation and taxes), we don't need to calculate the tax effects here. We will use the $ 70,500 $ directly for 9 years.

### 3. **Terminal Cash Flows**
At the end of the project, the equipment is sold for a salvage value of $ 82,000 $ (after-tax). Additionally, the net working capital will return to its original level, resulting in a cash inflow equal to the initial change in NWC:
\[
\text{Terminal Cash Flow} = 82,000 + 21,900 = 103,900
\]

### 4. **NPV Calculation**
Now, we discount all these cash flows using the required return of $ 11.7\% $.

- **Year 0**: Initial investment $ -278,100 $
- **Years 1–9**: Operating cash flows $ 70,500 $
- **Year 9**: Terminal cash flow $ 103,900 $

The formula for NPV is:
\[
\text{NPV} = \sum_{t=1}^{9} \frac{70,500}{(1+0.117)^t} + \frac{103,900}{(1+0.117)^9} - 278,100
\]

Let me calculate this step by step:

1. Discounted cash flow for each of the 9 years for $ 70,500 $ per year.
2. Discounted terminal cash flow at year 9 for $ 103,900 $.
3. Sum these present values and subtract the initial investment.

Let’s now compute thisThe net present value (NPV) of the project is approximately **$140,247**.

Given the options provided, the closest value is **$141,597**.

### Do you have any questions or would you like further details?

Here are 5 related questions for deeper exploration:
1. How is straight-line depreciation calculated and how does it affect cash flows?
2. Why is the recovery of net working capital added back at the end of the project?
3. How does the discount rate impact the net present value of a project?
4. What would happen to the NPV if the salvage value were lower or higher?
5. How do changes in the operating cash flow over the years affect project valuation?

**Tip:** Always remember that NPV considers the time value of money, so cash flows received earlier have a higher value than those received later.

Jasper Metals is considering installing a new molding machine which is expected to produce operating cash flows of $70,500 per year for 9 years. At the beginning of the project, inventory will decrease by $29,600, accounts receivables will increase by $27,800, and accounts payable will increase by $20,100. At the end of the project, net working capital will return to the level it was prior to undertaking the new project. The initial cost of the molding machine is $300,000. The equipment will be depreciated straight-line to a zero book value over the life of the project. The equipment will be salvaged at the end of the project creating an aftertax cash flow of $82,000. What is the net present value of this project given a required return of 11.7 percent?

This detailed solution covers the NPV calculation for Jasper Metals' new molding machine project, with annual operating cash flows of $70,500, an initial cost of $300,000, and a salvage value of $82,000. The problem also explores depreciation, net working capital adjustments, and discounting at a required return of 11.7%. Suitable for finance and business students.

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