10. A new factory at Arcata requires an initial outlay of $3.5 million to be paid immediately. The factory will last for eight additional years, after which it can be sold for a salvage value of $2,000,000. Sales will be $800,000 during the first year of operation and will grow at a rate of 9 percent a year after that. Variable costs will be 30 percent of sales and fixed costs will be $150,000 and grow at a rate of 5% per year. All costs are in cash. Assume cash flows occur at year-end. At a 6 percent required return. (Ignore taxes) The net present value of this project and is?

Question

10. A new factory at Arcata requires an initial outlay of $3.5 million to be paid immediately. The factory will last for eight additional years, after which it can be sold for a salvage value of $2,000,000. Sales will be $800,000 during the first year of operation and will grow at a rate of 9 percent a year after that. Variable costs will be 30 percent of sales and fixed costs will be $150,000 and grow at a rate of 5% per year. All costs are in cash. Assume cash flows occur at year-end. At a 6 percent required return. (Ignore taxes) The net present value of this project and is?

Answer 1

To find the net present value (NPV) of the project, we need to discount the cash flows from each year to their present value and then subtract the initial outlay.

First, let's calculate the cash flows for each year:

Year 0:
Initial Outlay: -$3,500,000

Year 1:
Sales: $800,000
Variable Costs (30% of sales): -$240,000
Fixed Costs: -$150,000
Cash Flow: $800,000 - $240,000 - $150,000 = $410,000

Years 2 to 8:
Sales growth rate: 9%
Fixed costs growth rate: 5%

To calculate the cash flows for these years, we will use the formula:
Cash Flow = Sales - Variable Costs - Fixed Costs

Year 2:
Sales: $800,000 * (1 + 9%) = $872,000
Variable Costs: $872,000 * 30% = $261,600
Fixed Costs: $150,000 * (1 + 5%) = $157,500
Cash Flow: $872,000 - $261,600 - $157,500 = $452,900

Similarly, you can calculate the cash flows for years 3 to 8 using the growth rates for sales and fixed costs.

Year 9 (Final Year):
Salvage Value: $2,000,000

Now let's calculate the present value of each cash flow. We will discount the cash flows at a 6% required return.

To calculate the present value, we use the formula:
PV = CF / (1 + r)^n
where PV is the present value, CF is the cash flow, r is the required return, and n is the number of years.

Present Value Calculation:

Year 0: PV0 = -$3,500,000 / (1 + 6%)^0 = -$3,500,000

Year 1: PV1 = $410,000 / (1 + 6%)^1 = $386,792.45

Years 2 to 8: Calculate the present value of each year's cash flow using the same formula.

Year 9: The salvage value does not need to be discounted, so PV9 = $2,000,000

Finally, we can calculate the net present value (NPV) by summing up the present values and subtracting the initial outlay:

NPV = PV0 + PV1 + PV2 + ... + PV8 + PV9 - Initial Outlay

Calculate the NPV by adding up all the present values and subtracting the initial outlay.