Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows:
Year Unit Sales
1 87,000
2 100,000
3 114,000
4 109,000
5 90,000
Production of the implants will require $1,660,000 in net working capital to start and additional net working capital investments each year equal to 15 percent of the projected sales increase for the following year. Total fixed costs are $1,560,000 per year, variable production costs are $295 per unit, and the units are priced at $410 each. The equipment needed to begin production has an installed cost of $21,600,000. Because the implants are intended for professional singers, this equipment is considered industrial machinery and thus qualifies as seven-year MACRS property. In five years, this equipment can be sold for about 20 percent of its acquisition cost. AAI is in the 35 percent marginal tax bracket and has a required return on all its projects of 18 percent.
What is the NPV?
What is the IRR?
To calculate the Net Present Value (NPV) and Internal Rate of Return (IRR) for this project, we need to consider the cash flows associated with the project.
Step 1: Calculate the cash flows for each year:
Year 0:
Initial investment = -$21,600,000 (equipment cost)
Net working capital = -$1,660,000
Years 1-5:
Sales revenue = Unit Sales * Price per unit
Fixed costs = $1,560,000
Variable costs = Unit Sales * Variable production cost per unit
Operating cash flow = Sales revenue - Fixed costs - Variable costs
Net working capital = 15% of projected sales increase for the following year
Year 5:
Terminal cash flow = Sale of equipment = 0.2 * Equipment cost
Step 2: Discount the cash flows to determine their present value:
The required rate of return is 18%. So, we will discount the cash flows by this rate.
Present Value = Cash Flow / (1 + Required Rate of Return)^Year
Step 3: Calculate NPV:
NPV represents the sum of the present values of all cash flows. Subtract the initial investment from the sum of discounted cash flows.
Step 4: Calculate IRR:
IRR is the discount rate at which the NPV equals zero. This can be determined through trial and error or by using financial software or spreadsheet functions.
Let's calculate the NPV and IRR:
Year 0:
Initial investment = -$21,600,000
Net working capital = -$1,660,000
Years 1-5:
Unit Sales: 87,000, 100,000, 114,000, 109,000, 90,000, respectively
Price per unit: $410
Fixed costs: $1,560,000
Variable production cost per unit: $295
Projected sales increase: 87,000 * 0.15, 100,000 * 0.15, 114,000 * 0.15, 109,000 * 0.15
Year 5:
Terminal cash flow = Sale of equipment = 0.2 * $21,600,000
Now, we can plug in these values and calculate NPV and IRR.