Problem 10-32 Project Evaluation [LO1]
Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows:
Year Unit Sales
1 86,000
2 99,000
3 113,000
4 108,000
5 89,000
Production of the implants will require $1,650,000 in net working capital to start and additional net working capital investments each year equal to 20 percent of the projected sales increase for the following year. Total fixed costs are $1,550,000 per year, variable production costs are $290 per unit, and the units are priced at $405 each. The equipment needed to begin production has an installed cost of $21,500,000. 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 25 percent of its acquisition cost. AAI is in the 34 percent marginal tax bracket and has a required return on all its projects of 19 percent. MACRS schedule
What is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
NPV $
What is the IRR? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
IRR $
jj98
To calculate the NPV (Net Present Value) of the project, we need to determine the cash flows for each year and discount them using the required rate of return. The formula for calculating NPV is:
NPV = (Cash Flow / (1 + Required Rate of Return)^Year) - Initial Investment
Let's break down the steps to calculate the NPV:
1. Calculate the annual cash flows:
Year 1:
Unit Sales: 86,000
Revenue (86,000 * $405): $34,830,000
Variable Costs (86,000 * $290): $24,940,000
Fixed Costs: $1,550,000
Net Cash Flow (Revenue - Variable Costs - Fixed Costs): $8,340,000
Working Capital Investment: $1,650,000
Year 2:
Unit Sales: 99,000
Revenue (99,000 * $405): $40,095,000
Variable Costs (99,000 * $290): $28,710,000
Fixed Costs: $1,550,000
Net Cash Flow (Revenue - Variable Costs - Fixed Costs): $9,835,000
Working Capital Investment: 20% of sales increase ($40,095,000 - $34,830,000) = $1,053,000
Similarly, calculate the net cash flow and working capital investment for each subsequent year (Year 3, Year 4, and Year 5) using the given sales data.
2. Calculate the discounted cash flows for each year using the required rate of return (19%):
Discounted Cash Flow = Net Cash Flow / (1 + Required Rate of Return)^Year
Calculate the discounted cash flow for each year using the respective net cash flows and years.
3. Calculate the initial investment:
Initial Investment = Equipment Cost + Initial Working Capital Investment
Equipment Cost: $21,500,000
Initial Working Capital Investment: $1,650,000
4. Calculate the NPV:
NPV = Sum of Discounted Cash Flows - Initial Investment
Calculate the NPV by summing up the discounted cash flows and subtracting the initial investment.
To calculate the IRR (Internal Rate of Return), we can use the NPV formula. We want to find the rate at which the NPV is zero. The IRR is the discount rate that makes the NPV equal to zero.
To calculate the IRR, we can use trial and error or a financial calculator/spreadsheet software that has built-in financial functions. Iterate through different discount rates until the NPV is very close to zero.
Once you have calculated the NPV and IRR, you can fill in the answers with the provided format.