Innovation Company is thinking about marketing a new software product. Upfront cost to market and develop the product are $5 million. The product is expected to generate profits of $1 million per year for 10 years. The company will have to provide product support expected to cost $100,000 per year in perpetuity. Assume all profits and expenses occur at the end of the year.
a. What is the NPV of this investment if the cost of capital is 6%? Should the firm undertake the project? Repeat the analysis for discount rates of 2% and 12%.
b. How many IRRs does this investment opportunity have?
c. Can the IRR rule be used to evaluate this investment? Explain.
To calculate the Net Present Value (NPV) of the investment, we need to discount the future cash flows at the appropriate discount rate. The formula for NPV is:
NPV = -Initial Investment + (Cash Flow / (1 + Discount Rate)^n)
Where:
- Initial Investment is the upfront cost to market and develop the product ($5 million).
- Cash Flow is the expected profits per year ($1 million).
- Discount Rate is the cost of capital.
- n is the number of years.
a. Let's calculate the NPV for a discount rate of 6%:
NPV = -5,000,000 + (1,000,000 / (1 + 0.06)^1) + (1,000,000 / (1 + 0.06)^2) + ... + (1,000,000 / (1 + 0.06)^10) - (100,000 / (0.06))
Using a financial calculator or spreadsheet software, we can simplify this calculation to find the NPV.
Repeat the calculations for discount rates of 2% and 12%.
For a discount rate of 2%:
NPV = -5,000,000 + (1,000,000 / (1 + 0.02)^1) + (1,000,000 / (1 + 0.02)^2) + ... + (1,000,000 / (1 + 0.02)^10) - (100,000 / (0.02))
For a discount rate of 12%:
NPV = -5,000,000 + (1,000,000 / (1 + 0.12)^1) + (1,000,000 / (1 + 0.12)^2) + ... + (1,000,000 / (1 + 0.12)^10) - (100,000 / (0.12))
Once you have calculated the NPV for each discount rate, compare them to determine whether the firm should undertake the project. The project is considered feasible if the NPV is positive; otherwise, it may not be financially viable.
b. To determine the number of Internal Rate of Returns (IRR), we can plot the cash flows over time and see how many times they cross the x-axis. Each intersection represents a potential IRR.
c. The IRR rule can be used to evaluate this investment opportunity if and only if there is a single IRR. If multiple IRRs exist, the IRR rule becomes unreliable as it fails to indicate whether the investment is profitable or not.