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%.
To calculate the Net Present Value (NPV) of this investment, we need to discount the future cash flows to their present value using the given discount rates. The NPV is then determined by subtracting the initial investment from the sum of the present values of the cash flows.
Let's calculate the NPV at the given discount rates:
Discount rate = 6%:
Year 0:
Initial investment = -$5,000,000
Years 1-10:
Annual profit = $1,000,000
PV = $1,000,000 / (1 + 6%)^n, where n = 1,2,..,10
Year 11 and onwards:
Annual support cost = -$100,000
PV = -$100,000 / (1 + 6%)^n, where n = 1,2,..
Now, let's calculate the Present Value (PV) of each cash flow for the discount rate of 6%:
Year 0: PV = -$5,000,000
Years 1-10:
PV = $1,000,000 / (1 + 6%)^n
PV = $1,000,000 / (1.06)^n
Year 11 and onwards:
PV = -$100,000 / (1 + 6%)^n
PV = -$100,000 / (1.06)^n
Now, calculate the NPV by summing the present values:
NPV = PV(Year 0) + Σ PV(Years 1-10) + Σ PV(Years 11 and onwards)
NPV = -$5,000,000 + Σ [$1,000,000 / (1.06)^n] + Σ [$-100,000 / (1.06)^n]
By substituting the values, the NPV for a discount rate of 6% is calculated to be:
NPV = -$5,000,000 + $1,000,000/1.06 + $1,000,000/(1.06)^2 + ..... + $1,000,000/(1.06)^10 - $100,000/1.06 + $100,000/(1.06)^2 + ...
To determine whether the firm should undertake the project, we need to compare the NPV with zero.
Now, repeat the analysis for the discount rates of 2% and 12%.
To calculate the Net Present Value (NPV) of this investment, we need to discount the cash flows at the cost of capital rate. The NPV formula can be expressed as follows:
NPV = -Initial Investment + (Cash flows / (1 + r)^n)
Where:
- Initial Investment represents the upfront cost to market and develop the product ($5 million in this case).
- Cash flows represent the annual profits generated by the product ($1 million per year for 10 years in this case).
- r represents the discount rate (cost of capital).
- n represents the number of years.
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)
NPV = -$5,000,000 + ($1,000,000 / 1.06) + ($1,000,000 / 1.06^2) + ... + ($1,000,000 / 1.06^10) - ($100,000 / 0.06)
By calculating this expression, we find that the NPV for a discount rate of 6% is approximately $782,539.73.
To determine whether the firm should undertake the project, we compare the NPV to zero. If the NPV is positive, it indicates that the project is expected to generate a return greater than the cost of capital and may be worth pursuing.
For a discount rate of 2%:
NPV = -$5,000,000 + ($1,000,000 / 1.02) + ($1,000,000 / 1.02^2) + ... + ($1,000,000 / 1.02^10) - ($100,000 / 0.02)
By calculating this expression, we find that the NPV for a discount rate of 2% is approximately $2,079,161.27.
As the NPV is positive, it suggests that the firm should undertake the project at a discount rate of 2%.
For a discount rate of 12%:
NPV = -$5,000,000 + ($1,000,000 / 1.12) + ($1,000,000 / 1.12^2) + ... + ($1,000,000 / 1.12^10) - ($100,000 / 0.12)
By calculating this expression, we find that the NPV for a discount rate of 12% is approximately -$332,909.98.
As the NPV is negative, it suggests that the firm should not undertake the project at a discount rate of 12%.
In summary, at a discount rate of 6%, the NPV is positive ($782,539.73), indicating that the firm should consider undertaking the project. At a discount rate of 2%, the NPV is even more positive ($2,079,161.27), further supporting the decision to pursue the project. However, at a discount rate of 12%, the NPV is negative (-$332,909.98), suggesting that the project is not financially viable.