Question

Innovation Company is thinking about marketing a new software product. Upfront costs to market and develop the product are $4.92

million. The product is expected to generate profits of $1.19 million per year for ten years. The company will have to provide product support expected to cost $91,000

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 5.7%​? Should the firm undertake the​ project? Repeat the analysis for discount rates of 1.0%

and 18.0%​,respectively.

b. What is the IRR of this investment​ opportunity?  

c. What does the IRR rule indicate about this​ investment?

Answer 1

Present value of perpetuity=Cash flow/discount rate
Present Value of n year annuity=Cash flow/discount rate*(1-1/(1+discount rate)^n)

NPV=-4.92+1.19/r*(1-1/(1+r)^10)-91000/10^6*1/r

1.
At 5.7%
NPV=-4.92+1.19/5.7%*(1-1/(1+5.7%)^10)-91000/10^6*1/5.7%=2.367856425 million

The firm should undertake the project at discount rate of 5.7% as NPV is positive

At 1%
NPV=-4.92+1.19/1%*(1-1/(1+1%)^10)-91000/10^6*1/1%=-2.749147608 million

The firm should not undertake the project at discount rate of 5.7% as NPV is negative

At 18%
NPV=-4.92+1.19/18%*(1-1/(1+18%)^10)-91000/10^6*1/18%=-0.077592865 million

The firm should not undertake the project at discount rate of 5.7% as NPV is negative

2.
IRR is the discount rate at which NPV is zero
Hence,
-4.92+1.19/r*(1-1/(1+r)^10)-91000/10^6*1/r=0

=>r=-180.83%, 1.50355%, 17.5265%

IRR=-180.83%, 1.50355%, 17.5265%

3.
As there are multiple IRRs, we cannot say anything from IRR