Question

Innovation Company is thinking about marketing a new software product. Upfront costs to market and develop the product are $4.91 million. The product is expected to generate profits of $1.05 million per year for ten years. The company will have to provide product support expected to cost $95,000 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 6.1%​? Should the firm undertake the​ project? Repeat the analysis for discount rates of 1.6 % and 13.8 % respectively.

If the cost of capital is 6.1 %,the NPV will be ​$_____. ​(Round to the nearest​ dollar.)

If the cost of capital is 1.6 %,the NPV will be ​$_____. ​(Round to the nearest​ dollar.)

If the cost of capital is 13.8 %,the NPV will be ​$_____. ​(Round to the nearest​ dollar.)

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

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

Answer 1

NPV at 6.1 = -Initial cost + PV of annuity profit – PV of perpetuity cost

= -4,910,000 + 1050000*(1-1/(1+0.061)^10)/0.061 – 95000/.061

=1224232.15 ; Yes the firm cn undertake the project since npv is positive

NPV at 1.6%= -Initial cost + PV of annuity profit – PV of perpetuity cost

= -4,910,000 + 1050000*(1-1/(1+0.016)^10)/0.016 – 95000/.016

= -1215306.62 ;should not take the project; npv negative

NPV at 13.8%= = -Initial cost + PV of annuity profit – PV of perpetuity cost

=-4,910,000 + 1050000*(1-1/(1+0.138)^10)/0.138 -95000/.138

= -78465.57 ;should not take the project; npv negative

IRR is that rate at which NPV = 0

Hence

Initial cost = PV of annuity profit – PV of perpetuity cost

4910,000= 1050000*(1-1/(1+IRR)^10)/IRR -95000/IRR

Using excel , we get 2 IRR as 2.15% and 13.4%

If the cost of capital is 6.1%, we can take this project ; we should not take any project above 13.4% and below 2.15%