Question

Innovation Company is thinking about marketing a new software product. Upfront costs to market and develop the product are $ 4.98 million. The product is expected to generate profits of $ 1.02 million per year for 10 years. The company will have to provide product support expected to cost $ 91 comma 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 6.2 %​? Should the firm undertake the​ project? Repeat the analysis for discount rates of 1.7 % and 12.6 %​, respectively.

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

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

Answer 1

A. Initial Investment

Initial Investment (Upfornt cost) = 4.98 million

B. Present Value of profits

= 1.02 * Present Value Annuity Factor 6.2%, 10 Years

= 1.02 * 7.290 = 7.436 million

C. Present value of product support

Present value of perpetuity = Amount / Interest Rate

Present Value = 91,000 / 0.062 = 1,467,741.94

NPV = B - (A+C)

NPV = 7.436 - (4.98 + 1.46)

NPV = 0.996 Million

NPV is positive project should be rejected

If the discount rate is 1.7%

A. Initial Investment

Initial Investment (Upfornt cost) = 4.98 million

B. Present Value of profits

= 1.02 * Present Value Annuity Factor 1.7%, 10 Years

= 1.02 * 9.125 = 9.308 million

C. Present value of product support

Present value of perpetuity = Amount / Interest Rate

Present Value = 91,000 / 0.017 = 5,352,941.18

NPV = B - (A+C)

NPV = 9.308 - (4.98 + 5.35)

NPV = -1.022 Million

NPV is negative project should be rejected

If the discount rate is 12.6%

A. Initial Investment

Initial Investment (Upfornt cost) = 4.98 million

B. Present Value of profits

= 1.02 * Present Value Annuity Factor 12.6%, 10 Years

= 1.02 * 5.514 = 5.624 million

C. Present value of product support

Present value of perpetuity = Amount / Interest Rate

Present Value = 91,000 / 0.126 = 722,222.22

NPV = B - (A+C)

NPV = 5.624 - (4.98 + 0.722)

NPV = -0.077 Million

NPV is negative project should be rejected

Calculation of IRR

First of all we will calculate total cash flow of the project

Since the product support expenses is till perpetuity we have taken cash flows till 100 years

Then we will use the formulae of IRR in excel

year	Initial Investment	Annual Profit	Product Support	Total Cash Flow
0	-4.98			-4.98
1		1.02	-0.091	0.929
2		1.02	-0.091	0.929
3		1.02	-0.091	0.929
4		1.02	-0.091	0.929
5		1.02	-0.091	0.929
6		1.02	-0.091	0.929
7		1.02	-0.091	0.929
8		1.02	-0.091	0.929
9		1.02	-0.091	0.929
10			-0.091	-0.091
11			-0.091	-0.091
.	.	.	.	.
.	.	.	.	.
.	.	.	.	.
95			-0.091	-0.091
96			-0.091	-0.091
97			-0.091	-0.091
98			-0.091	-0.091
99			-0.091	-0.091
100			-0.091	-0.091
			IRR	9.89%

IRR rule indicate

IRR rule indicate that at 9.89% discount rate NPV of the project will be zero

IRR rule indicate that for any discout rate above IRR (ie above 9.89%) project should not be accepted, this will lead to negative NPV