Question

Innovation Company is thinking about marketing a new software product. Upfront costs to market and develop the product are $5,200,000. The product is expected to generate profits of $1,000,000 per year for ten years. The company will have to provide product support expected to cost $99,000 per year in perpetuity. Assume all income and expenses occur at the end of each year.

a. What is the NPV of this investment if the cost of capital is 4.65%​?

Should the firm undertake the​ project? Repeat the analysis for discount rates of 2.95% and 9.73%​, respectively.

b. How many IRRs does this investment opportunity​ have? ​ (Hint: Consider the two alternative discount rates we used in our analysis in part​ a.)  

c. Can the IRR rule be used to evaluate this​ investment? Explain.

Answer 1

Answer A

By applying the NPV function tab at excel the NPV is calculated. when cost of capital is 4.65%

One of the image is showing down below where the formula is =NPV(C2,C4:L4) to determine the NPV of cash inflows. In the similar way the PV of recurring cash outflow is determined.

NPV of cash inflows
Discount rate		4.65%
Time period		Year 1	Y2	Y3	Y4	Y5	Y6	Y7	Y8	Y9	Y10
Cash flow		1000000	1000000	1000000	1000000	1000000	1000000	1000000	1000000	1000000	1000000
NPV	$78,54,682.69
NPV of Cash outflow
Discount rate		4.65%
Time period		Year 1	Y2	Y3	Y4	Y5	Y6	Y7	Y8	Y9	Y10
Cash flow		99000	99000	99000	99000	99000	99000	99000	99000	99000	99000
	$7,77,613.59

Computation of NPV of the project when cost of capital is 4.65%

	Amount($)	Amount($)
PV of cash inflow		$78,54,682.69
Less: Initial investment	5200000
PV of recurring cost	777613.59	5977613.59
NPV of the project is		$18,77,069.10

Since the NPV is positive the firm should undertake the project.

When the discount rate is 2.95% the following computation is done in the excel sheet. Here also the NPV comes positive so the project should be accepted

NPV of cash inflows
Discount rate		2.95%
Time period		Year 1	Y2	Y3	Y4	Y5	Y6	Y7	Y8	Y9	Y10
Cash flow		1000000	1000000	1000000	1000000	1000000	1000000	1000000	1000000	1000000	1000000
NPV	$85,52,010.71
NPV of Cash outflow
Discount rate		2.95%
Time period		Year 1	Y2	Y3	Y4	Y5	Y6	Y7	Y8	Y9	Y10
Cash flow		99000	99000	99000	99000	99000	99000	99000	99000	99000	99000
	$8,46,649.06

Cost of capital 2.95%	Amount($)	Amount($)
PV of cash inflow		$85,52,010.71
Less: Initial investment	5200000
PV of recurring cost	845649.06	6045649.06
NPV of the project is		$25,06,361.65

When the cost of capital is 9.73% the NPV is calculated in excel and transferred here. Here also the NPV comes positive but the margin of positive cash is low.

NPV of cash inflows
Discount rate		9.73%
Time period		Year 1	Y2	Y3	Y4	Y5	Y6	Y7	Y8	Y9	Y10
Cash flow		1000000	1000000	1000000	1000000	1000000	1000000	1000000	1000000	1000000	1000000
NPV	$62,16,488.75
NPV of Cash outflow
Discount rate		9.73%
Time period		Year 1	Y2	Y3	Y4	Y5	Y6	Y7	Y8	Y9	Y10
Cash flow		99000	99000	99000	99000	99000	99000	99000	99000	99000	99000
	$6,15,432.39

Cost of capital 9.73%	Amount($)	Amount($)
PV of cash inflow		$62,16,488.75
Less: Initial investment	5200000
PV of recurring cost	615432.39	5815432.39
NPV of the project is		$4,01,056.36

Answer B

Calculation of IRR

Factor is case of the project = InvestmentAveerage cash flows

                                             = 5200000 +990001000000

                                              = 5.299

The IRR rate lies in between 13% to 14% found in the PVFA table chart.

Therefore, the approximate IRR can be 13% or 14% which is closer to the exact IRR.

Answer C

A project whose acceptance and rejection is not depending upon other project is known as independent project. The present project is an independent project.

In case of independent project if the IRR is greater than cost of capital of the project should be accepted.

The cost of capital of the project primarily is 4.65%.

The two other cost of capital are 2.95% and 9.73%%

The IRRs are 13% or 14%

Therefore, IRR is greater than cost of capital.

Therefore the IRR can be applied in the project for evaluation.