Question

Innovation Company is thinking about marketing a new software product. Upfront costs 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%.
b. How many IRRs does this investment opportunity have?
c. Can the IRR rule be used to evaluate this investment? Explain.

Answer 1

Answer:

Explanation:

Initial Cost = $5.00 million

Annual Profit = $1.00 million

Annual Support Cost = $100,000 = $0.10 million

a. )

If Cost of Capital is 6%:

NPV = -$5,000,000 + $1,000,000*(1-(1/1.06)^10)/0.06 - $100,000/0.06

NPV = $693,420.38

Project should be accepted as its NPV is positive.

If Cost of Capital is 2%:

NPV = -$5,000,000 + $1,000,000*(1-(1/1.02)^10)/0.02 - $100,000/0.02

NPV = -$1,017,414.99

Project should be rejected as its NPV is negative.

If Cost of Capital is 12%:

NPV = -$5,000,000 + $1,000,000*(1-(1/1.12)^10)/0.12 - $100,000/0.12

NPV = -$183,110.30

Project should be rejected as its NPV is negative.

b.)

There are two IRR in this opportunity. NPV of this opportunity is 0 when cost of capital is 2.75% and 10.88%. So, IRR are 2.75% and 10.88%

c. )

IRR rule cannot be used to evaluate this investment as it has 2 IRR.

Answer 2

a) The NPV of the investment at the different costs of capital:

• When the cost of capital is 6% the NPV is $693,420.38
• When the cost of capital is 2% the NPV is -$1,017,414.99
• When the cost of capital is 12% the NPV is -$183,110.30

b) The investment opportunity has 2 IRRs.

c) No, the IRR rule cannot be used to evaluate the investment because there are 2 IRRs computed from the costs of capital.

Computation:

a)

Given,

Initial cost =$5 million

Annual profit =$1 million

Annual support cost =$0.10 million

The formula used for NPV is:

$\text{NPV}=[\dfrac{\text{Annual Profit}\times(1-(\dfrac{1}{1+\text{cost of capital}})^\text{n})}{\text{cost of capital}}]-\dfrac{\text{Annual support cost}}{\text{cost of capital}}-\text{Initial Cost}$

Computation of NPV at three different costs of capital:

When the cost of capital is 6%:

$\text{NPV}=[\dfrac{\ 1\text{million}\times(1-(\dfrac{1}{1+0.06})^{10})}{0.06}]-\dfrac{\ 100,000}{0.06}-\ 5\text{million}\\\\=\ 693,420.38$

The project at 6% cost of capital is accepted as the NPV is positive.

When the cost of capital is 2%:

$\text{NPV}=[\dfrac{\ 1\text{million}\times(1-(\dfrac{1}{1+0.02})^{10})}{0.02}]-\dfrac{\ 100,000}{0.02}-\ 5\text{million}\\\\=-\ 1,017,414.99$

The project at a 2% cost of capital is rejected as the NPV is negative.

When the cost of capital is 12%:

$\text{NPV}=[\dfrac{\ 1\text{million}\times(1-(\dfrac{1}{1+0.12})^{10})}{0.12}]-\dfrac{\ 100,000}{0.012}-\ 5\text{million}\\\\=-\ 183,110.30$

The project at 12% cost of capital is rejected as the NPV is negative.

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