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Assume a business is deciding whether to invest in a new project that is projected to generate profits of $90,000 each year for the next three years. The project start-up costs are $225,000.

a. If the business nominally earns 11 percent on its investments, should the business invest?
b. If the business normally earns 5 percent on its investments, should the business invest?

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Answer:

Instructions are below.

Explanation:

Giving the following information:

Initial investment= $225,000

The project generates profits of $90,000 each year for the next three years.

To determine whether it is convenient or not to invest, we need to calculate the net present value (NPV). If the NPV is positive, the project should proceed.

NPV= -Io + ∑[Cf/(1+i)^n]

A)

Year 1= 90,000/1.11= 81,081.08

Year 2= 90,000/1.11^2= 73,046.02

Year 3= 90,000/1.11^3= 65,807.22

Total= 219,934.32

NPV= -225,000 + 219,034.32= -$5,965.68

With a discount rate of 11%, the project is not profitable.

B)

Year 1= 90,000/1.05= 85,714.29

Year 2= 90,000/1.05^2= 81,632.65

Year 3= 90,000/1.05^3= 77,745.38

Total= 245,092.32

NPV= -225,000 + 245,092.32= 20,092.32

Under a discount rate of 5%, the project is convenient.

(A) NPV is = -$5,965.68 With a discount rate of 11%, the project is not profitable.

(B) NPV is = 20,092.32 Under a discount rate of 5%, the project is convenient.

What is Calculation of Cost?

Giving the following information as per question:

The Initial investment is = $225,000

When The project generates profits of $90,000 each year for the next three years.

When To determine whether it is convenient or not to invest, then we need to calculate the net present value (NPV). Also, If the NPV is positive, Then the project should proceed.

Therefore, The NPV is = [tex]-Io + ∑[Cf/(1+i)^n][/tex]

A) With a discount rate of 11%, and the project is not profitable.

First Year = [tex]90,000/1.11= 81,081.08[/tex]

Second Year = 90,000/1.11^2= 73,046.02

Third Year = [tex]90,000/1.11^3= 65,807.22[/tex]

Then The Total is = 219,934.32

After that NPV is = [tex]-225,000 + 219,034.32=[/tex] -$[tex]5,965.68[/tex]

B) Under a discount rate of 5%, the project is convenient.

First Year = [tex]90,000/1.05= 85,714.29[/tex]

Second Year = [tex]90,000/1.05^2= 81,632.65[/tex]

Third Year = [tex]90,000/1.05^3= 77,745.38[/tex]

Then the Total is = 245,092.32

Then NPV is = [tex]-225,000 + 245,092.32[/tex]= [tex]20,092.32[/tex]

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