# Considering three capital expenditure projects. Determine the internal rate of return for each project. Project             Investment                    Annual Income Life of Project Alpha               \$240,000                     \$13,300                       6 years Beta                   270,000                       19,000                       9 years Gamma              288,000                       18,400                       8 years The annual income is projected to remain constant over the life of each project. There will be no salvage value at the end of the projects and the company uses straight line depreciation.

The Internal Rate of Return is a way of estimating the overall value of a project and whether or not you will make your money back in a certain amount of time. To calculate the Internal Rate of Return, you need to find the discount rate that makes the net present value = 0.

To do this, you set the equation as such:

0 = Initial Investment + First Yearly Income/(1+IRR) + Second Yearly Income/(1+IRR)^2 + . . . + nth Yearly Income/(1+IRR)^n where n is the total number of years for each project.

The project will be profitable if the IRR is a positive number.

Solving for IRR for each of these projects yields the following values:

Alpha IRR = -0.2458

Beta IRR = -.082

Gamma IRR = -.129

Therefore, we can see that none of these projects is profitable, but Beta offers the lowest loss.

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The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) zero. The formula is as follows:

0 = Initial Investment + Cashflow of year 1/(1+1RR) + Cashflow of year 2/(1+IRR)2 + Cashflow of year n/(1+IRR)n

To calculate Project Alpha's IRR

1. Ppen Microsoft Excel and write the cashflows in a single column as follows:

Cashflows

(240,000) ... A2

13,300 ....... A3

13,300........ A4

13,300........ A5

13,300........... A6

13,300........ A7

13,300........ A8

2. At the bottom cell, define the range of these figures and cells in an IRR function as follows:

=IRR(A2:A8)

3. You should get -24.59%

To calculate Beta's IRR, you follow the same procedure on Microsoft excel. It should give you -8.27% as the IRR.

Using the Excel formula, the IRR for the Gamma project becomes -12.9%.

Generally, if one were to select a project based on the IRR, they go for the highest value, which in this case is -8.27% - Beta project.

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The internal rate of return of a project or IRR is the rate of return which when used to discount all cash-flows associated with the project and determine the net value gives as NPV of 0. If the IRR is a positive value, the project is a profit making one, else a loss is being on the project.

From the information provided about the three projects in the question the IRR can be calculated for each of them. It has to be kept in mind that depreciation does not play a role in calculating the IRR; only the cash inflows and outflows are relevant.

Consider project Alpha, here the initial cash outflow is \$240000; there is a cash inflow of \$13300 for the next 6 years which is the life of the project. Multiplying 13300 by 6 gives \$79800 which is less than the initial investment, it is evident that a loss is being on the project.

If the loss as a percentage is R, the equation 240000 = 13300/(1 + R) + 13300/(1 + R)^2 + 13300/(1 + R)^3+...+13300/(1+R)^6 has to be solved for R. This can be done using a calculator or software like EXCEL. The value obtained for R is -0.2458 or -24.58%. The IRR of project Alpha is -24.58%.

Similarly, the IRR for project Beta is -0.082 or -8.2% and the IRR for project Gamma is -0.1290 or -12.9%

None of the projects is profitable.

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