Crenshaw enterprises has gathered projected cash flows for two projects. year project i project j 0 –$189,000 –$189,000 1 93,500 73,600 2 84,600 72,800 3 63,200 76,800 4 57,800 84,000 a. at what interest rate would the company be indifferent between the two projects

10,47%

Explanation:

                         YEAR 1  YEAR 2     YEAR 3  YEAR 4  

-$189,000   $93,500  $84,600   $63,200  $57,800  Proj I

-$189,000   $73,600   $72,800   $76,800  $84,000Proj J

                        -$19,900   $11,800  -$13,600  -$26.200 Cash Dif.

                         10,47%RATE    

To calculate the interest rate that will be indifferent between the projects to the company, we have to do the detailed:

First find a third cash flow that emerge from the substrate of one project, the cash flow of the other project, in this way we will reach a third cash flow, the difference between the projects cash flow.

Then we calculate the present value of the third cash flow, and the IRR obtained it's the interest rate indifferent between the two projects.  

To verify that this is the correct rate, we can apply the present value to each cash flow project and the Present value would be the same.

Present Value Formula: CF/ (1+r)^t

CF : Cash Flow Projected

r :    indifferent interest rate

t : Each Period of the project.

      1       2       3     4  Year

93.500   84.600   63.200   57.800  Proj I

84.642   69.330   46.886   38.818   239.676  Present Value

73.600   72.800   76.800   84.000  Proj J

66.627   59.660   56.975   56.413   239.676  Present Value