Carlyle Inc. is considering two mutually exclusive projects. Both require an ini
ID: 2749712 • Letter: C
Question
Carlyle Inc. is considering two mutually exclusive projects. Both require an initial investment of $15,000 at t = 0. Project S has an expected life of 2 years with after-tax cash inflows of $7,000 and $12,000 at the end of Years 1 and 2, respectively. In addition, Project S can be repeated at the end of Year 2 with no changes in its cash flows. Project L has an expected life of 4 years with after-tax cash inflows of $5,200 at the end of each of the next 4 years. Each project has a WACC of 9.00%. What is the equivalent annual annuity of the most profitable project?
$ 569.97
$ 782.34
$ 865.31
$1,522.18
$1,846.54
Explanation / Answer
Evaluation of most profitable project
Project S:
In the above table, Project S has been repeated at the end of year 2 i.e at the end of year 2, again an investment of 15,000 was made. IRR calculated is 15.76% as shown in the above table
NPV of project s using WACC of 9%
Project L:
IRR of project L = 14.49%
NPV calculation:
Thus Project S has a higher IRR as well as higher NPV and so it is the most profitable project.
Calculation of equivalent annual annuity of Project S:
Present value of annuities at the end of 4 years, with discounting factor of 1.09% is 2803.36
So, the annual payment made at the end of each year starting from 1 and ending at 4, should have a PV of 2803.36
Thus annuity amount is $865.3094 (This can be calculated using the formula PV = amount/(discount factor^time)
The annuity can also be obtained using the solver function in excel.
Time Cash flow Discount PV 0 -15000 -15000 1 7000 1.157695 6046.497697 2 12000 8953.502303 2 -15000 -11191.87788 3 7000 4511.444255 4 12000 6680.433624 NPV 0