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? a. $ 569.97b. $ 782.34c. $ 865.31d. $1,522.18e. $1,846.54

c. $865.31

Explanation:

Data:

Project S

Initial Outlay = $15,000

Y1 CF = $7,000

Y2 CF = $12,000

Project L

Initial Outlay = $15,000

Y1 to Y4 CF = $5,200

To solve for Project S

In ordered to compare project S with project Project L, we shall prolong it to four years.

cashflow stream will be as follows:

Y0=-$15,000  Y1=$7,000  Y2=-$3,000($12,000 CF - $15,000 outlay for prolonging the project second time)  Y3=$7,000  Y4=$12,000

Following is the formula for Equivalent annual annuity

EAA = Equivalent annual equity

NPV = Net present value

r = Interest rate

n = Number of periods

To solve For Project L

In order to calculate present value of the annuity, following formula will be used:

NPV = Initial outflow - Present Value

Using the above formula we can calculate EAA:

The most profitable EAA is of project S

*all figures are rounded off to two decimal points*

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