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

Answer 1

c. $865.31

Step-by-step 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

`NPV=-15000/(1+0.09)^0+7000/(1+0.09)^1-3000/(1+0.09)^2+7000/(1+0.09)^3+12000/(1+0.09)^4`

`NPV=2803.37`

Following is the formula for Equivalent annual annuity

`EAA=(r*NPV)/(1-1/(1+r)^n)`

EAA = Equivalent annual equity

NPV = Net present value

r = Interest rate

n = Number of periods

`EAA=(.09*2803.37)/(1-1/(1+.09)^4)`

`EAA=865.31`

To solve For Project L

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

`PV=PMT(1+(1/(1+r)^n)/r+FV/(1+r)^n`

NPV = Initial outflow - Present Value

`PV=5200*(1+(1/(1+0.09)^4)/0.09`

`PV=16846.54`

`NPV=1846.54`

Using the above formula we can calculate EAA:

`EAA=(.09*1846.54)/(1-1/(1+.09)^4)`

`EAA=569.97`

The most profitable EAA is of project S

*all figures are rounded off to two decimal points*