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

Answer:

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

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

$NPV=2803.37$

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*