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
[tex]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[/tex]
[tex]NPV=2803.37[/tex]
Following is the formula for Equivalent annual annuity
[tex]EAA=(r*NPV)/(1-1/(1+r)^n)[/tex]
EAA = Equivalent annual equity
NPV = Net present value
r = Interest rate
n = Number of periods
[tex]EAA=(.09*2803.37)/(1-1/(1+.09)^4)[/tex]
[tex]EAA=865.31[/tex]
To solve For Project L
In order to calculate present value of the annuity, following formula will be used:
[tex]PV=PMT(1+(1/(1+r)^n)/r+FV/(1+r)^n[/tex]
NPV = Initial outflow - Present Value
[tex]PV=5200*(1+(1/(1+0.09)^4)/0.09[/tex]
[tex]PV=16846.54[/tex]
[tex]NPV=1846.54[/tex]
Using the above formula we can calculate EAA:
[tex]EAA=(.09*1846.54)/(1-1/(1+.09)^4)[/tex]
[tex]EAA=569.97[/tex]
The most profitable EAA is of project S
*all figures are rounded off to two decimal points*
