Hello again!!
a. Calculate the payback period for each project.
Payback (PB) calculation will give us an idea on how long it will take
for a project to recover the initial investment.
Then if:
Y = the year before full recovery of investment I;
U = Unrecovered cost at the start of last year;
CFi = CF of the year Y+1;
PB = Y + U/CFi
-Project A:
After the year 3 we will have recovered only $135,000 and we will
finish to recover the investment during the year 4, then:
Y = 4
CFi = $45,000
I = $150,000
and
U = $150,000 - $135,000 = $15,000
PB = 4 + 15,000/45,000 = 4 + 1/3 (4 years and 4 months)
-Project B:
After the year 2 we will have recovered only $135,000 and we will
finish to recover the investment during the year 3, then:
Y = 3
CFi = $30,000
I = $150,000
and
U = $150,000 - $135,000 = $15,000
PB = 3 + 15,000/30,000 = 3 + 1/2 (3 years and 6 months)
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Some definitions:
Present Value:
CF1 CF2 CF6
PV = --------- + ---------- + ... + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^6
Net Present Value:
NPV = PV - I where I = Initial Investment
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b. Calculate the NPV of each project at 0%
If r = 0 all divisors of the PV equation becomes 1, so the PV for this
special case is:
PV = CF1 + Cf2 + ... + CF6
Then:
NPV = CF1 + Cf2 + ... + CF6 - I =
-Project A:
NPV = CF1 + Cf2 + ... + CF6 - I =
= 6 * $45,000 - $150,000 =
= $120,000
-Project B:
NPV = CF1 + Cf2 + ... + CF6 - I =
= $75,000 + $60,000 + 4 * $30,000 - $150,000 =
= $105,000
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c. Calculate the NPV of each project at 9%
Now we must use the original formula of PV and a calculator to obtain:
-Project A:
PV = $201,866.34
NPV = $201,866.34 - $150,000 = $51,866.34
-Project B:
PV = $201,112.36
NPV = $201,112.36 - $150,000 = $51,112.36
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To calculate the IRR you must find r from the following equation:
CF1 CF2 CF6
PV = --------- + ---------- + ... + --------- = I
(1 + r)^1 (1 + r)^2 (1 + r)^6
In other words IRR is the discount rate at which the NPV equals zero.
You can use one of the following techniques to calculate the IRR:
-Trial & Error techniques
-Calculator
-Computer (spreadsheet)
Here is a brief guide to do this using an MS Excel spreadsheet for this problem:
1) Select a column for the project's Cash flows (lets say column "A").
2) Input the project's Cash Flows starting from the initial investment
and followed by the Y1 to Y4 cash flows, each one in one cell of the
column.
3) Click on the cell where you want your IRR calculated (say B1).
4) Enter "=IRR(" (without the quotes) and then highlight the column A
then close the parenthesis and hit enter.
d. Derive the IRR of each project
For the project A the column A will have (MS Excel spreadsheet):
A1: -150,000 ; A2: to A7: 45,000 ;
B1 =IRR(A1:A7)
We have for Project A:
IRR = 19.91%
For the project B the column A will have (MS Excel spreadsheet):
A1: -150,000 ; A2: 75,000 ; A3: 60,000 ; A4 to A7: 30,000 ;
B1 =IRR(A1:A7)
We have for Project B:
IRR = 22.71%
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e. Rank the projects by each of the techniques used. Make and justify
a recommendation.
Definition of Payback Criterion:
-Accept a project if its payback period is less than maximum
acceptable payback period.
-Reject a project if its payback period is longer than maximum
acceptable payback period.
-Mutually Exclusive Projects: Accept the one having the shortest PB.
Project B has the shorter PB so for this criterion this is the one you must choose.
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The NPV criterion says that in mutually exclusive projects we must
choose the project with the largest positive NPV.
Forget the NPVs at 0%, because they do not consider the time value of
money. So,in this case the best project by this criterion is the
project A. But note that both project have in practically the same
NPV.
--------------
The IRR criterion states that you must accept only projects with IRR
greater than the cost of capital (required rate of return). If you use
this criterion to choose between mutually exclusive projects you must
select the acceptable project with the higher IRR.
In this case the required rate of return is 9%,then both projects are
acceptable, but the project B is the winning by this criterion.
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Summing up the results:
Project Payback NPV(9%) IRR
A 3 1/3 $51,866.34 19.91%
B 4 1/2 $51,112.36 22.71%
Selection B A B
The recommendation:
The first observation is that both alternatives are acceptable by all
criteria but to different degrees.
The goal is to select the best of the two.
Note that the payback criterion is not a proper way to select between mutually
exclusive projects. It ignores any benefits that occur after the
payback period, and worst it ignores the time value of money. But the
theory of the Payback Criterion states that projects with shorter
paybacks are more liquid, and thus less risky and it gains importance
when two projects have similar NPVs and IRRs.
We can see that the NPV and the IRR criteria are in conflict saying us
"use other criteria".
You have noticed, from formulas, that NPV calculation assume cash
flows are reinvested at the required rate of return for the project
and IRR calculation assumes cash flows are reinvested at the IRR.
Normally the NPV criterion is the preferred because its uses a more
realistic discount rate.
Then the high IRR of project B (22.71%) can be an unrealistic rate for
future reinvestments.
But we have that both projects have the "same" NPV (they are
practically equal), now the PB criterion gains importance: the payback
period of the project B is one year shorter than the project A so,
with the same NPV, project B is preferable because it is more liquid,
and thus less risky. And also it has a higher IRR.
The recommended project is the Project B.
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I hope that this helps you. If you find something unclear, imcomplete
or wrong please let me know using the clarification feature giving me
the opportunity to complete, clarify, correct or improve this answer
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Best regards.
livioflores-ga |
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