comparing investment criteria year Cash Flow (A) Cash Flow (B) 0 -350,000 -35,00
ID: 2673911 • Letter: C
Question
comparing investment criteriayear Cash Flow (A) Cash Flow (B)
0 -350,000 -35,000
1 25,000 17,000
2 70,000 11,000
3 70,000 17,000
4 430,000 11,000
Whichever project you choose, if any, you require a 15% return on your investment
a) if you apply the payback crterion, which investment will you choose? why?
b) If you apply the discounted payback criterion, which investment will you choose? Why? Prof has this included for this questions (NPVA,NPVB,PBA,PBB, decision (PB period measured in years)
c) If you apply the NPV criterion, which investment will you choose? why?
d) If you apply the IRR criterion, which investment will you choose?why?
e) If you apply the profitability index criterion, which investment will you choose?why?
f)Based on your answers in (a) through (c) which project will you finally choose? why?
I
Please give as much detail as possible as I need to understand this for an exam in a few weeks. But I need this answer in a few hours for an assignment
Explanation / Answer
a. If you apply the payback criterion, which investment will you choose? Why?
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:
CFi = $430,000
I = $350,000
After the year 3 we will have recovered only $165,000 (25K + 70K + 70K) and we will
finish to recover the investment during the year 4, then:
Y = 3
and
U = $350,000 - $165,000 = $185,000
PB = 3 + 185,000/430,000 = 3.430 (a little more than 3 years and 5 months)
-Project B:
CFi = $17,000
I = $35,000
After the year 2 we will have recovered only $28,000 (17k+11K)and we will
finish to recover the investment during the year 3, then:
Y = 2
and
U = $35,000 - $28,000 = $7,000
PB = 2 + 7,000/17,000 = 2.412 (a little less than 2 years and 5 months)
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.
In this case, using the Payback Criterion you must choose the project
B, the theory of the Payback Criterion states that projects with
shorter paybacks are more liquid, and thus less risky. In general
projects with a project with Payback period less than three years is
preferred.
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b. If you apply the discounted payback criterion, which investment will you choose? Why?
When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is:
Value today of Year 1 cash flow for A = $25,000/1.15 = $21,739.13
Value today of Year 2 cash flow for A = $70,000/1.15^2 = $52,930.06
Value today of Year 3 cash flow for A = $70,000/1.15^3 = $46,026.14
Value today of Year 4 cash flow for A = $430,000/1.15^4 = $245,853.90
Value today of Year 1 cash flow for B = $17,000/1.15 = $14,782.61
Value today of Year 2 cash flow for B = $11,000/1.15^2 = $8,317.58
Value today of Year 3 cash flow for B = $17,000/1.15^3 = $11,177.78
Value today of Year 4 cash flow for B = $11,000/1.15^4 = $6,289.29
To find the discounted payback, we use these values to find the payback period as above
and we calculate:
-Project A:
CFi = $245,853.90
I = $350,000
After the year 3 we will have recovered only $120,695.33 and we will
finish to recover the investment during the year 4, then:
Y = 3
and
U = $350,000 - $120,695.33 = $229,304.67
PB = 3 + 229,304.67/245,853.90 = 3.933 years
-Project B:
CFi = $6289.29
I = $35,000
After the year 3 we will have recovered only $34,277.97 and we will
finish to recover the investment during the year 4, then:
Y = 3
and
U = $35,000 - $34,277.97 = $722.03
PB = 3 + 722.03/6289.29 = 2.145 years
so we get the same conclusion as in problem A.
-----------------------------------------------------------
c. If you apply the NPV criterion, which investment will you choose? Why?
Some definitions:
Present Value:
CF1 CF2 CF3 CF4
PV = --------- + ---------- + ---------- + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^3 (1 + r)^4
Net Present Value:
NPV = PV - I where I = Initial Investment
NPV Decision Rule that says:
-General Rule: Accept a project if NPV >= 0.
-Mutually Exclusive Projects: Accept the project that has the largest NPV >=0.
-Project A:
25,000/((1 + 0.15)^1)+70,000/((1 + 0.15)^2)+70,000/((1 + 0.15)^3)+430,000/((1 + 0.15)^4)
PV = $366,549.22
NPV = $366,549.22 - $350,000 = $16,549.22
-Project B:
17,000/((1 + 0.15)^1)+11,000/((1 + 0.15)^2)+17,000/((1 + 0.15)^3)+11,000/((1 + 0.15)^4)
PV = $40,567.25
NPV = $40,567.25 - $35,000 = $5,567.25
The NPV criterion says that in mutually exclusive projects we must
choose the project with the largest positive NPV, in this case the
best project by this criterion is the project A.
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d. If you apply the IRR criterion, which investment will you choose? Why?
Some definitions:
To calculate the IRR you must find r from the following equation:
CF1 CF2 CF3 CF4
PV = --------- + ---------- + ---------- + --------- = I
(1 + r)^1 (1 + r)^2 (1 + r)^3 (1 + r)^4
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.
For the project A the column A will have:
A1: -350,000 ; A2: 25,000 to A5: 430,000 ;
B1 =IRR(A1:A5)
We have for Project A:
IRR = 16.57%
and for project B:
IRR = 23.05%
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 15%,then both projects are
acceptable, but the project B is the winning by this criterion.
------------------------------------------------------------
e. If you apply the profitability index criterion, which investment
will you choose? Why?
Definitions:
PI = PV/I
Profitability Index criterion:
This decision criterion leads to accept a project only if it has a
Profitability Index (PI) greater than one. Using the profitability
index to compare mutually exclusive projects decision rule implies
select the acceptable project with the higher PI.
For the project A:
PI = PV/I = $366,549.22 / $350,000 =
= 1.047
For the project B:
PI = PV/I = $40,567.25 / $35,000 =
= 1.159
Using the Profitability Index criterion we select the project B.
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f. Based on your answers in (a) through (d), which project will you finally select?
Start summing up the results of the previous questions:
Project Payback NPV IRR PI
A 3.430 $16,549.22 16.57% 1.047
B 2.412 $5,567.25 23.05% 1.159
Selection B A B B
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.
We can see that the NPV and the IRR criteria are in conflict and the
PI criterion gives a very similar rank to both projects (PI criterion
says to us "see other criterion").
In cases like that we tend to select the project with the highest NPV,
this can be summed up as the following statement:
"If projects are mutually exclusive and not subject to capital
rationing, the project with the higher NPV should be selected."
Why this happens?
Remember that NPV and PI assume cash flows are reinvested at the
required rate of return for the project and IRR assumes cash flows are
reinvested at the IRR.
This means that "if the IRR method is used, the project must not be
accepted only because its IRR is very high. Management must ask
whether such an impressive IRR is possible to maintain. In other
words, management should look into past records, and existing and
future business, to see whether an opportunity to reinvest cash flows
at such a high IRR really exists. If the firm is convinced that such
an IRR is realistic, the project is acceptable. Otherwise, the
project must be reevaluated by the NPV method, using a more realistic
discount rate."
Then the high IRR of project B (23.05%) can be an unrealistic rate for
future reinvestments.
This result exceed the required rate of 15% but is not so attractive
as the IRR of the project B (the original project in this case). At
this point the question is whether the company has other projects that
will offer a higher return.
Proceeding with the project B you are saving money for other possible
projects, but if these possible projects does not exists or does not
offer a better return (this high rate will be the required
rate of return for these possible projects!!!) then project A must be
selected, this last thing almost happens.
As a conclusion we can state the following:
IRR and NPV always give the same accept/reject signal in respect of
independent projects, but sometimes they give conflicting answers to
mutually exclusive projects: IRR suggests that project B be selected
and NPV suggests tha project A must be selected.
This normally happens when both project have different initial
outlays, the patterns of cash flow are different, and/or one project
has a longer life than another. This situation can be overcome by
calculating the incremental yield, in other words, calculating the
IRR obtained by moving from the less expensive project to the most
expensive one. If the IRR on the additional investment and additional
benefits is greater than the required rate of return then the larger
project must be selected.
NOTE:
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.
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