I am here again k9queen!!!
I hope that I am helping you a little with this stuff.
1)-Which of the following statements is correct?
a) the project should be accepted since its NPV is $327.96
b) the project should be rejected since its NPV is -$327.96
c) the project should be accepted since it has a payback less than 4
years
d) the project should be accepted since its NPV is $10,327.96
Some concepts:
Payback Period (PB):
If CFs are equal each year, then
PB = I/CF where I = Initial Investment
If CFs are not equal each year, then
Year before full Unrecovered cost at start of last
year
PB = recovery of +
-------------------------------------- investment
Total CF during the last year
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
In this case the NVP is $327.96 >= 0.
Considering the NPV Decision Rule that says:
-General Rule: Accept a project if NPV >= 0.
-Mutually Exclusive Projects: Accept the one having the largest NPV >=
0.
We can say that the correct statement is a).
Obviously, statement b) is wrong; but I am not sure about c) and d).
In some textbooks the NVP is taken as the PV, in this case the "NVP"
is
$10,327.96 .
In this situation the "NVP" rule says:
-General Rule: Accept a project if NPV >= I.
-Mutually Exclusive Projects: Accept the one having the largest NPV >=
I.
May be this is your situation, and if it is the statement d) is
correct.
About the statement c), the payback calculation determines the length
of time it takes to recover an initial investment. This amount of time
is called the payback period (PB).
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.
The PB in this case is 3 years. Here we can interpret that the life of
the project is 4 years (then this is the maximum acceptable payback
period), in this case the Payback criterion could be applicable
accepting the project and the statement c) is correct too; but may be
we are misinterpreting the question, it is a little subjective.
In principle, without greater clarifications the answer c) is not
necessarily correct, because the maximum acceptable payback period
does not be explicitly defined.
Note about Payback Criterion:
This is the less recommended method of decision because:
1. Ignores the time value of money; does not discount cash flow.
2. Must choose an arbitrary cutoff point.
3. Ignores cash flows beyond the cutoff date.
4. Biased against long-term projects that take longer time periods to
become lucrative.
See the following webpage: "CCH Business Owner's Toolkit | Payback
Period Analysis":
http://www.toolkit.cch.com/text/P06_6510.asp
---------------------------------------------
2)- This project:
a) has an IRR of 9.86 percent
b) should be accepted based on the IRR criterion
c) has an IRR of 15 percent
d) both A & B are true statements about this project
The statement a) is correct.
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.
Calculating the IRR:
-Trial & Error techniques
-Calculator
-Computer
To do this using an MS Excel spreadsheet for this problem:
1) Input your total costs for the project in one column (lets say
column "A").
2) Input your income (derived savings etc...) for the project (lets
say column "B")
3) Set up a column that adds the total costs and the total savings per
year ("C1" = "A1" - "B1", "C2" = "A2" - B2", etc...).
4) Click on the cell where you want your IRR calculated
5) Enter "=IRR(" (without the quotes) and then highlight the total
costs + total savings column (C column)and hit enter.
The column A will have:
A1: 10,000 ; A2 to A5: 0 ;
the column B:
B1: 0 ; B2: 6,000 ; B3 to B5: 2,000 ;
The column C:
Ci =Bi-Ai for i=1 to 5
and
D1 =IRR(C1:C5)
The statement b) is corrct too!!
The IRR decision criterion
Accept a project if IRR > Cost of capital.
Reject a project if IRR < Cost of capital.
A simple definition of Cost of Capital is:
"The Required return for a Capital budgeting project."
http://www.marketvolume.com/glossary/c0472.asp
"The cost of capital of a project:
--The minimum required rate of return of the project
--The project will have a positive NPV only if its return exceeds
what the financial markets offer on investment of similar risks, i.e.,
required rate of return."
http://www.mi.chu.edu.tw/~yfkao/fm/ch11-2002.ppt
Here the cost of capital is the called required return, such is 8%.
An investment is acceptable if IRR is greater than or equal to the
cost of capital or required return, so in this case 9.86% > 8%, using
the IRR criterion the project should be accepted.
The statement c) is wrong.
The statement d) is correct.
-------------------------------------------
3)- The profitability index (PI) for this project
a) is 1.03 .
b) is less than .1 .
c) is 0.03 .
d) indicates that the project should be rejected.
PI =PV / I
PI gives the return per dollar invested.
PI = PV / I = $10,327.96 / $10,000 = 1.032796;
We can consider the statement a) correct, taking two significant
digits.
The statements b) and c) are both wrong.
PI Decision Rules:
-Independent Projects
Accept if PI > 1
When PI > 1, then the NPV > 0
When PI < 1, then the NPV < 0
-Mutually Exclusive Projects
When projects are of equal size (same I), NPV and PI will give the
same decision.
Accept if PI > 1 (Highest PI project)
When projects are of unequal size (unequal I), NPV and PI could
result in conflicting decisions.
Use NPV instead of PI
Accept if NPV > 0 (Largest NPV project).
In this case Independent Projects´rule is applicable:
PI = 1.03 > 1, then using this criterion should be accepted not
rejected, then the statement d) is wrong.
I hope this helps, excuse me the long answer, but several definitions
and clarifications was needed, please tell me if something appears
confused or obscure by a request of a clarification.
Best Regards.
livioflores-ga |
