•
A 0 NPV means in-difference in terms of the risk
–
reward. Taking or not
taking the project does not make a difference.
4
IE 492
–
Engineering Economics

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NET PRESENT VALUE (NPV) EXAMPLE
•
Assume you need to invest $50,000 in a project. You expect in the 1
st
year the
cash flow will be $20,000, 2
nd
year will be $30,000, and in the 3
rd
year will be
$30,000. You expect to use return rate of 10%. What is the net present value of the
investment.
Here we are going to use the NPV formula. In this problem,
CF
0
= -50,000
CF
1
= 20,000 x (P/F,i%,n) = 20,000 x (1.10-1,10%,1) = 18,181.82
CF
2
= 30,000 x (P/F,i%,n) = 30,000 x (1.21-1,10%,2) = 24,793.39
CF
3
= 30,000 x (P/F,i%,n) = 30,000 x (1.33-1,10%,3) = 22,539.44
Therefore,
NPV
= CF
0
+ CF
1
+ CF
2
+ CF
3
= -50,000 + 18,181.82 + 24,793.39 + 22,539.44
=
$15,514.65
Since the NPV is > 0, the project is worth considering
.
5
IE 492
–
Engineering Economics

RATE OF RETURN (ROR)
1
•
Rate of Return is an interest paid on the unpaid balance of an amortized loan /
unrecovered project balances.
•
Rate of Return is also a breakeven rate, denoted by i*, at which the present worth
of the project is ‘0.
PW(i*) = PW
Cash inflows
–
PW
Cash outflows
= 0
•
This is also a understandable method of project’s profitability, and is generally
preferred by managers over the PW method.
•
Internal Rate of Return (IRR) is another term for ROR that stresses the fact that we
are concerned with the interest earned on the project that is internally invested,
not those portions that are released by (borrowed from) the project.
•
In other words, IRR is the interest charged on the unrecovered balance of the
investment such that, when the project terminates, the unrecovered project
balance is 0.
6
IE 492
–
Engineering Economics

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RATE OF RETURN (ROR)
1
•
Example: Suppose $10,000 is invested in a project that is expected to generate
$4,021 every year. Considering the 3 year time frame, what is the internal rate or
return (IRR) for this project.

- Summer '16