Measures Used for Comparison of Alternatives
•Equivalent Present Worth (PW) or NPW
•Equivalent Future Worth (FW) or NFW
•Equivalent Annual Worth (AW) or EUAC
•Incremental Rate of Return ( ROR)
•Benefit-Cost Ratio (B/C)
•Payback Method
EGR 403, Jan 00
Please refer to the example in class notes on
Web page called
“Example on NPW, NFW, AW”
Net Present Worth = NPW = PWBenefit -PWCost
Looking for: NPW > 0, or highest NPW
Situations:
•Equal useful life (study period)
•Unequal useful life
•Least common multiple period
•A fixed period and consider terminal value
•Infinite analysis period, capitalized cost = P = A/i
Assumptions:
End-of-year convention, Stable prices, Sunk cost,
Analysis point of view
EGR 403, Jan 99
Equivalent Uniform Annual Cost, EUAC
Notation:
S =Salvage value at the end of the analysis period
EUAC = P(A|P,i,n) - S(A|F,i,n)
= (P - S)(A|P,i,n) + Si
= (P - S)(A|F,i,n) + Pi
= NPW(A|P, i, n)
(A|P, i,  ) = I
The Repeatability Assumption
EGR 403, Jan 99
Internal Rate of Return, IRR,
is the interest rate at which the discounted present
worth of benefits equals the discounted present
worth of costs, i.e. the Net Present Worth, NPW, = 0.
Minimum Attractive Rate of Return, MARR
is that interest rate which is equal to the highest
one of the following:
* The current interest rate for borrowing money from
various sources
* The average interest rate paid by the firm for the cost
of capital (Bank loans, Corporate Bonds, Stock Dividends)
* The opportunity cost which equals the rate of return
on the last accepted or best rejected project or
investment which is still available.
EGR 403, Jan 99
IRR analysis is generally a “trial and error” solution.
A plot of NPW vs. i will yield a value of
IRR for NPW = 0.
IRR criteria: If IRR >= MARR, the investment is
considered acceptable.
Problems with multiple changes in the sign of the net
cash flows may produce multiple rates of return.
The Cash Flow Rule of Signs states that the maximum
number of possible rates of return for any given
analysis is equal to the number of cash flow reversals
during the period of study.
EGR 403, Jan 99
Example: Find IRR for the following cash flow.
Initial cost (now)
$2,000
Annual income for 15 years
$120
Salvage value at the end of 15th year
$1,800
PW = -2000 + 120(P|A, i, 15) + 1800(P|F, i, 15)
Trial Interest rate
1
10%
2
7%
3
5%
4
6%
.
NPW
.
-2000 + 120(7.606) + 1800(0.2394) = -656.36
-2000 + 120(9.108) + 1800(0.3624) = -254.72
-2000 + 120(10.38) + 1800(0.481) = 111.4
-2000 + 120(9.712) + 1800(0.4173) = -83.42
Interpolation using Trial 1 and 2 >>>> IRR = 5.09
Interpolation using Trial 3 and 2 >>>> IRR = 5.61
Interpolation using Trial 3 and 4 >>>> IRR = 5.57
IRR = 5.56% using Excel!!
EGR 403, Jan 00
Example: Two possible investments (X and Y) are
under consideration. The following table shows
the estimated cash flow for each alternative and
their IRR. MARR = 20%
Alternative X
Alternative Y
.
Year
0
1
$500
0
-$1000
-$250
.
2
$500
0
3
$500
$500
IRR
23%
26%
Which one of the investments will you select and
why?
EGR 403, Jan 04
Rate of return analysis is performed by computing
the Incremental Rate of Return ( ROR) based
on the differences between the net cash flows of two
alternatives with equal analysis periods.
For increments of investment, set up a "decision tree"
starting with the lowest initial cost alternative and
work your way up to the highest initial cost alternative.
ROR criteria:
If  ROR >= MARR, choose the higher-cost alternative
If  ROR < MARR, choose the lower-cost alternative
EGR 403, Jan 99
Other Measures Used for Comparison:
Benefit-Cost Ratio
For
B a given MARR
C = (PW of benefits) / (PW of costs)
B
If C (X) > 1 , then accept X
For two
B alternatives use incremental cash flow:
If C B(X-Y) > 1 , then rank X > Y
If C (X-Y) < 1 , then rank Y > X
For the future cash flow we may argue if a cash
flow can be considered for numerator or denominator
for this calculation. However, the final conclusion
will not change.
EGR 403, Jan 2000
Please refer to the example in class notes on
Web page called
“Example on IRR and B/C”
Payback method
The period of time required for the profit to equal
the cost of investment.
Drawback:
* Ignores consequences that are beyond the end of
the payback period
Possible benefit:
* Prospective investments are highly uncertain
* Current capital is extremely limited and will
continue to be limited
EGR 403, Jan 99