技术经济学英文版演示文稿C(7)

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D, there in only one sign change in the cumulative cash flow profile. That is, we will obtain only one unique positive value of the ROR. For cash flow profiles B and C, the results of cumulative cash flow profiles are inconclusive. We cannot reduce the possible number of solutions by using the cumulative cash flow profile for these two profiles.
the cumulative cash flow Cj as,
j
Cj
j0
A
j
• If Cj starts with a negative number and changes sign only
once, we will obtain only one positive solution. This
Year
0 1 2 3 4 56
A(no drilling) 0 30 20 18 14 10 6
B(in-fill drilling) -20 60 40 6 4 2 0
The numbers are in millions. Assume that MROR is 20%.
14
• Solution • The first step in ROR analysis is to compare individual ROR's
• Solution
• We can calculate the cumulative cash flows for each of the profiles as follows:
Period
0 1 2 3 4 5 6
Project A
Project B
Aj
Cj
Aj
Cj
-100 -100 -100 -100
11
12
13
Example 3.27 An in-fill drilling project is being considered for an existing oil field to accelerate oil recovery. The following two scenarios, based on two alternatives (no infill drilling versus in-fill drilling) are predicted. Which alternative would you select?
2
NPV
唯一值 同一 ic,具有可加性 与基准点有关
可用于互斥方案优选
IRR
唯一值;无解;多解 无可加性 无关
不可用
3
• 3.4.2 Multiple Rates of Return • In addition to the requirement of incremental analysis, the ROR analysis
8
• The number of possible real solutions can be narrowed down
even further by applying cumulative cash flow sign test. If we
assume Aj to be a cash flow in period j, then we can define
Cj
-500 -500
300 -200
300 100
-100 0
100 100
-100 0
50 50
10
• As a sample calculation, for period 3 for Project A, we can calculate.
• C3 = -100+20+20+30 =-30 • For period 6, • C6 = -100+20+20 +30+20+30+30=50 • Looking at the cash flow profiles, for cash flow profiles A and
• For example, if we consider an investment of $1,000 which will result in a $300 annual benefit for the next six years with a $500 salvage value at the end of six years, the cash profile can be written as.
-30
-100
6
20
20
100
50
7
• Solution • To calculate the maximum number of possible real solutions
between -100% and ∞, we can calculate the number of sign changes. For cash flow A, there is only one sign change between period 0 and l. For B, there are three sign changes; between periods 0 and l, periods l and 2, and 3. • Similarly, for cash flow C, there are four sign changes, and for cash flow D, there are five sign changes. As stated before, the number of sign changes will indicate the maximum number of possible real solutions. That is, for cash flow profile C, the number of real solutions between –100% and ∞ can be either 4, 3, 2, l. or zero.
method also has another drawback. This method works well when a given alternative requires an initial investment which is followed by future benefits. For this type of alternative, the cash flow profile can be shown as negative cash flow in the first year followed by positive cash flow in the future years.
Year
Cash Flow
0
-1,000
1 2 345 6
7
300 300 300 300 300 300 300+500
4
• In this profile, there is only one sign change in cash profile between Years 0 and 1. Such profile is amenable to conventional ROR analysis.
6
• Example 3.25 For the following four cash ROR between • -100% and ∞.
Period
A
B
C
D
0
-100
-100
300
-500
1
20
120
-200
300
2
20
-30
100
300
3
30
50
100
-100
4
20
70
200
100
5
30
30
cumulative cash flow method may allow us to narrow down
the number of possible solutions for the ROR.
9
• Example 3.26 Reconsider the cash flows provided in Example 3.23. Applying the cumulative cash flow sign test, investigate the possibility of narrowing the number of positive ROR solutions.
• Note that the ROR calculation requires solving a polynomial of i. We calculate the value of i for which the NPV is zero. For economic analysis, we are only interested in obtaining positive, real values of i for which the NPV is equal to zero. When there is only one sign change in the cash flow profile, as shown above, we can only obtain one or zero positive solutions.
5
• In some instances, however, the sign changes more than once in a cash flow profile. Under these circumstances, we may obtain more than one real ROR. The rule of signs for polynomial solution states that the number of real solutions between -l and ∞ is never greater than the number of sign changes. That is, if we have two sign changes, we may obtain a maximum of two rates of return values between -100% and ∞. The following example illustrates the calculation of the number of feasible solutions.
20 -80 120 20
20 -60 -30 -10
30 -30 50 40
20 -10 70 110
30 10 30 140
20 50 20 160
Project C
AjLeabharlann Cj300 300
-200 100
100 200
100 300
200 500
-30 470
100 570
Project D
Aj
for each alternative with the MROR. For alternative A, there is no sign change in the cash flow profile. Therefore, the ROR for alternative A is ∞. For alternative B, ROR can be shown to be greater than 20% (the ROR for alternative B is 260%). Therefore, both alternatives satisfy the requirement that the ROR be greater than the MROR. The next step is to conduct the incremental analysis. The cash flow profile for incremental values can be written as,
ROR(IRR) 的优缺点:
易理解;与基准点无关; 在项目寿命期内任意时刻,使项目收益换 算值之和等于费用换算值之和的利率称为ROR (IRR)。 所以,ROR的计算,可以用NPV(i)=0, NFV(i)=0, NAV(i)=0 进行计算。
1
NPV >0 =0 <0
IRR >ic =ic <ic
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