Chapter 4. DISCOUNTING AND ALTERNATIVE INVESTMENT CRITERIA. Contents . Discounting Alernative Investment Criteria  Net Present Value Criteria  BenefitCost Ratio Criteria  Pay Back Period Criteria  Internal Rate of Return Criteria. 1.1 Discounting and Compounding.
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DISCOUNTING AND ALTERNATIVE INVESTMENT CRITERIA
 Net Present Value Criteria
 BenefitCost Ratio Criteria
 Pay Back Period Criteria
 Internal Rate of Return Criteria
An investment of $1, with a discount rate = r
ValueValue
PresentAfter One YearPresentAfter nYears
B/(1+r) B B/(1+r)n B
r is the discount rate
1/(1+r) is the discount factor
(1+r) is the compound factor
Ex: Present value of 250$ for 10 years at 6% discount rate
4PV = $250/ (1+0.06)10
PV = $250/1.79= $139.6 or $250* 1/(1+0.06)10 = 139.6
 the period (number of years)
 the size of the discount (r)
NPVr0= (B0C0)/(1+r)0 + (B1C1)/(1+r)1 ++
(BnCn)/(1+r)n
Table 41. Calculating the present value
of net benefits from an investment project
Adjustment of Cost of Funds Through Time
r0
r1
If funds currently are abnormally scarce
r2
r3
r4
r5
Normal or historical average cost of funds
r
*4
r
*3
If funds currently are abnormally abundant
r
*2
r
*1
r
*0
Years from present period
0
1
2
3
4
5
1/(1+r1), 1/[(1+r1)(1+r2)] & 1/[(1+r1)(1+r2)(1+r3)]
Financial AnalysisEconomic Analysis
* Financial discount rates * EOCK
* Market prices * Economic values
* More relevant to private sector * More rel. to public sector
* Owner’s and banker’s point of view * Economy point of view
First Criterion: Net Present Value (NPV)
a. When to reject projects?
b. Select project(s) under a budget constraint?
c. Compare mutually exclusiveprojects?
a. When to Reject Projects?
Rule:“Do not accept any project unless it generates a positive net present value when discounted by the opportunity cost of funds”
Examples:
Project A: Present Value Costs $1 million, NPV + $70,000
Project B: Present Value Costs $5 million, NPV  $50,000
Project C: Present Value Costs $2 million, NPV + $100,000
Project D: Present Value Costs $3 million, NPV  $25,000
Result:
Only projects A and C are acceptable. The country is made worse off if projects B and D are undertaken.
b. When You Have a Budget Constraint?
Rule: “Within the limit of a fixed budget, choose that subset of the available projects which maximizes the net present value”
Example:
If budget constraint is $4 million and 4 projects with positive NPV:
Project E: Costs $1 million, NPV + $60,000
Project F: Costs $3 million, NPV + $400,000
Project G: Costs $2 million, NPV + $150,000
Project H: Costs $2 million, NPV + $225,000
Result:
Combinations FG and FH are impossible, as they cost too much. EG and EH are within the budget, but are dominated by the combination EF, which has a total NPV of $460,000. GH is also possible, but its NPV of $375,000 is not as high as EF.
c. When You Need to Compare Mutually Exclusive Projects?
Rule:“In a situation where there is no budget constraint but a project must be chosen from mutually exclusive alternatives, we should always choose the alternative that generates the largest net present value”
Example:
Assume that we must make a choice between the following three mutually exclusive projects:
Project I: PV costs $1.0 million, NPV $300,000
Project J: PV costs $4.0 million, NPV $700,000
Projects K: PV costs $1.5 million, NPV $600,000
Result:
Projects J should be chosen because it has the largest NPV.
Constraints of Using NPV
It is a widely used by the analysts. Should be very careful, otherwise incorrect and misleading decisions can be made.
BenefitCost Ratio (R) = Present Value Benefits/Present Value Costs
Basic rule:
If benefitcost ratio (R) >1, then the project should be undertaken.
Problems?
Sometimes it is not possible to rank projects with the BenefitCost Ratio
First Problem:
The BenefitCost Ratio Does Not Adjust for Mutually Exclusive Projects of Different Sizes.
For example:
Project A: PV0of Costs = $5.0 M, PV0 of Benefits = $7.0 M
NPVA = $2.0 M RA = 7/5 = 1.4
Project B: PV0 of Costs = $20.0 M, PV0 of Benefits = $24.0 M
NPVB = $4.0 M RB = 24/20 = 1.2
According to the BenefitCost Ratio criterion, project A should bechosen over project B because RA>RB, but the NPV of project B is greater than the NPV of project A.
So, project B should be chosen
Second Problem:
The BenefitCost Ratio Does Not Adjust for MutuallyExclusive Projects where the Costs are treated in different ways.
Project AProject B
PV of gross benefits 2,000 2,000
PV of operating Costs 500 1,800
PV of capital costs 1,200 100
RA = (2000500)/1200 = 1.15 RB = (20001800)/100 = 2.0
Project B is preferred to Project A (RB > RA ).
2. B/C Ratio (Operating costs added to capital costs) RA = 2000/(1200+500)= 1.18 RB = 2000/(1800+100) = 1.05
Project A is preferred to Project B (RA > RB ).
NPV of a project is not sensetive to the way the acountants treat costs. Thus NPV is far more reliable than B/C ratio as a criterion for project selection.
Conclusion:The BenefitCost Ratio CANNOT be used to rank projects
There is no reason to expect that quick yielding projects are superior to long term invetments.
Ba
Bb
ta
0
tb
Time
Ca = Cb
Payout period for project a
Payout period for project b
Figure 4.2 Comparison of Two Projects With Differing Lives Using PayOut Period Criterion
i=0
2.4 Internal Rate of Return CriterionBt  Ct
(1 + K)t
Note: the IRR is a mathematical concept, not an economic or financial criterion
Common uses of IRR:
(a). If the IRR is larger than the cost of funds then the project should be undertaken
(b). Often the IRR is used to rank mutually exclusive projects. The highest IRR project should be chosen
= 0
+300
Time
100
200
2.4 Difficulties With the Internal Rate of Return CriterionFirst Difficulty: Multiple rates of return for project
Solution 1: K = 100%; NPV= 100 + 300/(1+1) + 200/(1+1)2 = 0
Solution 2: K = 0%; NPV= 100+300/(1+0)+200/(1+0)2 = 0
Bt  Ct
+
time

Bt  Ct
+
time

2.4.2 Difficulties With The Internal Rate of Return Criterion
(Cont’d)
Ґ
Year 0
1
2
3
...
...
Project A

2,000
+600
+600
+600
+600
+600
+600
Project B

20,000
+4,000
+4,000
+4,000
+4,000
+4,000
+4,000
NPV and IRR provide different Conclusions:
Opportunity cost of funds = 10%
0
NPV : 600/0.10

2,000 = 6,000

2,000 = 4,000
A
NPV : 4,000/0.10

20,000 = 40,000

20,000 = 20,000
0
B
Hence, NPV > NPV
0
0
B
A
IRR
: 600/K

2,000 = 0 or K
= 0.30
A
A
A
IRR
: 4,000/K

20,000 = 0 or K
= 0.20
B
B
B
Hence, K
>K
A
B
Second difficulty: Projects of different sizes and also strict alternatives
Projects of different lengths of life and strict alternatives
Opportunity cost of funds = 8%
Project A: Investment costs = 1,000 in year 0
Benefits = 3,200 in year 5
Project B: Investment costs = 1,000 in year 0
Benefits = 5,200 in year 10
0
5
NPV :

1,000 + 3,200/(1.08)
= 1,177.86
A
10
0
NPV :

1,000 + 5,200/(1.08)
= 1,408.60
B
0
0
Hence, NPV > NPV
B
A
IRR
:

1,000 + 3,200/(1+K
)
= 0 which implies that K
= 0.262
5
A
A
A
IRR
:

1,000 + 5,200/(1+K
)
= 0 which implies that K
= 0.179
10
B
B
B
Hence, K
>K
A
B
2.4.3 Difficulties With The Internal Rate of Return Criterion (Cont’d)Same project but started at different times
Project A: Investment costs = 1,000 in year 0
Benefits = 1,500 in year 1
Project B: Investment costs = 1,000 in year 5
Benefits = 1,600 in year 6
NPV
:

1,000 + 1,500/(1.08) = 388.88
A
6
5
NPV
:

1,000/(1.08)
+ 1,600/(1.08)
= 327.68
B
0
0
Hence, NPV > NPV
A
B
IRR
:

1,000 + 1,500/(1+K
) = 0 which implies that K
= 0.5
A
A
A
6
IRR
:

1,000/(1+K
)
+ 1,600/(1+K
)
= 0 which implies that K
= 0.6
5
B
B
B
B
Hence, K
>K
B
A
2.4.4 Difficulties With The Internal Rate of Return Criterion (Cont’d)