bnfn 521 investment appraisal lecture notes lecture three

BNFN 521INVESTMENT APPRAISAL

Lecture Notes

Lecture Three

2

DISCOUNTING

AND

ALTERNATIVE INVESTMENT

CRITERIA

3

Project Cash Flow Profile

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ben

efit

s L

ess

Cos

ts

(-)

(+)

Year of Project Life

Initial Investment Period

Operating StageLiquidation

Project Life

4

Discounting and Alternative Investment Criteria

Basic Concepts:A. Discounting

• Recognizes time value of money

a. Funds when invested yield a return

b. Future consumption worth less than present consumption

PVB = (B o/(1+r)

o

+(B 1/(1+r)1+.…….+(Bn /(1+r)

nPVC = (C

o /(1+r) +(C 1/(1+r)1+.…….+(Cn /(1+r)

o

o

r

rNPV = (B o-Co)/(1+r) o+(B 1-C1)/(1+r) 1+.…….+(B n-Cn)/(1+r) n

o n

o

r

5

Discounting and Alternative Investment Criteria (Cont’d)

B. Cumulative Values

• The calendar year to which all projects are discounted to is important

• All mutually exclusive projects need to be compared as of same calendar year

If NPV = (B o-Co)(1+r) 1+(B1-C1) +..+..+(B n-Cn)/(1+r) n-1 and

NPV = (B o-Co)(1+r) 3+(B1-C1)(1+r) 2+(B2-C2)(1+r)+(B 3-C3)+...(B n-Cn)/(1+r) n-3

Then NPV = (1+r) 2 NPV

1r

3r

3r

1r

6

Year 0 1 2 3 4

Net Cash Flow -1000 200 300 350 1440

Example of Discounting (10% Discount Rate)

25.676)1.1(

1440

)1.1(

350

)1.1(

300

1.1

2001000PV

4320

1.0

88.743)1.1(

1440

)1.1(

350

1.1

300200)1.1(1000PV

321

1.0

26.818)1.1(

1440

)1.1(

350300)1.1(200)1.1(1000PV

2122

1.0

Note: All of the transactions are done at the beginning of the year.

7

C. Variable Discount Rates• Adjustment of Cost of Funds Through Time

•For variable discount rates r1, r2, & r3 in years 1, 2, and 3, the discount factors

are, respectively, as follows:

1/(1+r1), 1/[(1+r1)(1+r2)] & 1/[(1+r1)(1+r2)(1+r3)]

0 1 2 3 4 5

r0r1r2r3

r4r5

r *4

r *3

r *2

r *1

r *0

If funds currently are abnormally scarce

Normal or historical average cost of funds

If funds currently are abnormally abundant

Years from present period

8

Year 0 1 2 3 4

Net Cash Flow -1000 200 300 350 1440

r 18% 16% 14% 12% 10%

Example of Discounting (multiple rates)

55.515)12.1)(14.1)(16.1(

1440

)14.1)(16.1(

350

16.1

300200)18.1(10001 NPV

04.598)12.1)(14.1(

1440

)14.1(

350300)16.1(200)16.1)(18.1(10002 NPV

91.436)12.1)(14.1)(16.1)(18.1(

1440

)14.1)(16.1)(18.1(

350

)16.1)(18.1(

300

18.1

20010000 NPV

Note: All of the transactions are done at the beginning of the year.

9

1. Net Present Value (NPV)

2. Benefit-Cost Ratio (BCR)

3. Pay-out or Pay-back Period

4. Internal Rate of Return (IRR)

ALTERNATIVE INVESTMENT

CRITERIA

10

Net Present Value (NPV)1. The NPV is the algebraic sum of the discounted values of the

incremental expected positive and negative net cashflows over a

project’s anticipated lifetime.

2. What does net present value mean?

– Measures the change in wealth created by the project.

– If this sum is equal to zero, then investors can expect to recover

their incremental investment and to earn a rate of return on their

capital equal to the private cost of funds used to compute the

present values.

– Investors would be no further ahead with a zero-NPV project than

they would have been if they had left the funds in the capital

market.

– In this case there is no change in wealth.

11

First Criterion: Net Present Value (NPV)

• Use as a decision criterion to answer following:a. When to reject projects?

b. Select project(s) under a budget constraint?

c. Compare mutually exclusive projects?

d. How to choose between highly profitable mutually exclusive projects with different lengths of life?

Alternative Investment Criteria

12

Net Present Value Criterion

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.

13

Net Present Value Criterion (Cont’d)

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.

14

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.

Net Present Value Criterion (Cont’d)

15

Benefit-Cost Ratio (R)

• As its name indicates, the benefit-cost ratio (R), or what is sometimes referred to as the profitability index, is the ratio of the PV of the net cash inflows (or economic benefits) to the PV of the net cash outflows (or economic costs):

)(

)(

CostsEconomicorOutflowsCashofPV

BenefitsEconomicorInflowsCashofPVR


16

Basic rule:

If benefit-cost ratio (R) >1, then the project should be undertaken.

Problems?

Sometimes it is not possible to rank projects with the Benefit-Cost Ratio

• Mutually exclusive projects of different sizes

• Mutually exclusive projects and recurrent costs subtracted out of

benefits or benefits reported gross of operating costs

• Not necessarily true that RA>RB that project “A” is better

Benefit-Cost Ratio (Cont’d)

17

First Problem:The Benefit-Cost 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

NPV0A = $2.0 M RA = 7/5 = 1.4

Project B: PV0 of Costs = $20.0 M, PV0 of Benefits = $24.0 M

NPV0B = $4.0 M RB = 24/20 = 1.2

According to the Benefit-Cost Ratio criterion, project A should be chosen 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 Benefit-Cost Ratio Does Not Adjust for Mutually Exclusive Projects and Recurrent Costs Subtracted Out of Benefits or Benefits Reported As Gross of Operating Costs. For example:Project A: PV0 Total Costs = $5.0 M PV0 Recurrent Costs = $1.0 M

(i.e. Fixed Costs = $4.0 M) PV0 of Gross Benefits= $7.0 MRA = (7-1)/(5-1) = 6/4 = 1.5

Project B: Total Costs = $20.0 M Recurrent Costs = $18.0 M(i.e. Fixed Costs = $2.0 M) PV0 of Gross Benefits= $24.0 MRB = (24-18)/(20-18) = 6/2 =3

Hence, project B should be chosen over project A under Benefit-Cost Criterion.Conclusion: The Benefit-Cost Ratio should not be used to rank projects

Benefit-Cost Ratio (Cont’d)

18

Pay-out or Pay-back period

• The pay-out period measures the number of years it will take for the undiscounted net benefits (positive net cashflows) to repay the investment.

• A more sophisticated version of this rule compares the discounted benefits over a given number of years from the beginning of the project with the discounted investment costs.

• An arbitrary limit is set on the maximum number of years allowed and only those investments having enough benefits to offset all investment costs within this period will be acceptable.


19

• Project with shortest payback period is preferred by this criteria

Comparison of Two Projects With Differing Lives Using Pay-Out Period

Bt - Ct Ba

Bb

ta

tbCa = Cb Payout period for

project aPayout period for

project b

0

Time

20

• Assumes all benefits that are produced by in longer

life project have an expected value of zero after the

pay-out period.

• The criteria may be useful when the project is

subject to high level of political risk.

Pay-Out or Pay-Back Period

21

Internal Rate of Return (IRR)

• IRR is the discount rate (K) at which the present value of benefits are just equal to the present value of costs for the particular project

Bt - Ct

(1 + K)t

Note: the IRR is a mathematical concept, not an economic or financial criterion

= 0t

i=0


22

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

• An advantage of the IRR is that it only uses

information from the project

23

First 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

Difficulties With the Internal Rate of Return Criterion

+300

Bt - Ct

-200-100

Time

24

Second difficulty: Projects of different sizes and also mutually exclusive

Year 0 1 2 3 ... ... ҐProject 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%

NPV : 600/0.10 - 2,000 = 6,000 - 2,000 = 4,000

NPV : 4,000/0.10 - 20,000 = 40,000 - 20,000 = 20,000

Hence, NPV > NPV

IRRA : 600/K A - 2,000 = 0 or K A = 0.30

IRRB : 4,000/K B - 20,000 = 0 or K B = 0.20

Hence, K A>KB

0B

0A

0B

0A

Difficulties With The Internal Rate of Return Criterion (Cont’d)

25

Third difficulty:Projects of different lengths of life and mutually exclusive

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


NPV : -1,000 + 3,200/(1.08) 5 = 1,177.86

NPV : -1,000 + 5,200/(1.08)10= 1,408.60

Hence, NPV > NPV

IRRA : -1,000 + 3,200/(1+KA)5 = 0 which implies that KA = 0.262

IRRB : -1,000 + 5,200/(1+KB)10 = 0 which implies that KB = 0.179

Hence, KA>KB

0B

0A

0B

0A


26

Fourth difficulty: Same project but started at different times

Project A: Investment costs = 1,000 in year 0


Project B: Investment costs = 1,000 in year 5


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

NPV B : -1,000/(1.08) 5 + 1,600/(1.08) 6 = 327.68

Hence, NPV > NPV

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

IRRB : -1,000/(1+K B) 5 + 1,600/(1+K B) 6 = 0 which implies that KB = 0.6

Hence, K B >KA

0B

0A


0

0

27

Year 0 1 2 3 4

Project A 1000 1200 800 3600 -8000

IRR A 10%

Compares Project A and Project B ?

Project B 1000 1200 800 3600 -6400

IRR B -2%

Project B is obviously better than A, yet IRR A > IRR B

Project C 1000 1200 800 3600 -4800

IRR C -16%

Project C is obviously better than B, yet IRR B > IRR C

Project D -1000 1200 800 3600 -4800

IRR D 4%

Project D is worse than C, yet IRR D > IRR C

Project E -1325 1200 800 3600 -4800

IRR E 20%

Project E is worse than D, yet IRR E > IRR D

IRR FOR IRREGULAR CASHFLOWSFor Example: Look at a Private BOT Project from the perspective of the

Government

bnfn 521 investment appraisal lecture notes lecture three

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