BNFN 521 INVESTMENT APPRAISAL Lecture Notes Lecture Three

1 DISCOUNTING AND ALTERNATIVE INVESTMENT CRITERIA

2 Project Cash Flow Profile Benefits Less Costs (-) (+) Year of Project Life Initial Investment Period Operating Stage Liquidation Project Life

3 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 +.…….+(B n /(1+r) n PVC = (C o /(1+r)+(C 1 /(1+r) 1 +.…….+(C n /(1+r) o o r r NPV = (B o -C o )/(1+r) o +(B 1 -C 1 )/(1+r) 1 +.…….+(B n -C n )/(1+r) n o n o r

4 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 -C o )(1+r) 1 +(B 1 -C 1 ) (B n -C n )/(1+r) n-1 and NPV = (B o -C o )(1+r) 3 +(B 1 -C 1 )(1+r) 2 +(B 2 -C 2 )(1+r)+(B 3 -C 3 )+...(B n -C n )/(1+r) n-3 Then NPV = (1+r) 2 NPV 1 r 3 r 3 r 1 r

5 Year Net Cash Flow Example of Discounting (10% Discount Rate) Note: All of the transactions are done at the beginning of the year.

6 C. Variable Discount Rates Adjustment of Cost of Funds Through Time For variable discount rates r 1, r 2, & r 3 in years 1, 2, and 3, the discount factors are, respectively, as follows: 1/(1+r 1 ), 1/[(1+r 1 )(1+r 2 )] & 1/[(1+r 1 )(1+r 2 )(1+r 3 )] r0r0 r1r1 r2r2 r3r3 r4r4 r5r5 r *4*4 r *3*3 r *2*2 r *1*1 r *0*0 If funds currently are abnormally scarce Normal or historical average cost of funds If funds currently are abnormally abundant Years from present period

7 Year Net Cash Flow r 18%16%14%12%10% Example of Discounting (multiple rates) Note: All of the transactions are done at the beginning of the year.

8 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

9 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.

10 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

11 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.

12 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.

13 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)

14 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): Alternative Investment Criteria

15 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 R A >R B that project “A” is better Benefit-Cost Ratio (Cont’d)

16 First Problem: The Benefit-Cost Ratio Does Not Adjust for Mutually Exclusive Projects of Different Sizes. For example: Project A:  PV 0 of Costs = $5.0 M, PV 0 of Benefits = $7.0 M NPV 0 A = $2.0 MR A = 7/5 = 1.4 Project B:  PV 0 of Costs = $20.0 M,PV 0 of Benefits = $24.0 M NPV 0 B = $4.0 MR B = 24/20 = 1.2 According to the Benefit-Cost Ratio criterion, project A should be chosen over project B because R A >R B, 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: PV 0 Total Costs= $5.0 M PV 0 Recurrent Costs = $1.0 M (i.e. Fixed Costs= $4.0 M)PV 0 of Gross Benefits= $7.0 M R A = (7-1)/(5-1) = 6/4 = 1.5 Project B: Total Costs= $20.0 MRecurrent Costs= $18.0 M (i.e. Fixed Costs= $2.0 M)PV 0 of Gross Benefits= $24.0 M R B = (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)

17 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. Alternative Investment Criteria

18 Project with shortest payback period is preferred by this criteria Comparison of Two Projects With Differing Lives Using Pay-Out Period B t - C t BaBa BbBb tata tbtb C a = C b Payout period for project a Payout period for project b 0 Time

19 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

20 Internal Rate of Return (IRR) IRR i s the discount rate (K) at which the present value of benefits are just equal to the present value of costs for the particular project B t - C t (1 + K) t Note: the IRR is a mathematical concept, not an economic or financial criterion = 0  t i=0 Alternative Investment Criteria

21 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

22 First Difficulty: Multiple rates of return for project Solution 1: K = 100%; NPV= /(1+1) /(1+1) 2 = 0 Solution 2:K = 0%; NPV= /(1+0)+-200/(1+0) 2 = 0 Difficulties With the Internal Rate of Return Criterion +300 B t - C t Time

23 Second difficulty: Projects of different sizes and also mutually exclusive Year Ґ Project A-2, Project B-20,000+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/ ,000 = 40,000-20,000 = 20,000 Hence, NPV > NPV IRR A : 600/K A -2,000 = 0 or K A = 0.30 IRR B : 4,000/K B -20,000 = 0 or K B = 0.20 Hence, K A >K B 0 B 0 A 0 B 0 A Difficulties With The Internal Rate of Return Criterion (Cont’d)

24 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 Benefits = 5,200 in year 10 NPV :-1, ,200/(1.08) 5 = 1, NPV :-1, ,200/(1.08) 10 = 1, Hence, NPV > NPV IRR A :-1, ,200/(1+K A ) 5 = 0 which implies that K A = IRR B :-1, ,200/(1+K B ) 10 = 0 which implies that K B = Hence, K A >K B 0 B 0 A 0 B 0 A Difficulties With The Internal Rate of Return Criterion (Cont’d)

25 Fourth difficulty: 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 A :-1, ,500/(1.08) = NPV B :-1,000/(1.08) 5 + 1,600/(1.08) 6 = Hence, NPV > NPV IRR A :-1, ,500/(1+K A ) = 0 which implies that K A = 0.5 IRR B :-1,000/(1+K B ) 5 + 1,600/(1+K B ) 6 = 0 which implies that K B = 0.6 Hence, K B >K A 0 B 0 A Difficulties With The Internal Rate of Return Criterion (Cont’d) 0 0

26 Year  Project A IRR A10% Compares Project A and Project B ? Project B IRR B-2% Project B is obviously better than A, yet IRR A > IRR B Project C IRR C-16% Project C is obviously better than B, yet IRR B > IRR C Project D IRR D4% Project D is worse than C, yet IRR D > IRR C Project E IRR E20% Project E is worse than D, yet IRR E > IRR D IRR FOR IRREGULAR CASHFLOWS For Example: Look at a Private BOT Project from the perspective of the Government