Discounted measures of project wealth.ppt
- 1. 1 Cost Benefit Analysis DISCOUNTED MEASURES: Fundamental concepts
- 2. 2 1. Time value of money • Discounted measures give consideration to the effect of time on the value of money, i.e. time value of money • Time value of money is an expression referring to the concept that values received earlier are worth more than values received later. • A dollar invested today will be worth more in the future because it earns interest (profit). • A dollar received in the future is worth less than a dollar received today because it cannot be invested and earn interest. • It is the concept underlying discounting & compounding
- 3. 3 2. Discounting and 3. compounding • Compounding is the process of finding the future worth (value) of a present amount (an amount due at the present time). • Discounting is the process of finding the present worth (value) of a future amount (an amount due at the present time). • Three arguments have been identified whether discounting is actually an appropriate means of appraising national investment. 1. People have innate (inborn) preference for earlier rather than later consumption 2. The riskiness of future benefits means less weight should be given to them 3. In a world of increasing income per head, successive additions to consumption have successively less additional value
- 4. 4 The need for the use discounting principles • In investment projects, costs normally occur at the beginning of the project life while benefits occur later e.g timber producing projects. • Because of time-value of money, it is not possible to compare directly the costs and benefits of a project that occur at different times. • To do so, costs and benefits should be brought to the same point in time. This can be done either by bringing back (discounting) future values to the present time, or by taking forward (compounding) the present values to specific point of time in the future.
- 5. 5 4. Discount rate and 5. discounting factor • Interest or profit margin (i) is a payment for the use of money generally stated as a percentage (%) of the amount borrowed (principal) for specific period of time e.g. 12% per annum, 0.12 per year, or 1% per month • To the borrower, interest is the cost of using money, while to the lender it the returns to capital. • It is referred to as the market price of money. • When used in discounting or compounding, (i) is termed as discount rate and compound rate, respectively
- 6. 6 Calculating Present Value (PV) of a SINGLE payment • Compounding factor is the expression: (1+i)n where (i) is the compounding rate, and (n) is time in years. • Discounting factor is the expression: 1/(1+i)n where (i) is the discount (interest) rate, and (n) is time in years. • Discounting is a reverse mathematical operation of compounding • Discount factor is the reciprocal of compounding factor: DF=1/CF • How to calculate the present value (PV) of a single payment due in the future? • PV (V0) is determined by multiplying the future amount (Vn) by the discount factor (df) for specific (i) and (n) n n n i V V df V V ) 1 ( 1 * * 0 0
- 7. 7 Example Calculation of PV Year Future Value $ Discount Rate Discount factor Present value $ (n) (Vn) (i) (1/(1+i)n ) (V0) 5 1 0.12 =1/1.125 0.567 10 1 0.12 =1/1.1210 0.322 13 1 0.12 =1/1.1213 0.229 50 1 0.12 =1/1.1250 0.003 0 1 0.12 =1/1.120 1
- 8. 8 Class room exercise on PV • Find the present value of the following sum of money due at (n) years in the future Vn n (i) df V0 100 2 0.08 100 9 0.08 100 9 0.06 • What is the effect of high/low discount rate on PV? • What is the effect of time on PV?
- 9. 9 Solution: Class room exercise on PV Vn n i 1/(1+i)n V0 100 2 0.08 0.857339 85.7339 100 9 0.08 0.500249 50.0249 100 9 0.06 0.591898 59.1898
- 10. 10 Table of Discount factor for 1. =1/(1+i)^n The present value of "1" due at the end of "n" years at annual discount rate "i" Year (n) Discount rate (i) 0.01 0.02 0.03 0.04 0.06 0.08 0.11 0.12 0.14 0.16 0.17 0.2 0.21 0.22 1 0.990 0.980 0.971 0.962 0.943 0.926 0.901 0.893 0.877 0.862 0.855 0.833 0.826 0.820 2 0.980 0.961 0.943 0.925 0.890 0.857 0.812 0.797 0.769 0.743 0.731 0.694 0.683 0.672 3 0.971 0.942 0.915 0.889 0.840 0.794 0.731 0.712 0.675 0.641 0.624 0.579 0.564 0.551 4 0.961 0.924 0.888 0.855 0.792 0.735 0.659 0.636 0.592 0.552 0.534 0.482 0.467 0.451 5 0.951 0.906 0.863 0.822 0.747 0.681 0.593 0.567 0.519 0.476 0.456 0.402 0.386 0.370 6 0.942 0.888 0.837 0.790 0.705 0.630 0.535 0.507 0.456 0.410 0.390 0.335 0.319 0.303 7 0.933 0.871 0.813 0.760 0.665 0.583 0.482 0.452 0.400 0.354 0.333 0.279 0.263 0.249 8 0.923 0.853 0.789 0.731 0.627 0.540 0.434 0.404 0.351 0.305 0.285 0.233 0.218 0.204 9 0.914 0.837 0.766 0.703 0.592 0.500 0.391 0.361 0.308 0.263 0.243 0.194 0.180 0.167 10 0.905 0.820 0.744 0.676 0.558 0.463 0.352 0.322 0.270 0.227 0.208 0.162 0.149 0.137
- 11. 11 Class assignment: Using discounting tables for 1, find the present values of the followings Year (n) Future Value $ (Vn) Discount Rate (i) Discount factor (1/(1+i)n ) Present value $ (V0) 5 1 0.12 0.567 0.567 10 1 0.12 0.322 0.322 13 1 0.12 0.229 0.229 50 1 0.12 0.003 0.003 0 1 0.12 1.000 1
- 12. 12 Discounted measures of project worth (value) • Three discounted measures: 1. Net present value (NPV) 2. Benefit: Cost ratio (B/C ratio) 3. Internal rate of returns (IRR)
- 13. 13 1. Net present Value (NPV) • NPV is also termed net present worth (NPW), net discounted revenues (NDR), and net discounted cash flow. • It is sum of all revenues, suitably discounted, minus the sum of all costs, suitably discounted; or • it is equal to the present value of the benefits less the present value of the costs of a project at specific discounting rate. • Mathematically NPVi = n N n N i% n n n n n 0 n 0 1 1 NPV B * C * (1 i) (1 i)
- 14. 14 NPV- Criterion of selection • When using the NPV, the selection criteria is to accept all independent projects with a NPV of zero or greater (NPV≥0) • i.e. to accept project when discounted costs are equal to or less than discounted benefits. In case of single project: accept a project with NPV0 In case of more than one project, selection is made for the project with the highest NPV Example: A tree growing project for the production of building poles has the tabulated total costs (TC) and total benefits (TB) during a project life of 7 years. Using the NPV measure, indicate whether the project is acceptable if i= 17%?
- 15. 15 Example on NPV17% Year TC TB 0.17 PVC PVB NPV17% "1" "2" "3" "4" "5"="2"*4" "6"="3"*"4 " "7" = ∑"6" -∑"5" 1 24000 0 0.855 20512.8 0.0 2 18000 0 0.731 13149.2 0.0 3 12000 0 0.624 7492.4 0.0 4 3000 30000 0.534 1601.0 16009.5 5 3000 0 0.456 1368.3 0.0 6 3000 0 0.390 1169.5 0.0 7 3000 70000 0.333 999.6 23323.7 ∑ 46292.9 39333.2 NPV17% -6959.7
- 16. 16 Example on NPV11% Year TC TB 0.11 PVC PVB NPV11% "1" "2" "3" "4" "5"="2"*4" "6"="3"*"4 " "7" = ∑"6" -∑"5" 1 24000 0 0.901 21621.6 0.0 2 18000 0 0.812 14609.2 0.0 3 12000 0 0.731 8774.3 0.0 4 3000 30000 0.659 1976.2 19761.9 5 3000 0 0.593 1780.4 0.0 6 3000 0 0.535 1603.9 0.0 7 3000 70000 0.482 1445.0 33716.1 51810.6 53478.0 NPV11% 1667.5
- 17. 17 Effect of discount rate on NPV Annual discount rate Sum PVB Sum PVC NPV 17 39333.2 46292.9 -6959.7 11 53478.0 51810.6 1667.5 • As annual discount rate increases (decreases), NPV decreases (increases)
- 18. 18 NPV: Selection among independent projects • Criterion: In case of more than one project competing for limited fund, selection is made for the project with the highest NPV Project NPVi% selection Tilapia Fish production 100 X Broiler production 350 Wood production 275 X Range improvement 200 X
- 19. 19 2. Benefit: Cost ratio • The B/C ratio is equal to the sum of present value of benefits divided by sum of present value of costs. • Formally, it may be expressed as N n n n n N n n n n i i C i B Cratio B 0 0 % ) 1 ( 1 * ) 1 ( 1 * /
- 20. 20 B:C ratio: selection criteria • When B/C ratio is used, the selection criteria is to accept all independent projects with a B/C ratio of one or greater (B/C ratio ≥1.0), when discounted at a suitable discount rate. • Projects are profitable if B/C 1; not profitable with B:C ratio 1; and break-even when B/C ratio =1.0. In case of a single project: accept a project with B:C ratio >1 In case of more than one project, selection is made for the project with the highest B:C ratio • `Is B/C ratio and C/B ratio same? Annual discount rate Sum PVB Sum PVC B:C ratio selection 17 39333.2 46292.9 0.85 X 11 53478.0 51810.6 1.03
- 21. 21 3. Internal rate of returns (IRR) • The IRR is the discount rate that just makes the sum of present value of benefits and the sum of present value of costs equal, or IRR is the discount rate that makes the NPV of a project = ? • Three methods of determining IRR. 1. It is determined by a process of trial and error until a high (i) results in –ve NPV and a low (i) that produces a +ve NPV are determined (preferably with a difference of ≤5%). 2. Graph method 3. Formulae method
- 22. 22 IRR- Criterion of selection • It can also be expressed as the discount rate i such that: • The formal selection criterion for the IRR is to accept all independent projects having an IRR equal to or greater than the opportunity cost of capital (e.g. annual interest rate in commercial banks). In case of single project: accept a project with IRR OPPORTUNITY COST OF CAPITAL In case of more than one project, selection is made for the project with the highest IRR n N n n n n N n n n i C i B 1 1 * 1 1 * 0 0
- 23. 23 Calculation of IRR Where: i1 = lower discount rate, i2 = higher discount rate • Example: i NPV 11% 1667.5 17% -6959.7 • IRR = 11+6*(1667.5/ (1667.5 + │-6959.7)│) = 11+6*(1667.5/(1667.5+6959.7) =11+6*(1667.5/8627.2) = 11+6*(0.193) = 11 + 1.16 =12.16% i1 1 2 1 i1 i2 NPV IRR i (i i )* (NPV NPV )
- 24. 24 Estimating IRR: Graph method -50 0 50 100 6 8 10 11 12 Discount rate N P V
- 25. 25 Estimating IRR: Educated guess method Discount rate NPV 4 +15 6 +10 8 -10 9 -14
- 26. 26 Class room assignment A private landowner is willing to undertake tree-growing investment. The following table shows estimates of benefits and costs throughout the project life. a. Indicate whether the project is profitable when the opportunity cost of capital is 8% and 11%, using the criteria of NPV and B/C ratio. b. Indicate the minimum rate of returns acceptable to the landowner. Year Benefits Costs Discount factor 8% 11% 1 0 40000 2 0 18000 3 0 6000 4 8000 6000 5 8000 6000 6 10000 6000 7 7000 6000 8 126000 26000
- 27. 27 Discounted measures and the environment
- 28. 28 Internalizing Externalities • An Externality is Internalized if the persons or group that generated the externality incorporate into their own private or internal cost-benefit calculations the external benefits (positive externality) or the external costs (negative externality) that third parties bear. • An externality has been internalized or adjusted for completely if, as a result, the socially optimal output emerges.
- 29. 29 Internalizing environmental externalities: an example • A negative externality of the tree harvesting project is manifested in soil erosion down stream and flooding hazard. Estimated annual cost of soil erosion (value of crop lost) was estimated as 1000 throughout the project life. Annual cost of protective anti-flood measures is estimated at 500 throughout the project life. Class assignment (groups1-5): Internalize externalities and re- calculate 1. NPV and indicate whether the tree growing project is acceptable at ??% annual discount rate. 2. What is the effect on internalizing negative externalities on NPV?
- 30. 30 Solution: Estimation of NPV with externality internalized at 11% discount rate Year TC TB 0.11 PVC PVB "1" "2" "3" "4" "5"="2"*4" "6"="3"*"4" "7" = ∑"6" -∑"5" 1 25500 0 0.901 22973.0 0.0 2 19500 0 0.812 15826.6 0.0 3 13500 0 0.731 9871.1 0.0 4 4500 30000 0.659 2964.3 19761.9 5 4500 0 0.593 2670.5 0.0 6 4500 0 0.535 2405.9 0.0 7 4500 70000 0.482 2167.5 33716.1 58878.9 53478.0 NPV -5400.8
- 31. 31 Home Assignment: Internalization of externalities and NPV An environmental friendly group is assessing the economics of aquaculture project. The project life is 6 months. It starts with construction of 4 fish bonds (100m*21m) in the establishment year at a cost of SD. 1 per m2 . in the same year a water system at total cost of SD. 5000 was installed. Fingerlings (fish seeds), costing SD. 5 each, at a rate of 3 per m2 were added. Fertilizer was added every 15 days at a rate of 0.05 gm per m2 . Fish feed was added at a rate of 1 gm per m2 per month. The cost of 1 kg of fertilizer is SD 400. The cost of fish feed is SD 1000 per kg. if by the end of 6 months, 15000 fish of an average body weight of 0.5 kg were harvested and farm-gate price was SD. 100 per kg. a. Using NPV criterion, determine the economic feasibility of this project, provided that the farm gets a loan from commercial bank at 12% annual profit margin. b. If the project pays at harvesting time a pollution tax of SD. 500000. re- estimate NPV of the project.