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- 1. Definition process of making long-term investment decisions that maximizes the wealth of the shareholders. Three Parts: Estimating Cash Flows (Most tedious) Estimating discount rate (Cost of Capital, base rate computed once a year) Applying decision rules (Topic of today’s class)
- 2. Decision Criteria Payback Period Time value adjusted payback period Internal Rate of Return Modified Internal Rate of Return Net Present Value Profitability Index
- 3. Some Assumptions Projects belong in the same risk class. Project lives are identical. Project sizes are roughly identical. Project decisions are not affected by the project financing decisions. All projects are financed according to the company’s target capital structure. Cost of capital is constant over project life We will relax the assumptions as we move along
- 4. Payback Period How long does it take to recover investment Steps Compute cumulative cash flows Identify the payback year (the year CCF changes to positive) In what fraction in the payback year the investment is fully recovered (Payback year -1) + (last negative CCF/CF in PBY)
- 5. Payback Year-Example Incremental Cumulative Year Cash Flows Cash Flow(CCF) Project A Project A 0 (Taka 10,000) (Taka 10,000) 1 1,000 (9,000) 2 2,000 (7,000) 3 3,000 (4,000) 4 5,000 1,000 5 6,000 6 6,000 (Payback year -1) + (last negative CCF/CF in PBY) = 3+4000/5000 = 3.8 years
- 6. Time Value Adjusted Payback Period After factoring in time value of money, how long does it take to recover initial investment. Incremental Cumulative Pv of Year Cash Flows Pv of Cash Flows Cash Flow (CPV) Project A Project A Project A 0 (Taka 10,000) (Taka 10,000) (10,000) 1 1,000 869.57 ( 9,130.43) 2 2,000 1,512.29 ( 7,618.14) 3 3,000 1,972.55 ( 5,645.59) 4 5,000 2,858.77 ( 2,786.82) 5 6,000 2,983.06 196.24 6 6,000 2,593.97 Adjusted Payback Period = (Adjusted payback year -1) + (Last negative CPV/PV in PBY) = 4 + (2786.82/2983.06 = 4.93
- 7. Internal Rate of Return (IRR) It is that rate that makes present value of inflows equal to the present value of outflows, NPV = 0, it is the geometric rate of return. ∑CFt(Outflows)/(1+i)t = ∑CFt(Inflows)/(1+i)t Good to have normal projects Solve by interpolation. Solve by using Financial Calculators. You must have both inflows and outflows. Some projects may not have IRR Some projects may have multiple IRR
- 8. IRR- Financial Calculator Example Incremental CFo = - 10,000 Year Cash Flows CO1 = 1,000 Project A FO1 = 1 0 (Taka 10,000) CO2 = 2,000 1 1,000 FO2 = 1 2 2,000 - 3 3,000 - 4 5,000 CO6 = 6,000 5 6,000 FO6 = 1 6 6,000 IRR [CPT] 22.35%
- 9. Net Present Value Residual Value after All Capital Suppliers are Satisfied. Present Value of inflows minus present value of outflows at a given discount rate NPV on Financial Calculator. You still have the cash flows on your calculator. Hit [NPV]. Calculator asks for I, the discount rate. You enter it, then hit [CPT]. It will produce
- 10. NPV Profile NPV Profile.xlsx
- 11. NPV Profile ($2,000.00) ($1,000.00) $0.00 $1,000.00 $2,000.00 $3,000.00 $4,000.00 $5,000.00 $6,000.00 $7,000.00 $8,000.00 7% 9% 11% 13% 15% 17% 19% 21% 23% 25% 27% 29% 31% 33% NPV A B
- 12. Finding Crossover Rate Define the Difference between the Two Cash Flows. Compute the Differences Accordingly Determine the IRR of the Differences. The NPVs cross over at this rate Why Does this process work?
- 13. The Reinvestment Rate Assumption of IRR IRR assumes that interim flows are reinvested at IRR rate. What is the rate of return for project B if interim flows earn only 12 percent? -75,000 38000 38000 38000 38000(1+.12) 38000(1+.12)2 PV = -75000 FV = 128227.20 Rate of return = 19.57%
- 14. Modified Internal Rate of Return (MIRR) Find the Future Value of (only) inflows (Value 1) You can find the PV and convert it FV (Value 1)(Normal projects only) Find the Present Value of Outflows (Value 2). If the Project has just the Initial Outlay as the only outflow, Initial Outflow is Value 2 Compute the implied interest rate using Value 2 as PV, Value 1 as FV, n for the time frame. The implied interest rate is MIRR
- 15. Profitability Index PI = Present Value of Inflows/Initial Outlay If you know the NPV and that the initial outlay is the only outflow, then PI = (NPV + IO)/IO
- 16. Decision Rules for Ranking Projects Accept/Reject Rules for Independent Projects Payback or Adjusted Payback Period Quicker Payback better, Rank higher Should be less than company’s required maximum payback IRR/MIRR Must be greater than discount rate. The higher rate, the better rank NPV Must be Positive. The higher the NPV the better rank. Profitability Index Must be greater than 1. Higher PI ranks higher
- 17. Decision Rules for Mutually Exclusive Situation. Can Choose only One IRR/MIRR: Choose the Best, Reject others. (Must exceed cost of Capital) NPV: Choose Project with Highest NPV, Reject Others. (NPV must be positive) PI : Choose the Project with Greatest PI Value(Must exceed 1), Reject Others.
- 18. Discount rate vary over life Use NPV NPV = -IO + CF1/(1+k1) + CF2 /(1+k1)(1+k2) + CF3/(1+k1)(1+k2)(1+k3) ……. CFn/(1+k1)(1+k2)….(1+kn)
- 19. Project Size Difference Consider the following two projects. (Mutually Exclusive) Year 0 1 2 3 Project A -10,000 6000 6,000 6,000 Project B -75,000 38000 38000 38000 IRRA : 36.31% IRRB : 24.26% NPV of A (at 20%): 2,638.89 NPV of B (at 20%): 5,046.30 NPV Profile1-Scale Difference.xlsx
- 20. Incremental Cash Flow Year 0 1 2 3 Project A -10,000 6000 6,000 6,000 Project B -75,000 38000 38000 38000 Project B – A -65000 32000 32000 32000 NPV of A: 2,638.89 NPV of Project B-A at 20%: 2,407.01 Conclusion: The incremental investment in B creates Value.
- 21. Projects with Unequal Lives Mutually Exclusive Replacement Chain Keep renewing the projects until both Projects end in The Same Year Find the NPV on a common life basis. Project with Higher NPV is The Better Value Creator
- 22. Example: Page 122 Year CF(X) CF(Y) 0 (6,000) (8,500) 1 2,800 4,000 2 3,500 4,000 3 4,600 3,000 4 2,000 5 2,000 6 1,000 Project(X) Project(Y) IRR 33.44% 28.34% NPV@16% Taka 1,961.89 Taka 2,310.15 PI 1.33 1.27
- 23. Common Life (Replacement Chain) Year CF(X) CF(Y) 0 (6,000) (8,500) 1 2,800 4,000 2 3,500 4,000 3 4,600 -6,000 3,000 4 2,800 2,000 5 3,500 2,000 6 4,600 1,000 Project(X) Project(Y) IRR 33.44% 28.34% NPV Taka 3,218.79 Taka 2,310.15
- 24. Projects with Unequal Lives Mutually Exclusive Equivalent Annual Annuity (EAA)/Annual Net Present Value (ANPV)/Uniform Annual Series (UAS) First find Regular one Cycle NPV Second, Divide Above by Appropriate PVIFA. This is Equivalent Annual Annuity or ANPV. Assumption: Unlimited Renewal
- 25. Equivalent Annual Annuity EAA = NPV (Based on one cycle)/PVIFAi,n Project(X) Project (Y) NPV 1,961.89 2,310.15 PVIFA 2.2459 3.6847 EAA 873.54 626.96
- 26. Capital Rationing Choose as Many Projects You Can fund Given the Capital Budget. Keep in Mind That Cost of Capital, WACC, is likely to go up as you increase the Budget for Capital Investment.
- 27. Project Selection with Capital Rationing Total Budget: Taka 80,00,000. Discount rate 20% Project Cost IRR NPV PI A. 20,00,000 27% 7,00,000 1.35 B. 30,00,000 25% 8,00,000 1.27 C. 18,00,000 24% 5,50,000 1.31 D. 10,00,000 23.25% 2,80,000 1.28 E. 8,00,000 22% 2,00,000 1.25 F. 6,00,000 21.5% 1,60,000 1.27 G. 6,00,000 21% 1,50,000 1.25
- 28. Project Selection On the Basis of IRR A+B+C+D Total Cost 78,00,000 Total NPV 23,30,000 On the Basis of NPV B+A+C+D Total Cost 78,00,000 Total NPV 23,30,000 On the Basis PI B+A+C+D Total Cost 78,00,000 Total NPV 23,30,000 Best Mix A+B+C+F+G Total Cost 80,00,000 Total NPV 23,60,000

Full NameComment goes here.Pookster2 months ago