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# Capital budgeting the basics-2

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### Capital budgeting the basics-2

1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 10. NPV Profile  NPV Profile.xlsx
11. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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