Capital Budgeting Reading Material PDF

10/30/2024 Module 3: Capital Budgeting Capital Budgeting Capital budgeting is the process of evaluating and selecting long-term investments that are consistent with the goal of the firm Stages in Capital Budgeting Identification Stage Search Stage Information-Acquisi...

10/30/2024 Module 3: Capital Budgeting Capital Budgeting Capital budgeting is the process of evaluating and selecting long-term investments that are consistent with the goal of the firm Stages in Capital Budgeting Identification Stage Search Stage Information-Acquisition Stage Selection Stage Financing Stage Implementation and Control Stage 1  10/30/2024 Nature of Capital Budgeting Huge investments Time consuming Irreversible Long term implication Independent and Mutually Exclusive Projects Independent The cash flows of one are unaffected by the acceptance of the other Mutually Exclusive The acceptance of one project precludes accepting the other Hurdle rate or Discount rate : Minimum acceptable rate of return that should be earned on a project 2  10/30/2024 Capital Budgeting Techniques - Meaning and Decision Rule Payback Period: Meaning: Time required to recover the initial investment from cash flows. Decision Rule: Select the project with the lower PBP. Accept if the payback period is less than or equal to the predetermined acceptable period. Post Payback period amount: Meaning: Cash inflows generated after the initial investment has been fully recovered. Decision Rule: Projects with substantial cash flows beyond the payback period are generally more attractive Net Present Value (NPV) Meaning: It represents the extra money a project or investment is expected to generate, beyond its initial cost, after adjusting for the value of money over time. By definition, NPV = Present value of cash inflows minus initial investment. Decision Rule: Choose projects with the highest positive NPV Profitability Index (PI) Meaning: Ratio of present value of cash flows to initial investment. Decision Rule: Accept if PI > 1 Internal Rate of Return (IRR) Meaning: Discount rate that makes NPV zero. This is the minimum rate required to recover the cost of capital. Decision Rule: Select projects with IRRs above the cost of capital and prioritize those with higher IRRs if required. Modified IRR (MIRR) Meaning: Is the adjusted rate of return that assumes consistent reinvestment of cash flows. Decision Rule: Select projects with MIRRs above the cost of capital and prioritize those with higher MIRRs if required. Meaning of Cash Inflow Cash inflow = In flow after tax but before depreciation for all the techniques except ARR. For ARR, Cash flow means cash flow after tax only Cash flow before depreciation and tax : Rs. 20,000 , 25,000 and 27,000 Cash flow Depreciation Cash flow Tax Cash flow after tax Cash flow after tax before 1 2 before tax 50% 5 (3- 4) depreciation 3 (1-2) 4 6 (5 +2) 20000 5000 15000 7500 7500 12500 25000 5000 20000 10000 10000 15000 27000 5000 22000 11000 11000 16000 3  10/30/2024 General Format for Income Calculation Particulars Rs Rs Profit (Revenue) **** Less :Operating Expenses **** Less : Depreciation **** ***** Earning Before Tax ***** Less: Tax ***** Earning After Tax ***** Add: Depreciation (For, PBP, NPV, PI, IRR and ***** not for ARR) Earnings after tax but before Depreciation. *****  Calculate it for given number of years Pay back Period – Ex. 1 Pay back Period : Number of years required to recover the initial investment If an investment of Rs. 100000 in a machine is expected to generate cash inflow of Rs. 20,000 p.a. what is its PBP? 4  10/30/2024 Pay back Period. Ex- 2 Year Proj. A Cumulative Proj. B Cumulative 1 100000 1,00,000 40,000 40,000 2 60000 1,60,000 40,000 80,000 3 40000 2,00,000 40,000 1,20,000 4 20000 2,20,000 80,000 2,00,000 5 60,000 2,60,000 Project A is selected 3 Years 4 Years Project X Project Y Initial Investment Rs. 1000000 Rs. 1000000 Cash Inflows CF X CF Y Year 1 300000 250000 300000 250000 Year 2 400000 200000 700000 450000 Year 3 300000 500000 1000000 950000 Year 4 500000 450000 1500000 1400000 Assume Cost of Capital to be 10% 5  10/30/2024 Year Annual CFAT Cumulative CFAT A B A B 0 40000 40000 1 14000 22000 14000 22000 2 16000 20000 30000 42000 3 18000 18000 48000 60000 4 20000 16000 68000 76000 5 25000 * 17000* 93000 93000 5th year CFAT includes Rs. 3,000 salvage value also. 𝐵𝑎𝑙𝑎𝑛𝑐𝑒 𝐴𝑚𝑜𝑢𝑛𝑡 to be recovered 𝑃𝐵𝑃 𝐴 = 𝐶𝑜𝑚𝑝𝑙𝑒𝑡𝑒𝑑 Years + 𝐵𝑎𝑙𝑎𝑛𝑐𝑒 𝐴𝑚𝑜𝑢𝑛𝑡 to be recovered Profit in the year under consideration 𝑃𝐵𝑃 𝐵 = 𝐶𝑜𝑚𝑝𝑙𝑒𝑡𝑒𝑑 Years + Profit in the year under consideration 𝑃𝐵𝑃 𝐴 = 2 + = 2. 55 Years 𝑃𝐵𝑃 𝐴 = 1 + = 1. 90 Years 18000 20000 0.55  12 = 6. 6 Months 0.90  12 = 10. 8 Months 0.60  30 = 18 Days 0.80  30 = 24 Days 2 Years , 6 Months and 18 Days 1 Year , 10 Months and 24 Days Discounted Payback Period Investment = Rs. 100. Interest is 10%. FCF are given 2 1 below Investment = Rs. 100,000. Interest is 10%. FCF are Year FCF DF @ 10% PVS CPVS given below Year 1: Rs. 30,000 1 40 0.909 36.36 36.36 Year 2: Rs. 40,000 2 30 0.826 Year 3: Rs. 20,000 24.78 61.14 Year 4: Rs. 15,000 3 30 0.751 22.53 83.67 Year 5: Rs. 10,000 4 24 0.683 16.39 100.06 Rs. 1,15,000 5 15 0.621 9.32 109.38 Post PBP Profitability = Rs. 1,15,000 – Rs. 1,00,000= 15,000 Non-discounted PBP = 3 Years Post PBP Profitability Index = (Rs. 15 / Rs100 )  100 = 15% Discounted PBP PBP = 3 + 16.33 16.39 PBP = 3 + 0.996 ≈ 4 Years Post PBP Profitability = Rs. 39 (24+15) Post PBP Profitability Index = (Rs. 39 / Rs100 )  100 = 39% 6  10/30/2024 Calculate PBP, Post PBP, NPV, PI and IRR Initial investment = Rs. 106000 Life of the Project = 6 Years PBP ? Cost of Capital = 4% Post Payback Period amount = Rs. 14,000 Estimated Net Cash Flows : Year CFAT PV factor PVs at 4% PV factor PVs at 3% Year 1 Rs. 10,000 (4%) (3%) Year 2 Rs. 15,000 Year 1 Rs. 10,000 0.962 Rs. 9,620 0.971 Rs. 9,710 Year 3 Rs. 20,000 Rs. 15,000 0.925 Rs. 13,875 Year 2 0.943 Rs. 14145 Year 4 Rs. 22,000 Year 5 Rs. 25,000 Year 3 Rs. 20,000 0.889 Rs. 17,780 0.915 Rs. 18300 Year 6 Rs. 28,000 Year 4 Rs. 22,000 0.855 Rs. 18,810 0.888 Rs. 19536 Year 5 Rs. 25,000 0.822 Rs. 20,250 0.863 Rs. 21575 702 (4 − 3) 𝐼𝑅𝑅 = 3 + Rs. 28,000 0.790 Rs. 22,120 702 − (−3245) Year 6 0.837 Rs. 23436 PV of Cash Inflows Rs. 1,02,755 Rs. 1,06,702 702 (4 − 3) 𝐼𝑅𝑅 = 3 + Less: Cash Outflow Rs. 1,06,000 Rs. 1,06,000 702 − (−3245) NPV Rs. - 3245 Rs.702 702 𝐼𝑅𝑅 = 3 + 3947 𝑁𝑃𝑉@𝐿𝐷𝐹 𝐼𝑅𝑅 = 3 + 0.1778 = 𝟑. 𝟏𝟖 % 𝐼𝑅𝑅 = 𝐿𝐷𝐹 + (𝐻𝐷𝐹 − 𝐿𝐷𝐹) 𝑁𝑃𝑉@𝐿𝐷𝐹 − 𝑁𝑃𝑉@𝐻𝐷𝐹 Initial Investment Rs. 1,00,000. Expected rate of return 10%. Inflows for 4 years are : Rs30,000, Rs 30,000, 2 Rs 40,000 and Rs50,000 Solution - PBP Solution - NPV Year Cash Flow Cumulative CF Year Cash Flow PV factors (@10%) PVS 1 30,000 30,000 1 30,000 0.909 27,273 2 30,000 0.826 24,793 2 30,000 60,000 3 40,000 0.751 30,053 3 40,000 1,00,000 4 50,000 0.683 34,151 4 50,000 1,50,000 1,16,269 PBP = 3 Years Less: Outflow 1,00,000 NPV 16269 Solution – PI PI = PV of Cash Flows ÷ Initial Investment = 1,16,269 ÷ 100000 = 1.163 Solution : IRR Year Cash Flow PV factors (@16%) PV factors (@17%) PVS @ 16% PVS @ 17% 1 30000 0.862 0.855 25862 25641 2 30000 0.743 0.731 22295 21915 3 40000 0.641 0.624 25626 24975 4 50000 0.552 0.534 27615 26683 101398 99214 Less: Outflow 100000 100000 NPV 1398 -786 7  10/30/2024 12% 14% Verification 3 -10,000 1 -10,000 1 -10,000 13% PVS 4000 0.8929 3571 0.8772 3509 1 -10,000 3000 0.7972 2392 0.7695 2308 0.8850 3540 2100 0.7118 1495 0.6750 1417 0.7831 2349 2737 0.6355 1739 0.5921 1621 0.6931 1456 1800 0.5674 1021 0.5194 935 0.6133 1679 219 -210 0.5428 977 13.00% NPV 0 NPV and ARR A company is considering whether to buy specialized machines For a new production line. The purchase price of machinery is Rs 400000 and its estimated useful life is four years. There is no scrap Value after four years The project income statements: Year1 Year 2 Year 3 Year 4 Revenue 310000 280000 280000 310000 Depreciation 100000 100000 100000 100000 Other expenses 150000 100000 110000 120000 Profit before tax 60000 80000 70000 90000 Taxation (15%) 9000 12000 10500 13500 51000 68000 59500 76500 Should the company buy the new machinery if the minimum acceptable Rate of return is 20% (Hurdle rate of return)? 8  10/30/2024 Year1 Year 2 Year 3 Year 4 Revenue 310000 280000 280000 310000 Depreciation 100000 100000 100000 100000 Other expenses 150000 100000 110000 120000 Profit before tax 60000 80000 70000 90000 Taxation (15%) 9000 12000 10500 13500 51000 68000 59500 76500 Add : Depn 100000 100000 100000 100000 151000 168000 159500 176500 DFS (10%) 0.909 0.826 0.751 0.683 137273 138843 119835 120552 516502 Less: OF 400000 NPV 116502 Example A Ltd is considering to invest Rs. 2,00,000. Forecasted annual income after depreciation but before tax is as under Year Income 1 1,00,000 2 1,00,000 3 80,000 4 80,000 5 40,000 Calculate: PBP NPV PI IRR Assume cost of capital be 10 parent 9  10/30/2024 Profitability statement Year Profit after Tax PAT Depn. PAT but Cumulative Depn. before depn. Flow 1 1,00,000 50,000 50,000 40,000 90,000 90,000 2 1,00,000 50,000 50,000 40,000 90,000 1,80,000 3 80,000 40,000 40,000 40,000 80,000 2,60,000 4 80,000 40,000 40,000 40,000 80,000 3,40,000 5 40,000 20,000 20,000 40,000 60,000 4,00,000 Total 2,00,000 PBP = 2 + 20,000 = 2.25 years ARR = Average earnings  100 80,000 Average investment Average earnings = Total earnings after tax / No. years ARR = 40,000  100 Average earnings = 2,00,000 / 5 = 40,000 1,00,000 Average Investment = 2,00,000 / 2 = 1,00,000 = 40% Calculation of NPV Year PAT but Discount factor at 10 Present Value before depn. percent 1 90,000 0.909 81,810 2 90,000 0.826 74,340 3 80,000 0.751 60,080 4 80,000 0.683 54,640 5 60,000 0.621 37,260 Total Present value 3,08,130 Less: Initial Investment 2,00,000 NPV 1,08,130 PI = Total Present value  100 = 3,08,130  100 Initial Investment 2,00,000 = 1.54 10  10/30/2024 Calculation of IRR Year FCF DF @ 30% DF @ 34% PV @ 30% PV @ 34 % 1 90,000 0.7692 0.7463 69,228 67,167 2 90,000 0.5917 0.5569 53,253 50,121 3 80,000 0.4552 0.4156 36,416 33,248 4 80,000 0.3501 0.3102 28,008 24,816 5 60,000 0.2693 0.2315 16,158 13,890 PVS 203,063 189,242 OF 200,000 200,000 NPV 3,063 -10,758 IRR = 30% + 3063 (34%-30%) 3063 - (-10758) = 30.8% Year 0 1 2 3 4 5 The cost of capital is 12% Cashflow -1385000 300000 400000 600000 300000 200000 Fake PBP = 3.85 IRR of the project is 9.4%. Since the IRR is less (300000 + 400000 + 600000 + 300000 + 200000)/ 5 = 360000 than the cost of capital, i.e. 12%, the project cannot Fake PBP = 13,85,000 / 360000 = 3.85 be selected. Year Cashflow 9% NPV @ 9% 10% NPV @ 10% 0 -1385000 1 -1385000 1 -1385000 1 300000 0.917 275229 0.9091 272727 2 400000 0.842 336672 0.8264 330579 3 600000 0.772 463310 0.7513 450789 4 300000 0.708 212528 0.6830 204904 5 200000 0.650 129986 0.6209 124184 360000 32725 -1817 Fake PBP 3.85 IRR = 9% + 32725 (10%-9%) 32725 - (-1817) = 9.95% 11  10/30/2024 Cash Inflow Particulars Project A Project B Year 1 2 3 4 5 Initial Investment Rs. 40,000 Rs. 60,000 Project A Rs. 10,000 Rs. 20,000 Rs. 20,000 Rs. 6,000 Rs. 4,000 Estimated Life 5 Years 5 Years Project B Rs. 40,000 Rs. 20,000 Rs. 10,000 Rs. 6,000 Rs. 4,000 Scrap Value Rs. 2,000 Rs.4,000 Discounting Rate 10% Year Cash Flow 10% NPV @ 10% Year Cash Flow 10% NPV @ 10% 0 -40000 1 -40000 0 -60000 1 -60000 1 10000 0.909 9091 1 40000 0.909 36364 2 20000 0.826 16529 2 20000 0.826 16529 3 20000 0.751 15026 3 10000 0.751 7513 4 6000 0.683 4098 4 6000 0.683 4098 5 (Inflow + Scrap ) 6000 0.621 3726 5 (Inflow + Scrap ) 8000 0.621 4967 48470 69471 NPV 8470 NPV 9471 Discounting Rate 10% Year 0 1 2 3 4 Project A (60,000) Rs. 9,000 Rs. 10,000 Rs. 25,000 Rs. 30,000 Project B (60,000) Rs. 30,000 Rs. 25,000 Rs. 10,000 Rs. 9,000 PBP – Miscellaneous Problem Bharath Electronics Ltd is planning to introduce mechanization to replace the labour force. Two alternatives are available. Advise the management to select the machine under pay back period method Particulars Machine X Machine Y Cost of the machine 50000 40000 Estimated life 10 Years 8 Years Estimated scrap savings per year 1000 1000 Estimated cost of materials per year 2000 3000 Maintenance Cost p.a 2500 3100 Additional Cost of Supervision 1500 2000 Estimated savings in wages per year 10000 12500 Depreciation method SLM Tax Rate 50% 12  10/30/2024 Calculation of Annual Cash flow Particulars Machine X Machine Y Savings in wages 10000 12500 Savings in scrap 1000 1000 11000 13500 Less : Additional cost of Materials 2000 3000 Additional Cost of Supervision 1500 2000 Additional Cost of Maintenance 2500 6000 3100 8100 Net Savings 5000 5400 Less : Depreciation 5000 5000 Savings after Depreciation 0 400 Less: Tax at 50% 0 200 Savings after Depreciation and tax 0 200 Add: Depreciation 5000 5200 Profit After tax before Depreciation ( Annual Cash flow) 5000 5200 PBP =Original Investment  Annual Cash flow 50000/ 5000 40000 / 5200 10 Years 7.7 Years PBP, NPV, PI and IRR Year FCF 9% NPV @ 9% 10% NPV @ 10% CFCF 1 300000 0.917 275100 0.909 272700 300000 2 400000 0.842 336800 0.826 330400 700000 3 600000 0.772 463200 0.751 450600 1300000 IRR = 9% + 32500 (10%-9%) 4 300000 0.708 212400 0.683 204900 1600000 32500 - (-2200) 5 200000 0.650 130000 0.621 124200 1800000 = 9.93% PV of Future Cashflows 1417500 1382800 Initial Investment 1385000 1385000 NPV 32500 -2200 PI =1 + (NPV ÷ Initial Investment) PI =(PV of Future Cashflows ÷ Initial Investment) PI = 1+ 32500 = 1.023 PI = 1417500 = 1.023 1385000 1385000 PBP= Years before Break-even + (Unrecovered Amount ÷ Cash flow in the recovery year) PBP = 3 + 85000 300000 PBP = 3 + 0.28 = 3. 28 Years 13  10/30/2024 Year 0 1 2 3 4 Initial Investment = Rs. 20000 Free Cashflow (20000) 5000 8000 10000 4000 Average Cashflow = Rs. 6750 Year Inflow DF @ 12% DF @ 14% PVs @ 12% PVs @ 14% 1 5000 0.893 0.877 4465 4385 2 8000 0.797 0.769 6376 6152 IRR = 12 + 505 (14 - 12) 3 10000 0.712 0.675 7120 6750 505 + 345 4 4000 0.636 0.592 2544 2368 = 13.18% PV of Cash flows 20505 19655 Initial Investment 20000 20000 NPV 505 -345 MIRR Vs Terminal Method In MIRR the reinvestment rate of intermittent cash flow is the cost of capital of the firm; however in case of TV method, the reinvestment differs (generally lower) than the cost of capital of the firm 14  10/30/2024 1 MIRR The project cost is Rs.10 cr and the CF stream is as follows. The cost of capital of the firm is 15%. Year Free CF Formula Compounding Factor Compounded n-1 (5-t) (1+r) (1+15%) Sum 1 2.5 (1.15)^5-1 1.75 4.37 2 3.5 (1.15)^5-2 1.52 5.32 3 3.5 (1.15)^5-3 1.32 4.63 4 3.5 (1.15)^5-4 1.15 4.03 5 3.5 (1.15)^5-5 1.00 3.5 Total Compounded Future Value 21.85 0 1 2 3 4 5 For 5th year – No Rs. 10 Cr Rs. 2.5 Cr Rs. 3.5 Cr Rs. 3.5 Cr Rs. 3.5 Cr Rs. 3.5 Cr interest For 1 year @ 15% 4.03 Cr For 2 years @ 15% 4.63 Cr For 3 years @ 15% 5.32 Cr For 4 years @ 15% Cashflow 4.37 Cr 21.85 Cr 2.5 3.5 21.85 10 = 3.5 𝐹𝑉 1+𝑟 𝑃𝑉 = 21.85 3.5 1+𝑟 1+𝑟 = 10 (1 + 𝑟) = (2.185) / 3.5 16.5 Cr 1+ r = 1.1692 r = 1.1692 – 1 = 16.92% 15  10/30/2024 Terminal Method The project cost is Rs.10cr and the CF stream is as follows The cost of capital of the firm is 15%. The reinvestment rate of the intermittent cash flow is 12% Year Free CF Compounding Factor Future value of Free (Rs.cr) (1+12%)(5-t) CF @12% (Rs.cr) (1) (2) (3) (4) = (3) X (2) 1 2.5 1.574 3.93 2 3.5 1.405 4.92 3 3.5 1.254 4.39 4 3.5 1.120 3.92 5 3.5 1.000 3.50 Total Future Value of Free CF 20.66 20.66 Total future value of the Free CF after 5 years would be Rs.20.66cr if the 10 = 𝐹𝑉 1+𝑟 reinvestment is 12%. 𝑃𝑉 = 20.66 1+𝑟 1+𝑟 = 10 (1 + 𝑟) = (2.066) / 1+ r = 1.1562 r = 1.1562 – 1 = 15.62% 0 1 2 3 4 5 K = 15% For 0 year Rs. 10 Cr Rs. 2.5 Cr Rs. 3.5 Cr 3.5 Cr Rs. 3.5 Cr Rs. 3.5 Cr @ 12% For 1 year @ 12% 3.92 Cr For 2 years @ 12% 4.39 Cr For 3 years @ 12% 4.92 Cr For 4 years @ 12% Cashflow 3.93 Cr 20.66 Cr 2.5 3.5 3.93 10 = 20.66 𝐹𝑉 1+𝑟 3.5 4.92 𝑃𝑉 = 20.66 4.39 1+𝑟 1+𝑟 = 3.5 10 / 3.92 (1 + 𝑟) = (2.066) 3.5 3.50 1+ r = 1.1562 16.5 Cr 20.66 r = 1.1562 – 1 = 15.62% 16  10/30/2024 0 1 2 3 4 2 Rs. 300 Rs. 140 Rs. 120 Rs. 80 Rs. 60 For 0 year @ 14% 60.00 For 1 years @ 14% 91.20 For 2 years @ 14% 155.95 For 3 years @ 14% 207.42 514.67 514.67 300 = 𝐹𝑉 1+𝑟 𝑃𝑉 = 514.67 1+𝑟 1+𝑟 = As MIRR (14.44)> K (14%), the project is accepted 300 (1 + 𝑟) = (1.7156) / 1+ r = 1.144 r = 1.144 – 1 = 14.44% MIRR- Terminal Method Discount rate is 10% and Reinvestment Rate is 8% 17  10/30/2024 Future Value of Positive Cash Flows: Inflows 3 Present Value of Negative Cash Flows: Outflows and Negative Cash inflows (Loss) Reinvestment Rate: The rate at which positive cash flows are reinvested. 100000 + 45351 = 145,351 @5% 309104 145351 = 1+𝑟 309104 𝐹𝑉 1+𝑟 = Financing Cost = 5% 𝑃𝑉 = 145351 Reinvesting Rate = 10% 1+𝑟 (1 + 𝑟) = (2.1266) / 1+ r = 1.1629 r = 1.1629 – 1 = 16.29% 4 Financing Cost = 5% (1000) + (1809) = (2809) Reinvesting Rate = 10% 0 (1000) 1 800 2 1000 3 1300 4 (2200) 1430 1210 1065 = 3705 3705 2809 = 1+𝑟 3705 𝐹𝑉 1+𝑟 = 𝑃𝑉 = 2809 1+𝑟 / (1 + 𝑟) = (1.3189) 1+ r = 1.0716 r = 1.0716 – 1 = 7.16% 18  10/30/2024 Negative cash flows (Discounted) Positive cash flows M I R R (Compounded) 19