COMPUTATION OF NET INVESTMENT Case 1 Kendra Enterprises plans to add a new machine to increase production capacity. The machine cost P180,000 plus P20,000 for installation and transportation costs and requires P40,000 additional working capital. Purchase price of new machine Installation and transportation costs Additional net working capital Net Investment ₱ ₱ ₱ ₱ 180,000 20,000 40,000 240,000 ₱ ₱ ₱ 180,000 20,000 200,000 The depreciable basis of the machine is: Purchase price of new machine Installation and transportation Depreciable basis General format for computing the net investment: Purchase price of new asset Add: Installation and transportation costs Add: Additional net working capital Less: Proceeds from sale of old asset Add/Less: Tax effects on disposal of old asset And/or the purchase of new one Net Investment NET OPERATING CAS Case 2 The management of Maingat Company plans to replace a sorting machine that was acquired several years ago at a cost of P60,000. The machine has been depreciated to its residual value of P10,000. A new sorter can be purchased for P96,000. The dealer will grant a trade-in allowance of P16,000 on the old machine. If a new machine is not purchased, Maingat Company will spend P10,000 to repair the old machine. Gains and losses on trade-in transactions are not subject to income taxes. The cost to repair the old machine can be deducted in computing income taxes. Income taxes are estimated at 40% of the income subject to tax. Additional working capital required is P50,000. Required: Compute the net initial investment in this project. Solution: Purchase price of new sorter Add: Additional working capital Total Less: Trade-in allowance on old sorter Avoidable repairs cost on old sorter (net of increase in income taxes) Net Investment ₱ ₱ ₱ ₱ ₱ 96,000 50,000 146,000 6,000 ₱ ₱ 22,000 124,000 16,000 Determination of Ann The Visayan Division o considering a new prod materials costs by an e The new method is als of labor and overhead the estimated depreci over a period of ten ye of income before incom (or savings) expected f Solution: Annual savings in direc Annual savings in direc Total savings before de Less: Savings after depreciat Less: Net increase in income Add: Net cash returns (savin NET OPERATING CASH FLOWS OR RETURNS Determination of Annual Cash Savings The Visayan Division of Marlow Supply Company has been considering a new production method that can reduce materials costs by an estimated amount of P52,000 a year. The new method is also expected to result in an annual savings of labor and overhead method amounting to P64,000 and the estimated depreciation at P60,000 a year over a period of ten years. Income taxes are estimated at 30% of income before income taxes. What are the annual net returns (or savings) expected from the new production method? Solution: Annual savings in direct materials costs Annual savings in direct labor and overhead costs Total savings before depreciation Depreciation Savings after depreciation Incremental income taxes (30%) Net increase in income Depreciation Net cash returns (savings) ₱ ₱ ₱ ₱ ₱ ₱ ₱ ₱ ₱ 52,000 64,000 116,000 60,000 56,000 16,800 39,200 60,000 99,200 CONCEPT OF NET INVESTMENT COSTS CAPITAL BUDGETING INVESTMENT PROPO THOSE THAT DO NOT A company is considering to replace Machine A with Machine B. Machine B will cost P150,000 and will result in annual savings of P40,000 before tax because of expected increase in operating efficiency. Machine B has an estimated useful life of 10 years and salvage value of P10,000. Machine A has a book value of P16,000 and a disposal value of P20,000 now. Straight line depreciation is used and the company has an average income tax rate of 35%. Required: Determine the Net Investment Solution: Net Investment: Cost of Machine B Adjustment: Proceeds from disposal of Machine A Tax on gain Net investment cost ₱ ₱ ₱ ₱ Assume that Great Com which will be depreciate The machine will gener Great will not incur add tax rate is 35%. Required: 1 2 3 4 5 150,000 Solution: 1 (20,000) 1,400 131,400 2 𝐴𝑐𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 Rate 𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡) if the problem is silent: 3 4 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜�= 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥) 5 CAPITAL BUDGETING TECHNIQUES IN EVALUATING CAPITAL INVESTMENT PROPOSALS THOSE THAT DO NOT CONSIDER TIME VALUE OF MONEY Assume that Great Company is planning to spend P60,000 for a machine which will be depreciated on a straightline basis over a ten-year period. The machine will generate additional cash revenues of P12,000 a year. Great will not incur additional costs except for depreciation. The income tax rate is 35%. Required: Determine the net income after tax Determine the accounting rate of return (ARR) Determine the after tax annual cash flow Determine the payback period and the payback reciprocal Determine the payback bailout period. Solution: Incremental Cash revenues per year Less: Annual depreciation Taxable Income Income tax Net Income after tax ₱ ₱ ₱ ₱ ₱ 12,000 6,000 6,000 2,100 3,900 𝐴𝑐𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 Rate of Return=(𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥)/(𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡) Accounting Rate of Return 6.50% 𝐴𝑐𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 Rate of Return=(𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥)/(𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡) Accounting Rate of Return Incremental Cash Revenues per year Income tax Annual Cash Flow after tax 13% ₱ ₱ ₱ 12,000 2,100 9,900 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜�=(𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡)/(𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥) Payback Period 6.06 years 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑅𝑒𝑐𝑖𝑝𝑟𝑜𝑐𝑎𝑙=(𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥)/(𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡) 4.1 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑅𝑒𝑐𝑖𝑝𝑟𝑜𝑐𝑎𝑙=(𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥)/(𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡) Payback Reciprocal 16.5% 16.5% 5.1 In some cases cash inflows are not equal throughout the life of investments. In such cases the computation of payback period will be different from what has been presented. Assume the following cash inflow patterns: Initial investment Cash flows: Year 1 Year 2 Year 3 Year 4 ₱ 60,000 ₱ ₱ ₱ ₱ 20,000 40,000 20,000 10,000 Payback could be computed as follows: Year 0 1 2 3 4 Net cash inflows Initial Each year Cumulative Investment Unrecovered cost ₱ (60,000) 0 ₱ (60,000) ₱ 20,000 ₱ (40,000) ₱ 40,000 ₱ ₱ 20,000 ₱ 20,000 ₱ 10,000 ₱ 30,000 The payback period is exactly two years. But in some cases, the payback period may not happen at an exact number of years. Assume that instead of having an investment of P60,000 but P62,000, payback will be presented as follows: Year 0 1 2 3 4 Net cash inflows Initial Each year Cumulative Investment Unrecovered cost ₱ (62,000) 0 ₱ (62,000) ₱ 20,000 ₱ (42,000) ₱ 40,000 ₱ (2,000) ₱ 20,000 ₱ 18,000 ₱ 10,000 ₱ 28,000 Notice that on the second year, the initial investment was almost recovered and only a small portion of the next year's cash inflow is needed to fully recover the initial investment. Thus, the exact payback can be computed using the following formula: 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜�=2 𝑦𝑒𝑎𝑟𝑠+ 2,000/20,000 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜�=2 𝑦𝑒𝑎𝑟𝑠+ 2,000/20,000 Payback Period Payback Reciprocal 2.10 years 36.29% Average CF Divided by Net Investment cost Payback Reciprocal ₱ ₱ 22,500 62,000 36.29% 6 Payback bailout period: End of year 1 2 3 4 5 6 7 8 9 10 Scrap values ₱ 40,000 ₱ 35,000 ₱ 30,000 ₱ 25,000 ₱ 20,000 ₱ 15,000 ₱ 10,000 ₱ 5,000 ₱ 2,000 ₱ - The completed table would show the following: Year Net Annual Cumulative Scrap Value Total value cash flow net cash inflow recovered 0 1 ₱ 9,900 ₱ 9,900 ₱ 40,000 ₱ 49,900 2 ₱ 9,900 ₱ 19,800 ₱ 35,000 ₱ 54,800 3 ₱ 9,900 ₱ 29,700 ₱ 30,000 ₱ 59,700 4 ₱ 9,900 ₱ 39,600 ₱ 25,000 ₱ 64,600 5 ₱ 9,900 ₱ 49,500 ₱ 20,000 ₱ 69,500 6 ₱ 9,900 ₱ 59,400 ₱ 15,000 ₱ 74,400 7 ₱ 9,900 ₱ 69,300 ₱ 10,000 ₱ 79,300 8 ₱ 9,900 ₱ 79,200 ₱ 5,000 ₱ 84,200 9 ₱ 9,900 ₱ 89,100 ₱ 2,000 ₱ 91,100 10 ₱ 9,900 ₱ 99,000 ₱ ₱ 99,000 Note that at year 3, initial investment is almost recovered. However, an exact Payback bail-out could be computed similar to uneven returns as follows: Payback Bail-out Period 3.47 years 3.47 years 3.74 years No. of years prior to recovery Add divided by Total amount recoverable ₱ (62,000) ₱ (12,100) ₱ (7,200) ₱ (2,300) ₱ 2,600 ₱ 7,500 ₱ 12,400 ₱ 17,300 ₱ 22,200 ₱ 29,100 ₱ 37,000 an exact Payback bail-out . of years prior to recovery Unrecovered cost at the beg. Of the period (Total value recovered on the year of recovery - Total value recovered prior to recovery) THOSE THAT DO CONSIDER TIME VALUE OF MONEY DISCOUNTED PAYBACK PERIOD Assume the following proposals were available to Company A: PROJECT 1 PROJECT 2 Cost of Capital 10% 10% Amount of invesment ₱ 1,000 ₱ 1,000 Yearly Net Cash Inflows Year 1 ₱ 500 ₱ 100 Year 2 ₱ 400 ₱ 300 Year 3 ₱ 300 ₱ 400 Year 4 ₱ 100 ₱ 600 ₱ 1,300 ₱ 1,400 𝐷𝐶�=𝐶�∗ 〖 (1+𝑖) 〗 ^(−𝑡) Year Annual PV of 1 factor Discounted cash flows cash flows PROJECT 1 0 1 2 3 4 ₱ ₱ ₱ ₱ ₱ Discounted Payback Period PROJECT 2 Discounted Payback Period 500 400 300 100 1,300 1.00 0.91 0.83 0.75 0.68 ₱ 454.55 ₱ 330.58 ₱ 225.39 ₱ 68.30 ₱ 1,078.82 2.95 years 0 1 2 3 4 ₱ ₱ ₱ ₱ ₱ 100 300 400 600 1,400 3.88 years 1.00 0.91 0.83 0.75 0.68 ₱ 90.91 ₱ 247.93 ₱ 300.53 ₱ 409.81 ₱ 1,049.18 DISCOUNTED CASH FLOW METHODS NET PRESENT VALUE Assume that a certain project will cost P6,075 and will earn cash inflows, after tax, of P2,000 for four years with a minimum desired rate of return of 10% Determine whether the project is acceptable or not by using the net present valu (NPV) method. PV of cash inflows PV of cash outflows Net Present Value Cumulative Unrecovered cost ₱ ₱ ₱ ₱ ₱ (1,000) (545.45) (214.88) 10.52 78.82 ₱ ₱ ₱ ₱ ₱ (1,000) (909.09) (661.16) (360.63) 49.18 Year 1 to 4 0 0 1 2 3 4 Cash Flow PV factor ₱ 2,000 3.1698654463 ₱ (6,075) 1 ₱ ₱ ₱ ₱ ₱ (6,075) 2,000 2,000 2,000 2,000 ₱ ₱ ₱ ₱ ₱ (6,075) 1,800 1,800 1,800 1,800 INTERNAL RATE OF RETURN OR TIME ADJUSTED RATE OF RETURN ll earn cash inflows, sired rate of return of 10% y using the net present value Present Value ₱ 6,339.73 ₱ (6,075.00) ₱ 264.73 Using the same example, the PV factor is determined as follows: P6,075 = P2,000 x PV Factor PV Factor IRR 3.0375 12% Suppose the expected cash flow is P1,800 instead of P2,000. Exact Rate 7% 8% PV Factor 3.375 3.3872112565 3.31212684 IRR 7.16% Looking in the PV factor table for the period Year 4, 3.375 is closest to 7% which is 3.3872 and 8% which is 3.3121. The two interest rates where the factor is between will be used as the guide in determining the IRR. So we could say that the IRR is between 7% and 8%. However, to get an exact rate, an interpolation of the two rates could be done as follows: At 7% PV factor At 8% Difference Exact rate Present Value Factors 3.3872 3.3872 3.375 3.3121 0.0751 0.0122 7.16% These computations become more complex if annnual cash inflows and outflows w not uniform. Assume the following: Initial investment Cash inflows from operations for Year 1 Year 2 Year 3 Year 1 ₱ 90,000 ₱ ₱ ₱ 20,000 40,000 60,000 At trial of 12% Cash Present Value Total Present Inflows Factor Values ₱ 20,000 0.8928571429 ₱ 17,857.14 2 3 ₱ ₱ 40,000 0.7971938776 ₱ 31,887.76 60,000 0.7117802478 ₱ 42,706.81 ₱ 92,451.71 To interpolate: Total Present Values At 12% ₱ 92,451.71 ₱ 92,451.71 At true rate ₱ 90,000 At 14% ₱ 88,820.85 Difference ₱ 3,630.86 ₱ 2,451.71 Exact rate 13.35% 13.34% USTED RATE OF RETURN mined as follows: Cost of Capital Yearly Net Cash Inflows Year 0 Year 1 Year 2 Year 3 Year 4 ad of P2,000. IRR r 4, 3.375 is closest to 7% wo interest rates where the termining the IRR. So we However, to get an exact rate, Table 1 Year 1 2 3 4 Table 2 nnnual cash inflows and outflows were ₱ ₱ ₱ ₱ (90,000) 20,000 40,000 60,000 At trial of 14% Present Value Total Present Factor Values 0.8771929825 ₱ 17,543.86 Year 1 2 3 4 Table 3 Year 1 2 3 4 PROJECT 1 10% ₱ ₱ ₱ ₱ ₱ ₱ (1,000) 500 400 300 100 1,300 14.49% If the cost of capital is equal to IRR Loan Balance ₱ ₱ ₱ ₱ 1,000 644.89 338.33 87.34 Cash flows ₱ 500 ₱ 400 ₱ 300 ₱ 100 ₱ 1,300 If the cost of capital is less than the IRR Loan Balance ₱ ₱ ₱ ₱ 1,000 630.00 311.90 52.45 Cash flows ₱ 500 ₱ 400 ₱ 300 ₱ 100 ₱ 1,300 If the cost of capital is greater than the IRR Loan Balance ₱ ₱ ₱ ₱ 1,000 660.00 365.60 124.10 Cash flows ₱ 500 ₱ 400 ₱ 300 ₱ 100 ₱ 1,300 0.7694675285 ₱ 0.6749715162 ₱ ₱ 30,778.70 40,498.29 88,820.85 PROJECT 2 10% ₱ ₱ ₱ ₱ ₱ ₱ (1,000) 100 300 400 600 1,400 11.79% Rate 14.49% 14.49% 14.49% 14.49% Payment applied to Interest Principal ₱ 144.89 ₱ 355.11 ₱ 93.44 ₱ 306.56 ₱ 49.02 ₱ 250.98 ₱ 12.66 ₱ 87.34 Loan Balance ₱ 644.89 ₱ 338.33 ₱ 87.34 ₱ (0.00) Rate 13.00% 13.00% 13.00% 13.00% Payment applied to Interest Principal ₱ 130.00 ₱ 370.00 ₱ 81.90 ₱ 318.10 ₱ 40.55 ₱ 259.45 ₱ 6.82 ₱ 93.18 Loan Balance ₱ 630.00 ₱ 311.90 ₱ 52.45 ₱ (40.73) Rate 16.00% 16.00% 16.00% 16.00% Payment applied to Interest Principal ₱ 160.00 ₱ 340.00 ₱ 105.60 ₱ 294.40 ₱ 58.50 ₱ 241.50 ₱ 19.86 ₱ 80.14 Loan Balance ₱ 660.00 ₱ 365.60 ₱ 124.10 ₱ 43.95 than the IRR