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Methods of Evaluating Capital Investment Proposals Methods that do not consider the time value of money Methods that consider the time value of money
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Methods that do not consider the time value of money1. Payback Period This refers to the length of period or number of years it would take to recover an investment.Formula: Investment Annual Cash Returns
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2. Payback Reciprocal This indicates the percentage of investment that is expected to be recovered in one year.Formula: Annual Cash Returns Investment or: 1 Payback Period This ratio indicates the rate of return on a venture or project when the economic life of the investment is more than double the payback period. It has the same advantages and disadvantages as the payback period.
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3. Accounting Rate of Return It indicates the amount of net income realized per peso of investment.Formula: Net Income Investment This method does not take into consideration cash inflows and time value of money and may result in erroneous decisions specially in cases where depreciation charges materially vary among the different alternatives.
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4. Average Rate of Return It indicates the amount of net income per peso of average investment. It is double the accounting rate of return.Formula: Net Income or: Investment Average Investment 2 This method has the same disadvantages as the accounting rate of return.
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5. Payback Bailout Period This refers to the length of period or number of years it would take to recover an investment considering accumulated cash returns and terminal values. Procedure: Accumulate cash returns and add terminal cash flows at the end of each year. When the total is equal to investment, the payback bailout period has been arrived at. This method disregards the time value of money and additional future cash flows. It implies that the proposed venture or project will be terminated at the end of the payback bailout period.
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Standards in Evaluation of ProjectProposals Illustrative Problem An investment of Php 100,000( including depreciable assets of Php 80,000 ) is expected to enable ABC Corp. to realize an annual net income of Php 12,000 for 10 years. Cost of capital is 12%.
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The computation are as follows:Annual cash returns: Net income Php 12,000 Add back depreciation (80,000/10 yrs.) 8,000 Php 20,000Payback period = Investment of Php 100,000 = 5 years Annual cash returns of Php 20,000
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Payback Reciprocal = Php 20,000 = 20% Php 100,000Or: 1 Payback period of 5 years = 20%
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Payback Bailout Period As stated earlier, the payback bailout period is equal to the length of period it takes the accumulated cash returns plus salvage value at the end of the particular period to equal the investment on a project.
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Example: A project requires investment of Php 25,000. Cash returns and salvage value at the end of each year are as follows: Cash Returns Salvage Value Year 1 Php 8,000 Php 12,000 Year 2 Php 6,000 Php 10,000 Year 3 Php 5,000 Php 6,000 Year 5 Php 8,000 Php 2,000
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The Payback bailout period is computed as follows: Accumulated Salvage Value Total Cash ReturnsYear 1 Php 8,000 Php 12,000 Php 20,000Year 2 Php 14,000 Php 10,000 Php 24,000Year 3 Php 19,000 Php 6,000 Php 25,000
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The payback bailout period is threeyears because as of the end of the third year,the total of accumulated cash returns andsalvage value at the end of 3-year period isexpected to be equal to the investment forthe particular project.
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Methods that consider the timevalue of money1. Internal Rate of Return (IRR). This refers to the rate of return that a long term investment earns. It is also called the discounted or time adjusted rate of return.Procedure:Compute for payback periodWith the payback period as the present value factor, locate it on an annuity table considering the economic life of the investment. The corresponding interest rate for the column in which it can be found is the IRR.
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2. Net Present Value (NPV). This refers to the excess of the present value of cash returns discounted at a chosen cut-off rate over the amount of investment. Formula: Present value of annual cash returns discounted at the cut-off rate less – investment When net present value is positive, it implies that the rate of return on the proposed investment is higher than the cut-off rate and vice-versa. A zero difference indicates that the rate of return on the investment shall be equal to the cut-off rate used.
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3. Profitability index (benefit/cost ratio or present value index). This refers to the ratio of the present value of cash returns discounted at a chosen cut- off rate to the investment requirement. Formula: Present value of annual cash returns discounted at the cut-off rate Investment A ratio higher than 100% indicates that the proposed investment will be earning at a rate higher than the cut-off rate and vice-versa. A 100% ratio implies that the rate of return on the investment shall be equal to the cut-off rate used.
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4. Discounted payback period. This refers to the number of years it would take the present value of cash returns to equal the investment. Procedure: Discount the cash returns at the chosen cut-off rate and accumulate them. The length of period or number of years it would require to make the accumulated figure equal to investment is the discounted payback period.
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Standards in Evaluation of ProjectProposalsIllustrative Problem An investment of Php 100,000 ( including depreciable assets of Php 80,000) is expected to enable ABC Corp. to realize an annual net income of Php 12,000 for 10 years. Cost of capital is 12%
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Internal rate of return (IRR) Investment ofPayback period = Php 100,000 = 5 years Annual cash returns of Php 20,000 Locate the payback period of 5 periods in the PV of an annuity table on line 10 periods (economic life) and it can be found between 15% (5.019) And 16% (4.833). The (discounted or internal) rate of return is therefore higher than 15% and lower than 16%.
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Net present value: Present value of annual cash returns discounted at 12% ( Php 20,000 x 5.650) Php 113,000 Less – Investment 100,000 Php 13,000Profitability (present value) index or benefit/cost ratio: Present value of annual cash returns discounted at 12%(Php 20,000 x 5.650) Php 113,000 Divide by – investment 100,000 113%
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Discounted payback period:Year PV of CR Accumulated No. of Years PV of CR 1 Php 20,000 x 0.893 = Php 17, 860.00 Php 17,860.00 1.00 2 Php 20,000 x 0.797 = Php 15, 940.00 Php 33,800.00 1.00 3 Php 20,000 x 0.712 = Php 14, 240.00 Php 48,040.00 1.00 4 Php 20,000 x 0.635 = Php 12, 700.00 60,740.00 1.00 5 Php 20,000 x 0.567 = Php 11, 340.00 72,080.00 1.00 6 Php 20,000 x 0.507 = Php 10, 140.00 82,220.00 1.00 7 Php 20,000 x 0.452 = Php 9,040.00 91,260.00 1.00 8 Php 20,000 x 0.404 = Php 8,080.00 99,340.00 1.00 Fraction of the 9th year: 9 Php 20,000 x 0.361 = Php 7,220.00 660.00 0.09 Investment Php 100,000.00 8.09
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Payback Period – Uneven Cash Returns When cash returns are uneven, the payback period is computed by accumulating the cash returns until the total is equal to investment.Example: On investment of Php 50,000, cash returns are as follows:Year 1 17,000 Year 4 18,000.00Year 2 22,000 Year 5 25,000.00Year 3 11,000 Year 6 10,000.00Payback period is (3) years arrived at as follows: Php 17,000 + 22,000 + 11,000 = Php 50,000
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Internal Rate of Return (IRR) – Uneven Cash Returns When cash returns are uneven, the discounted or internal rate of return is computed by using average annual cash returns in estimating the tentative payback period. The tentative payback period is subsequently located in the present value of an annuity table. The rate of return is arrived at when at that rate, the present value of cash returns is equal to investment. When the present value of cash returns arrived at is smaller than investment, it means that the rate of return is lower than the rate used in discounting the cash returns so that the analyst should try the next lower rate and vice-versa. When cash inflows are bigger in earlier years, the rate of return must be higher than what it seems and vice-versa.
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Example: On an investment of Php 7,047, cash returns have been estimated as follows: Year 1 3,000.00 Year 2 2,000.00 Year 3 5,000.00The discounted rate of return is computed as follows: Investment of Php 7,407Tentative payback = = 2.222 years period Average cash returns per year ( 3,000+ 2,000 + 5,000)/3
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Locating 2.222 in the present value of anannuity table, it is between 16% and 18%.However, in as much as cash returns in the thirdyear is much bigger than that in the first andsecond years, it is advisable to start with the lowerrate, 16%. At 16% Year 1 Php 3,000 x .862 = Php 2,586 Year 2 2,000 x .743 = 1,486 Year 3 5,000 x .641 = 3,205 Php 7,277
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The present value of cash returns exceedsinvestment, so try the next lower rate, 15%. At 15% Year 1: Php 3,000 x .870 = Php 2,610 Year 2: 2,000 x .756 = 1,512 Year 3: 5,000 x .657 = 3,285 Php 7,407 In as the present value of cash returns is equalto investment of Php 7,407, the rate of return mustbe 16%.
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Net Present Value – Uneven Cash Returns Even if the cash returns are uneven, the procedure in determining the net present value remains the same. The different cash returns are discounted using the cut-off rate and the total of the present values is compared with the amount of investment. Using the figures in the preceding example and assuming that cost of capital is 12%, the net present value is computed as follows:
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Net present value: Present value of cash returns discounted at 12% Year 1: Php 3,000 x .893 = Php 2,679 Year 2: 2,000 x .797 = 1594 Year 3: 5,000 x .712 = 3560 Php 7833 Less Investment 7,407 Net present value Php 426
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Exact Internal Rate of Return When the payback period does not exactly fall in one column in the present value of an annuity table, interpolation is applied to arrive at the exact discounted rate of return. Example: Annual cash returns amount to Php 20,000 on an investment of Php 80,000 having economic life of 10 years. With payback period of 4 years (that is, Php 80,000/ 20,000), the rate of return must be between 20% and 22%. The exact discounted rate of return is computed as follows:
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At 20% 4.192 4.0 At 22% 3.923 2% .269Exact discounted .192 rate of return = 20% + ( .269 x 2%) = 21.4% or: .077 22% - ( .269 x 2%) = 21.4%
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