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Capital Budgeting & Investment Analysis Decisions on acquisition of property, plant & equipment are called capital budgeting decisions. They differ from other decisions cos –(1) they usually involve large amounts of money, –(2) once undertaken they are normally nonreversible, & –(3) they involve long-run commitments that can influence the earnings of the firm for many years. –(4) amount & timing of the costs & benefits from each differ. To ensure wise investment decisions mgers must have procedures to –(1) determine the amount of capital required for investment, –(2) develop a forecast of added earnings & benefits that will occur, –3) selecting an objective method to evaluate the alternatives.

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General Considerations or Principles for Managers 1. Future Earnings: Investments affect firm’s future profitability, thus mgers need to determine amount & timing of the actual earnings & costs. This means mgers shld analyze future earnings of all capital budgeting using cash flow analysis in which: –a. Larger benefits/earnings are preferred to smaller ones –b. Early benefits are preferred to later ones –c. Safety is preferred to risks. Evaluating Investment Alternatives without Consideration of the Time Value of Money Capital investments affect a firm's earning power, growth & survival. Mgers can rely on techniques that do not consider the time value of money to evaluate the acceptability of investment opportunities. These include:

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1. Payback method:Its used to determine number of periods required before sum of earnings from an investment equals the initial outlay. If net earnings are constant each year, then Payback period P = I (investment) E (earnings) –e.g. a $5,000 investment with yields/benefits of $1,000/yr will have a payback of 5 yrs ($5,000/$ 1,000 ) Mgers normally set MAX length for payback period & accept all investments with paybacks the MAX. –Advantages: Easy to use & quickly identifies investments with most immediate cash returns

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–Disadvantages: –1. It ignores cash flows occurring after end of the payback period. –2. It ignores timing of cash flows during the payback period. e.g. Selecting A in the table below using PB ignores the higher returns form B in yrs 5&6 as well as its greater total return. –Analysis of Investments A & B ($1000) Using Payback Method AFTER-TAX BENEFITS YEARA B 1 $500 $100 2400 200 3300a 300 4200 400a MAX payback allowed 5100 500 6- 600 Total benefits $1,500 $2,100 Payback in years2.3 4.0 –3. The PB method does not measure profitability but is more a measure of how quickly the investment will contribute to the liquidity of the business. For these reasons PBP can easily lead to poor investment decisions & is not the best method of investment analysis.

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2a. Simple Rate of Return:It expresses ave. annual net revenue as a %age of the investment. –Rate of return = average annual net revenue x 100 cost of the investment –Net Cash Revenue For 2 $10,000 Investments (No terminal value) Net cash revenues $ Year Returns A Investment AReturns B Investment B 1 3,000 8,000 1,000 $10,000 2 3,000 6,000 2,000 8,000 3 3,000 4,000 3,000 6,000 4 3,000 2,000 4,000 4,000 5 3,0000___ 6,000 0___ Total 15,000 20,000 16,000 20,000 Av after tax return/invest 3,000 4,000 3,200 4,000 Less annual depreciation 2,000 2,000 Ave. Annual Net revenue 1,000 1,200 Simple Rate of Return A = $1000/$10,000 x 100 =10% B = $1200/$10,000 x 100 =12% 2b The Average or Accounting Rate of Return: Its same as the simple rate of return but its calculated by dividing the ave. after tax yearly benefit by ave. investment. –Ave. Rate of Return = ave. annual after tax revenue x 100 ave. cost of the investment Ave. Rate of Return A = $3,000/$4,000 x 100 =75% B = $3,200/$4,000 x 100 =80%

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Advantages: Better than the payback cos it considers an investment's earnings over its entire life. Disadvantages: 1. It uses ave annual earnings, which fails to consider the size & timing of annual earnings & can thus cause errors in selecting investments, especially when there are increasing or decreasing net revenues –e.g. A wld have the same 10% rate of return with $0 cash revenue in the 1 st 4 yrs & $15,000 in 5 th yr, as ave. return is still $3,000/yr. 2. Benefits received in first years are given same weight as one received in the last years. 3. The method cannot tell which project is most profitable as it cannot differentiate btwn returns on investment in terms of $s.

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Evaluating Investments Using Time Value of Money A $ today is worth more than a $ at some future date. Why? –1 st Interest Earnings: A $ received today can be invested to earn interest & thus increase to a dollar + future interest i.e. its opportunity cost of receiving $ in future rather than now. –2 nd Consumption: If the $ was be spent on goods like TV, car etc we wld prefer to have it now in order to enjoy the items now rather later. –3 rd Risks: The risk that unforeseen circumstances will prevent us from collecting the $ in the future. Terms, Definitions, and Abbreviations –Present Value (PV): Value of $ available now or the current value of some amount(s) to be received at some future time. –Future Value (FV):$value to be received at future time or the amount a present value will become at future date when invested at a given interest rate. –Payment (PMT):$ value to be paid/ received at end of time periods. –Interest Rate (i): or discount rate is used to find present & future values. Its also the opportunity cost of capital.

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–Time Periods (n): The number of time periods to be used for computing present & future values. –Annuity: A term used to describe series of equal periodic payments (PMT). The payments may be either receipts or expenditures. 1. Finding Future Values FV (Compounding) FV of money is value of investment at a specific future date – i.e. interest earned during each time period is reinvested at end of each period so it will also earn interest in the future. –Thus, FV = original investment + interest earned + interest on the accumulated interest. –Its used for a one-time lump sum investment (a PV) or for investment requiring a series of payments (PMT) over time. PV FV PMT PMT PMT FV Timetime $ ? ?

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FV of PV or Compounding:A procedure for finding FV when accumulated interest also earns interest –The FV of a PV money depends on three things the: 1. PV, 2. interest rate it will earn, 3. length of time it will be invested. If $ 100 is invested in savings account earning 12% interest compounded annually, FV of the $100 after 2 yrs will be: Value atInterest Interest Value at yr Year start of yrrate % earned ($)end 1100.0012 12.00112.00 2112.0012 13.00125.00 Thus a PV of $100 has a FV of $125 if invested at 12% interest for 2 years. This is expressed mathematically as: FV = PV(1 + i) N where i = interest rate per period N = number of times interest is paid FV & PV = future & present values FV = $100(l + 0.12) 2 = $100(l.25) = $125.00

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How often interest is paid affects FV of investment. If interest is paid twice a year for 2 yrs in our example then N=2 x2 =4 FV = PV(1 + i/2) Nx2 FV = $100(l + 0.12/2) 4 = $100(l.26) = $126 compared to $125 previously Thus the more frequent the payment of interest the higher the FV.

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2. PV of FV or Discounting. FV is discounted back to the PV. Its reverse of compounding -i.e. the current value of a sum of money to be received or paid in the future. The interest rated used is called discounted rate. The PV shld be less (discounted) than FV due to interest payments. PV can be solved from the FV compounding equation: FV =PV (I + i) N FV = PVor PV = FV (I + i) N (1 + i) N What is PV of $1.25 received in 2 yrs if you can earn 12% PV = $1.25 = 1.25 = $1.00 (1 + 0.12) 2 1.25 i.e. PV of $1.25 to be received in 2 yrs = $1.00 today if the opportunity cost is 12%, or receiving $1.25 in 2 yrs is same as having $1.00 today if discount rate (opportunity cost of money) is 12% per yr.

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2b. Net Present Value The NPV or discounted cash flow method is a preferred method cos it considers the time value of money as well as the stream of cash flows over entire life of an investment. NPV of an investment is sum of PVs for each year's net cash flow (or net cash revenue) less initial investment cost. The equation for finding NPV of an investment is: NPV =P 1 + P 2 + P n - C (1 + i) l (1 + i) 2 (1 + i) n where Pn is the net cash flow in year n, i is discount rate, & C is initial cost of investment.

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Net Present Value Calculations for 2 Investments of $10,000 (8% Discount Rate and No Terminal Values) Investment AInvestment B Net Present Present Net Present Present Year cash flow x value factor = value cash flow value factor value 1 3,000 0.926 2,7781,000 0.926 926 2 3,000 0.857 2,5712,000 0.8571,714 3 3,000 0.794 2,382 3,000 0.7942,382 4 3,000 0.735 2,2054,000 0.7352,940 5 3,000 0.681 2,0436,000 0.6814,086 Total 11,979 Total 12,048 Less cost 10,000 Less cost 10,000 Net present value 1,979Net present value2,048 Investment with +ve NPV is accepted & those with -ve NPV rejected. Investments with +ve NPV are accepted cos: –1 st, rate of return on investment > discount rate used or return > opportunity cost of capital used as discount rate. –2 nd investor can pay more for the investment & still achieve a rate of return equal to discount rate used for the NPV

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2c. Internal Rate of Return:The IRR provides some info not available directly from the NPV method. Both investments A & B have +ve NPV using the 8% discount rate. But what is the actual rate of return on these investments? Its the discount rate that makes the NPV = 0. IRR is also called the marginal efficiency of capital or yield on the investment. IRR is found from NPV 0 =P 1 + P 2 + P n - C (1 + i) l (1 + i) 2 (1 + i) n where 0 = NPV & equation is solved for i. But this is very difficult & the IRR is therefore found by trial & error. The IRR computation from investments A & B requires finding a discount rate that can discount the future cash flows until they equal $10,000.

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3. Future Value of an Annuity –What’s FV of a number of (PMT) made at end of each yr for a given number of ys? Each pymyt will earn interest from the time it is invested until the last pymt. –e.g. What is the FV of $100 if deposited at end of each yr earning 12% interest for 3 yrs. It is calculated in the ff manner: –1st$ 1,00 = 1,00(l + 0.12) 2 = 125 –2nd$ 1,00 = 1,00(l + 0.12) 1 = 112 –3rd$1,00 = 1,00(l + 0.12) 0 = 100 –Future value $337 –1 st $100 earns interest for only 2 yrs, the 2 nd $100 earns interest for 1yr, & 3 rd $100 earns no interest as is deposited at end of 3 rd yr. A total of $300.00 is invested & a total of $37 of interest is earned. PMT PMT PMT FV time ? ?

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The FV of an annuity can be found using the equation: FV of Annuities = PMT x (1 + i) n – 1 i 4. Present Value (PV) of an Annuity Determines the PV of an annuity or number of pymts to be received over time. –e.g. What is the PV of $1,000 if its received at end of each yr earning 12% interest for 3 yrs. It is calculated in the ff manner: –1st$ 100 = 1,00x(1/0.12) 1 = 100 x 89 = 89 PV=FV/(1+i) 1 –2nd$ 100 = 1,00x(l/0.12) 2 = 100 x 80 = 80 PV=FV/(1+i) 2 –3rd$100 = 1,00x(l/0.12) 3 = 100 x 71 = 71 PV=FV/(1+i) 3 –Present value $240 PMT PMT PMT PV time ? ?

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–1 st $100 is discounted for 3 yrs, the 1 st $100 is discounted by $11, the 2 nd $100 is discounted by $20 and the 3 rd $100 is discounted by $29. A total of $240 is received & a total of $60 is discounted. PV of an annuity can be found using the equation: PV of Annuities = PMT x 1 - (1 + i) -n i

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