# rdlc barcode font Equation (2021) is termed the annuity compound-amount factor, and (1 the compound-amount factor in Software Encode PDF-417 2d barcode in Software Equation (2021) is termed the annuity compound-amount factor, and (1 the compound-amount factor

Equation (2021) is termed the annuity compound-amount factor, and (1 the compound-amount factor
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The reciprocal of Eq (2021) is known as the annuity sinking-fund factor and can be used to determine yearly depreciation cost It is expressed as follows: R S (1 i i)n 1 (2022)
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where i / [(1 i)n 1] is the sinking-fund factor An analysis of Eq (2022) shows that equal amounts of R, when invested at i percent interest, will accumulate to some speci ed future amount S over a period of n years In terms of depreciation expense, it shows that equal yearly depreciation costs invested at an i percent interest rate for n years will accumulate to an amount equal to the original cost of the equipment The present worth (PW) of an annuity is the principal which would have to be invested at the present time at compound interest i to yield a total amount at the end of the annuity term equal to the amount of the annuity In other words, it is the present amount (PW) that can be paid off through equal annual payments of R over n years at i percent interest Combining Eq (2024) with Eq (2021) gives PW(1 or PW R (1 i)n 1 i(1 i)n i)n S R (1 i)n i 1 (2023)
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Equation (2023) is known as the annuity present-worth factor, where [(1 i)n 1] / i(1 i)n is the present-worth factor The reciprocal of Eq (2023) is known as the annuity capital-recovery factor It is the annual payment R required to pay off some present amount PW over n years at i percent interest It can be expressed as follows: R PW i(1 i)n (1 i)n 1 (2024)
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3 Maximum Payback Time This is the maximum acceptable payback time (PTM) which is set by the rm based on minimum acceptable return on investment and on the time value of money Accordingly,
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length of useful life of the project minimum acceptable return on investment depreciation rate income tax rate (federal plus state)
4 Discounted-Cash-Flow Analysis The most popular method for evaluating investment alternatives, taking into account the time value of money, is the discounted-cash- ow (DCF) method It includes all cash ows over the entire life of
CHAPTER TWENTY
the project and adjusts them to one point xed in time, usually the time of the original investment The method requires a trial-and-error calculation to determine the compound interest rate at which the sum of all the time-adjusted cash out ows (investment) equals the sum of all the time-adjusted cash in ows (net pro t plus depreciation) The main attractiveness of this technique is that it considers both the amount and the timing of all cash in ows and out ows The discounted-cash- ow rate of return is the after-tax interest rate i at which capital could be borrowed for the investment and just break even at the end of the useful life n of the project To determine the DCF rate of return, the present worth PW of the project or net cash ow (NCF) (net pro t plus depreciation) compounded on the basis of end-of-year income is expressed as PW NCF1 1 (1 i)1 i)2 i)n i)1 NCF2 1 (1 i)2 NCFn 1 (1 i)n (2026)
where 1 / (1 1 / (1 1 / (1
present worth at the end of year 1 present worth at the end of year 2 present worth at the end of the project
Then the present worth of the xed investment I compounded at interest rate i plus working capital (Iw) is expressed as PW (I Iw)0 1 (1 i)
Iw)1
1 (1 I)
Iw)n
1 (1 i)n (2027)
where 1 / (1 i)0 is the present worth at the start of the project If only one time investment is made, at the beginning of the project, then Eq (2027) becomes PW (I Iw)0 1 (1 i)0 I 1 Iw I Iw
The present worth of the investment must be equal to the present worth of the cash ows; that is, investment (cash out ows, or O) must equal the sum of all the timeadjusted cash in ows Therefore, we set Eq (2026) equal to Eq (2027): I Iw NCF1 (1 i)1 NCF2 (1 i)2 NCFn (1 i)n (2028)
or expressed differently, O (I Iw) NCF1 (1 i)1 NCF2 (1 i)2 NCFn (1 i)n (2029)
A trial-and-error calculation is required to determine the DCF rate of return i Since the discounted-cash- ow rates of return are only approximated by the process of interpolation, a slight error is introduced To keep the error to a minimum, interpolation should only be attempted between adjacent tabled values, for example, between 10 and 11 percent Interpolation between, say, 2 and 10 percent would increase the error greatly