Cash flows discounting

Internal return rate. The internal return rate (IRR), also known as the discounted cash flow return rate, is the iteratively calculated discounting rate that would make the sum of the annual cash flows, discounted to the present, equal to zero. As shown in Figure 2, the IRR for Project Chem-A is 38.3%/yr. 

The fundamental value of a company, on the other hand, is the net present value of the expected future cash flows, discounted by the cost of capital (DCF). This only alters for the better or the worse if fundamental changes occur, for example if prices change, new technologies are introduced or the company achieves a breakthrough into new markets. 

YEAR CASH FLOWS ( ) CUMULATIVE CASH FLOWS ( ) DISCOUNT FACTOR PRESENT VALUE ( )... 

PRINT THE VALUES OF THE YEARLY CASH FLOWS, CUMULATIVE CASH FLOWS DISCOUNT FACTORS AND THE PRESENT VALUES... 

The sales budget, to be of value to the organization as a whole, must be related to future profits or rather to anticipated cash flow discounted to the present. The concept of cash flow can be described briefly as the difference between revenues and direct costs, not to include depreciation. It represents the amount of cash thrown off from the sales and production of a product regardless of the investment. Consequently, for each product in the sales budget, the anticipated cash flow for the coming year can be determined. 

Combining Independent and Perfectly Correlated Cash Flows Suppose that it is feasible, in a given problem situation, to identify two types of cash flows those that are statistically independent and those that are perfectly correlated. In this case the variance of the PW distribution is the sum of (a) the sum of the variances of the independent cash flows, discounted, and (b) the sum of the variances of each of the subsets of perfectly correlated cash flows, where the variance of each subset is the square of the sum of the standard deviations of the cash flows in that subset. That is. 

In the traditional approach the duration value is calculated using nominal cash flows, discounted at the nominal yield. A more common approach is to assume a constant average rate of inflation, and adjust cash flows using this inflation rate. The real yield is then used to discount the assumed future cash... 

The approaches to shareholder value include all aspects of corporate governance that aim at the shareholder s property. The value of the corporation can be computed as its expected cash flows discounted with its... 

For example, consider a 10-year government bond denominated in euros with an 8% coupon rate. Suppose that coupon payments are delivered semiannually and the annual spot rates are shown in the fourth column of Exhibit 3.4. The third column of the exhibit shows the cash flow every six months. The last column shows the present value of each cash flow discounted at the corresponding spot rate. The total in the last column is the arbitrage-free value of the bond, 115.2619. 

Coupon Period Day Count Forward Quoted Required Rate Margin Margin (%) (%) (%) Cash Flow ( ) Discount Factor PVof Cash Flow ( )... 

The OAS-derived yield spread is based on the present values of expected cash flows discounted using government bond—derived forward rates. The spread berween the cash flow yield and the government bond yield is based on yields to maturity. The OAS spread is added to the entire yield curve, whereas a yield spread is over a single point on the government bond yield curve. For these reasons, the two spreads are not strictly comparable. 

Liquidity diflferences often produce yield differences among bonds with similar durations. Institutional investors prefer to hold the benchmark bond—the current 2-, 5-, 10-, or 30-year issue— which both increases its liquidity and depresses its yield. The converse is also true because more-liquid bonds are easier to convert into cash if necessary, demand is higher for them, and their yields are thus lower. The effect of liquidity on yield can be observed by comparing the market price of a six-month bond with its theoretical value, derived by discounting its cash flow at the current 6-month T-bill rate. The market price— which is equal to the present value of its cash flow discounted at its yield— is lower than the theoretical value, reflecting the fact that the T-bill yield is lower than the bond yield, even though the two securities cash flows fall on the same day. The reason is liquidity the T-bill is more readily realizable into cash at any time. 

Decommissioning costs may also be a factor to be considered in economic evaluation, but deferred cash flow discounting usually greatly reduces the significance. An exception may be plants which create lasting pollution, but such plants are increasingly unlikely to be licensed for operation in the first place. 

DPBP - required, after start-up, to recover the fixed capital investment, FCIi, required for the project, with all cash flows discounted back to time zero... 

NPV = (present value of cash flow discounted at a given i) - capital investment... 

Time is taken into account by discounting the annual cash flow Acf with the rate of interest to obtain the anitual discounted cash flow -Adcf- Thus, at the end of year 1,... 

The sum of the annual discounted cash flows over n years SAdcf is known as the net present value (NPV) of the project ... 

Discounted cash-flow rate of return. Discounted cash-flow rate of return is defined as the discount rate i which makes the NPV of a project zero (curve 3 in Fig. A.2) ... 

The value of i given by this equation is known as the discounted cash-flow rate of return (DCFRR). It may be found graphically or by trial and error. 

The project cashflow discussed so far follows a pattern typical of E P projects a number of years of expenditure (giving rise to cash deficits) at the beginning of the project, followed by a series of cash surpluses. The annual cashflows need to be evaluated to incorporate the timing of the cash flows, to account for the effect of the time value of monef. The technique which allows the values of sums of money spent at different times to be consistently compared is called discounting. 

Ref 91. Discounted cash-flow models account for use of capital, working capital, income taxes, time value of money, and operating expenses. Real after-tax return assumed to be 12.0%. Short-rotation model used for sycamore and poplar. Herbaceous model used for other species. Costs ia 1990 dollars. Dry tons. 

Fig. 2. (— —) Cumulative and (—° —) 8% discounted cash flow rate for development of a hypothetical agrochemical in constant 1994 U.S. dollars, where A represents the time the patent was first issued B, first registered use C, manufacturing plant start-up D, positive cumulative cash flow and E, patent...

DecoveTj of Capital. In Figure 1, the annual book depreciation is used to retire the fixed capital investment. Whereas this accounting model does not correspond to the typical money flow, it is one possible model for recovery of capital. This model assumes that the investment is reduced each year by the amount of the annual depreciation. Another model (22) assumes that a uniform yearly book depreciation payment is made to an interest-bear sinking fund that accumulates to the depreciable fixed capital amount at the end of the venture. Using this second model, the investment is outstanding throughout the lifetime of the project. This also does not correspond to the actual money flow in most cases. ProfitabiUty analysis utilizes a third model based on discounted cash flows. 

Discounted Ca.sh Flows. Because the flows below the cash flow box in Figure 1 tend to be arbitrary management decisions that are generally difficult to predict, the prediction of profitabiUty is based on the expected cash flows instead of earnings. As a result, some logical assumptions to account for the cost of capital and the recovery of the investment must be made. 

If money is borrowed, interest must be paid over the time period if money is loaned out, interest income is expected to accumulate. In other words, there is a time value associated with the money. Before money flows from different years can be combined, a compound interest factor must be employed to translate all of the flows to a common present time. The present is arbitrarily assumed often it is either the beginning of the venture or start of production. If future flows are translated backward toward the present, the discount factor is of the form (1 + i) , where i is the annual discount rate in decimal form (10% = 0.10) and n is the number of years involved in the translation. If past flows are translated in a forward direction, a factor of the same form is used, except that the exponent is positive. Discounting of the cash flows gives equivalent flows at a common time point and provides for the cost of capital. 

Net Present Va.Iue, Each of the net annual cash flows can be discounted to the present time using a discount factor for the number of years involved. The discounted flows are then all at the same time point and can be combined. The sum of these discounted net flows is called the net present value (NPV), a popular profit criterion. Because the discounted positive flows first offset the negative investment flows in the NPV summation, the investment capital is recovered if the NPV is greater than zero. This early recovery of the investment does not correspond to typical capital recovery patterns, but gives a conservative and systematic assumption for investment recovery. 

This gives two choices ia interpreting calculated NRR values, ie, a direct comparison of NRR values for different options or a comparison of the NRR value of each option with a previously defined NRR cutoff level for acceptabiUty. The NPV, DTC, and NRR can be iaterpreted as discounted measures of the return, iavestment, and return rate, analogous to the parameters of the earher example. These three parameters characterize a venture over its entire life. Additional parameters can be developed to characterize the cash flow pattern duting the early venture years. Eor example, the net payout time (NPT) is the number of operating years for the cumulative discounted cash flow to sum to zero. This characterizes the early cash flow pattern it can be viewed as a discounted measure of the expected operating time that the investment is at risk. 

Internal Return Rate. Another rate criterion, the internal return rate (IRR) or discounted cash flow rate of return (DCERR), is a popular ranking criterion for profitabiUty. The IRR is the annual discounting rate that makes the algebraic sum of the discounted annual cash flows equal to zero or, more simply, it is the total return rate at the poiat of vanishing profitabiUty. This is determined iteratively. 

The relationships among the various annual costs given by Eqs. (9-1) through (9-9) are illustrated diagrammaticaUy in Fig. 9-1. The top half of the diagram shows the tools of the accountant the bottom half, those of the engineer. The net annual cash flow Acp, which excludes any provision for balance-sheet depreciation Abd, is used in two of the more modern methods of profitability assessment the net-present-value (NPV) method and the discounted-cash-flow-rate-of-return (DCFRR) method. In both methods, depreciation is inherently taken care of by calculations which include capital recoveiy. 

Contribution and Breakeven Charts These can be used to give valuable preliminary information prior to the use of the more sophisticated and time-consuming methods based on discounted cash flow. If the sales price per unit of sales is Cs and the variable expense is Cy per unit of produc tion, Eq. (9-7) can be rewritten as... 

The ways of assessing profitabihty to be considered in this section are (1) discounted-cash-flow rate of return (DCFRR), (2) net present value (NPV) based on a particiilar discount rate, (3) eqmvalent maximum investment period (EMIP), (4) interest-recovery period (IRP), and (5) discounted breakeven point (DEEP). 

Discounted Cash Flow The present value P of a future sum of money F is given by... 

Time is taken into account by using the annual discounted cash flow Adcf, which is related to the annual cash flow Acf and the discount factor by... 

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