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<br />The capital costs, however, are initial costs that must be amoritized <br />over the service life of the structure. The annual amoritization series <br />is determined by multiplying the capital costs by the capital recovery <br />factor, CRF. The CRF is defined as "an annuity whose present value is <br />one;" it can be computed from <br /> <br />CRF <br /> <br />i(1 ... i)n <br />= <br />(1 + i) n - 1 <br /> <br />(1) <br /> <br />where <br />i = interest rate <br />n = service life of the structure <br /> <br />The capital recovery factor is tabulated in most interest tables. <br />(See, for example, C. D. Hodgman, 1957, pp. 427-434.) <br /> <br />Backwater Damage.--Backwater is the increase in upstream water- <br />surface elevations required to force the discharge through the bridge <br />and, at times, over the embankment. <br /> <br />Backwater usually causes more land to flood compared to the natural <br />condition. On land flooded naturally, backwater causes flooding to be <br />deeper. The damages associated with increased flooding may be computed <br />from data obtained during a land use survey and from stage damage <br />relations. The upstream valley which may be affected by backwater <br />should be surveyed to determine the land use. At many sites, there are <br />a limited number of land uses that must be identified. The Corps of <br />Engineers (1977), Sumrall (1970, 1972), G. T. McDonald (1977, written <br />commun.), F. V. Reilly (1978, written commun.), and others have procedures <br />to develop stage damage relations for various land uses. <br /> <br />A survey adequate to satisfy the requirements of a risk analysis is <br />as follows: <br /> <br />1. Estimate the reach that would be affected by backwater. <br /> <br />2. Identify features, such as residences, schools, warehouses, <br />fields, and woods that can be assigned a value as a unit. <br /> <br />3. Determine the elevation at which damage from flooding first <br />occurs such as the floor elevation of a house or the typical <br />elevation of a field. larger fields may have to be split <br />into several subareas when the elevation changes significantly. <br /> <br />. <br /> <br />Table 3 could be a useful guide in tabulating the data. The data <br />can be either used for hand computation or by computer. <br /> <br />18 <br />