Annuity Method - Revision history

Ranisha at 11:31, 16 July 2014

2014-07-16T11:31:05Z

Ranisha at 11:10, 21 March 2014

2014-03-21T11:10:41Z

Fungai Cecilia Sandamu at 12:28, 19 April 2013

2013-04-19T12:28:52Z

Katharina Wiedemann at 12:27, 4 May 2012

2012-05-04T12:27:01Z

Katharina Wiedemann at 12:25, 4 May 2012

2012-05-04T12:25:47Z

Show changes

Katharina Wiedemann: moved Annuity method to Annuity Method

2012-05-04T12:17:38Z

moved Annuity method to Annuity Method

Zieglerf at 12:49, 23 June 2010

2010-06-23T12:49:22Z

JanS at 16:45, 2 August 2009

2009-08-02T16:45:18Z

JanS at 12:47, 28 April 2009

2009-04-28T12:47:10Z

JanS at 16:10, 26 April 2009

2009-04-26T16:10:58Z

@@ Line 98: / Line 98: @@
 The assumed interest rate must be determined with due regard to specific individual conditions. In this context, the assumed interest rate is defined as a real interest rate, i.e. after adjustment for inflation. In the case of cash outlay, the real interest rate would equal the rate of interest that the capital would have borne on the money market. Accordingly, the assumed interest rate is equal to the current mean debt interest rate demanded by the bank for the loan capital, when the entire project is financed with borrowed money. Moreover, money costs in the form of bank service charges, the owner's own administrative overhead, etc. must also be included. Since, however, most projects involve a certain degree of mixed financing, the assumed interest rate will take on a value located somewhere between the debt interest rate and the credit-interest rate, depending on the case situation. (Note: All rates adjusted for inflation!).
-[[Category:Financing_and_Funding]]
+<br/>
 [[Category:Impacts_Economic]]

@@ Line 30: / Line 30: @@
 ----
-==== Annual benefits (B) ====
+==== Annual Benefits (B) ====
 The '''annual benefits '''comprise the monetarily evaluable returns, savings, etc. yielded by the investment. These may derive from:
@@ Line 41: / Line 41: @@
 <br/>
-==== Annual costs (C)<br/> ====
+==== Annual Costs (C)<br/> ====
 The current annual costs are made up of the expenses incurred for:
@@ Line 61: / Line 61: @@
 <br/>
-==== Total investment volume (I0)<br/> ====
+==== Total Investment Volume (I0)<br/> ====
 The total investment volume includes the capital outlay for:
@@ Line 98: / Line 98: @@
 The assumed interest rate must be determined with due regard to specific individual conditions. In this context, the assumed interest rate is defined as a real interest rate, i.e. after adjustment for inflation. In the case of cash outlay, the real interest rate would equal the rate of interest that the capital would have borne on the money market. Accordingly, the assumed interest rate is equal to the current mean debt interest rate demanded by the bank for the loan capital, when the entire project is financed with borrowed money. Moreover, money costs in the form of bank service charges, the owner's own administrative overhead, etc. must also be included. Since, however, most projects involve a certain degree of mixed financing, the assumed interest rate will take on a value located somewhere between the debt interest rate and the credit-interest rate, depending on the case situation. (Note: All rates adjusted for inflation!).
 [[Category:Financing_and_Funding]]

@@ Line 1: / Line 1: @@
 == Introduction<br/> ==
@@ Line 5: / Line 6: @@
 According to the simplified approach presented here, however, a single cost increase factor is applied for all inputs, i.e. energy, services, spare parts, etc. As we have seen in the course of the past few years, though, the cost of energy and of wares with a close tie-in to the cost of energy (such as chemical fertilizers) has been increasing more rapidly than, say, the national wage index of most countries. Also, discrepancies can always be expected to be particularly pronounced in countries where the state intervenes in the price structure. Thus, if the economic efficiency of a particular system is to be projected with any real degree of accuracy, the price-increase rates for each individual product must be taken into account.
+<br/>
 == Calculation<br/> ==
@@ Line 25: / Line 26: @@
 As long as the annuity AN is positive, the project may be regarded as profitable in absolute terms under the postulated conditions. If it is negative, the project must be regarded as unprofitable. The annuity can be equated with the anticipated mean annual profit/loss. It is calculated for the year 0, i.e. the year in which the investment is undertaken.
+<br/>
 ----
@@ Line 32: / Line 33: @@
 The '''annual benefits '''comprise the monetarily evaluable returns, savings, etc. yielded by the investment. These may derive from:
 *Power generation<br/>Naturally, only the net energy gain can be counted, i.e. the process energy fraction (for agitators, pumps, heating, and any outside energy input) must be subtracted from the total gas yield. If the generated power is sold, the returns are included in the calculation. Any energy used to replace previous outside energy inputs counts as savings.
 *The substitution of digested sludge for chemical fertilizers can often yield savings in developing countries, where in the past, much of the material used as substrate has so far not been used as fertilizer. Accurate monetary evaluation is difficult, because the fertilizing effect of digested sludge is substantially influenced by the type of storage, the climate, the techniques employed in spreading the sludge and working it into the soil, etc.
@@ Line 39: / Line 39: @@
 ----
+<br/>
 ==== Annual costs (C)<br/> ====
 The current annual costs are made up of the expenses incurred for:
 *maintenance and repair,
 *plant operation,
@@ Line 50: / Line 49: @@
 *system attendance.
-Most such items can only be estimated, whereby 1 - 3&nbsp;% of the investment volume is generally accepted as rule-of-thumb quota for maintenance and repair. For simple biogas systems in developing countries, the percentage is usually somewhat lower, though it could be even higher for the more complicated types of systems used in industrialized countries.
+Most such items can only be estimated, whereby 1 - 3 % of the investment volume is generally accepted as rule-of-thumb quota for maintenance and repair. For simple biogas systems in developing countries, the percentage is usually somewhat lower, though it could be even higher for the more complicated types of systems used in industrialized countries.
 Operating costs are largely attributable to the depletion of consumables (such as desulfurizer cleaning agents) and to outside energy requirements, e.g. electricity for running agitators and mixers.
@@ Line 60: / Line 59: @@
 ----
+<br/>
 ==== Total investment volume (I0)<br/> ====
 The total investment volume includes the capital outlay for:
 *the digester, including agitating, mixing and heating equipment,
 *gas storage and safety provisions,
@@ Line 80: / Line 78: @@
 ----
+<br/>
 ==== Capital Recovery Factor (CR)<br/> ====
@@ Line 94: / Line 92: @@
 ----
+<br/>
 ==== Assumed Interest Rate (i)<br/> ====
@@ Line 100: / Line 98: @@
 The assumed interest rate must be determined with due regard to specific individual conditions. In this context, the assumed interest rate is defined as a real interest rate, i.e. after adjustment for inflation. In the case of cash outlay, the real interest rate would equal the rate of interest that the capital would have borne on the money market. Accordingly, the assumed interest rate is equal to the current mean debt interest rate demanded by the bank for the loan capital, when the entire project is financed with borrowed money. Moreover, money costs in the form of bank service charges, the owner's own administrative overhead, etc. must also be included. Since, however, most projects involve a certain degree of mixed financing, the assumed interest rate will take on a value located somewhere between the debt interest rate and the credit-interest rate, depending on the case situation. (Note: All rates adjusted for inflation!).
 [[Category:Impacts_Economic]]

← Older revision		Revision as of 12:27, 4 May 2012
Line 4:		Line 4:

	According to the simplified approach presented here, however, a single cost increase factor is applied for all inputs, i.e. energy, services, spare parts, etc. As we have seen in the course of the past few years, though, the cost of energy and of wares with a close tie-in to the cost of energy (such as chemical fertilizers) has been increasing more rapidly than, say, the national wage index of most countries. Also, discrepancies can always be expected to be particularly pronounced in countries where the state intervenes in the price structure. Thus, if the economic efficiency of a particular system is to be projected with any real degree of accuracy, the price-increase rates for each individual product must be taken into account.		According to the simplified approach presented here, however, a single cost increase factor is applied for all inputs, i.e. energy, services, spare parts, etc. As we have seen in the course of the past few years, though, the cost of energy and of wares with a close tie-in to the cost of energy (such as chemical fertilizers) has been increasing more rapidly than, say, the national wage index of most countries. Also, discrepancies can always be expected to be particularly pronounced in countries where the state intervenes in the price structure. Thus, if the economic efficiency of a particular system is to be projected with any real degree of accuracy, the price-increase rates for each individual product must be taken into account.
		+
		+
		+
		+	== Calculation<br/> ==

	Basically, the annuities method converts the investment into fixed annual costs suitable for direct comparison with the annual benefits.		Basically, the annuities method converts the investment into fixed annual costs suitable for direct comparison with the annual benefits.

@@ Line 1: / Line 1: @@
 Compared to other approaches, the annuities method is more suitable for assessing absolute economic efficiency and for comparing various investments with very divergent projected lifetimes. The annuities method is a reliable means of comparing the economic viability of various investment options. It takes into account reinvestments and differences in system mortality.
-According to the simplified approach presented here, however, a single cost increase factor is applied for all inputs, i.e. energy, services, spare parts, etc. As we have seen in the course of the past few years, though, the cost of energy and of wares with a close tie-in to the cost of energy (such as chemical fertilizers) has been increasing more rapidly than, say, the national wage index of most countries. Also, discrepancies can always be expected to be particularly pronounced in countries where the state intervenes in the price structure. Thus, if the economic efficiency of a particular system is to be projected with any real degree of accuracy, the price-increase rates for each individual product must be taken into account.
+According to the simplified approach presented here, however, a single cost increase factor is applied for all inputs, i.e. energy, services, spare parts, etc. As we have seen in the course of the past few years, though, the cost of energy and of wares with a close tie-in to the cost of energy (such as chemical fertilizers) has been increasing more rapidly than, say, the national wage index of most countries. Also, discrepancies can always be expected to be particularly pronounced in countries where the state intervenes in the price structure. Thus, if the economic efficiency of a particular system is to be projected with any real degree of accuracy, the price-increase rates for each individual product must be taken into account..
 Basically, the annuities method converts the investment into fixed annual costs suitable for direct comparison with the annual benefits.
@@ Line 8: / Line 8: @@
 ''AN = R - ANI''
-<blockquote>where </blockquote> <blockquote>
+<blockquote>where </blockquote><blockquote>
-AN = annuity, i.e. the annual gain, calculated for the first year (year 0)''<br> ANI= annuity of the investment<br> B = annual benefits (savings and/or returns on investment), calculated for the year 0 <br> C = annual costs, calculated for the year 0 <br> R = annual reflux (R = B - C)<br> I0 = total initial investment volume, calculated for the year 0 <br> CR = capital recovery factor<br> i = assumed interest rate (discount rate) <br> T = projected service life or time required for amortization of the investment''
+AN = annuity, i.e. the annual gain, calculated for the first year (year 0)''<br>ANI= annuity of the investment<br>B = annual benefits (savings and/or returns on investment), calculated for the year 0 <br>C = annual costs, calculated for the year 0 <br>R = annual reflux (R = B - C)<br>I0 = total initial investment volume, calculated for the year 0 <br>CR = capital recovery factor<br>i = assumed interest rate (discount rate) <br>T = projected service life or time required for amortization of the investment''
 </blockquote>
 ----
@@ Line 16: / Line 16: @@
 The purpose of the annuities calculation is to convert all net payments in connection with an investment project to a series of uniform annual payments - the so-called annuities. Conversion is effected by multiplying the individual payments by the capital recovery factor CF.
-<blockquote>''AN = ANR - ANI<br> AnI = I0 CR (i, T)<br> ANR= R for constant annual benefits'' </blockquote>
+<blockquote>''AN = ANR - ANI<br>AnI = I0 CR (i, T)<br>ANR= R for constant annual benefits'' </blockquote>
 As long as the annuity AN is positive, the project may be regarded as profitable in absolute terms under the postulated conditions. If it is negative, the project must be regarded as unprofitable. The annuity can be equated with the anticipated mean annual profit/loss. It is calculated for the year 0, i.e. the year in which the investment is undertaken.
@@ Line 25: / Line 25: @@
 The annual benefits comprise the monetarily evaluable returns, savings, etc. yielded by the investment. These may derive from:
-*Power generation<br> Naturally, only the net energy gain can be counted, i.e. the process energy fraction (for agitators, pumps, heating, and any outside energy input) must be subtracted from the total gas yield. If the generated power is sold, the returns are included in the calculation. Any energy used to replace previous outside energy inputs counts as savings.
+*Power generation<br>Naturally, only the net energy gain can be counted, i.e. the process energy fraction (for agitators, pumps, heating, and any outside energy input) must be subtracted from the total gas yield. If the generated power is sold, the returns are included in the calculation. Any energy used to replace previous outside energy inputs counts as savings.
 *The substitution of digested sludge for chemical fertilizers can often yield savings in developing countries, where in the past, much of the material used as substrate has so far not been used as fertilizer. Accurate monetary evaluation is difficult, because the fertilizing effect of digested sludge is substantially influenced by the type of storage, the climate, the techniques employed in spreading the sludge and working it into the soil, etc.
 *Savings attributable to the superior properties of digested sludge: These may result from the improved fertilizing effect of the sludge, its hygienization, reduced odor nuisance, and more advantageous handling properties such as reduced viscosity, improved homogeneity, etc. However, it is normally quite difficult to attach a monetary value to such benefits. Legal regulations pertaining, for example, to reducing odors or improving hygiene can be of decisive influence.
@@ Line 61: / Line 61: @@
 Reinvestment costs for the replacement of individual components (pumps, floating gas holder, etc.) with service lives that expire prior to the end of the projected system service life T must be included in the total investment volume. For the purposes of this simplified approach, the cost of such reinvestments may be quoted for the year 0:
-<blockquote>''I = I0 + I1 + I2 + ....'' </blockquote> <blockquote>
+<blockquote>''I = I0 + I1 + I2 + ....'' </blockquote><blockquote>
 where
-</blockquote> <blockquote>
+</blockquote><blockquote>
-''I = total investment volume<br> I0 = initial investment volume<br> I1, I2, .... = reinvestments''
+''I = total investment volume<br>I0 = initial investment volume<br>I1, I2, .... = reinvestments''
 </blockquote>
 ----
@@ Line 73: / Line 73: @@
 CR is calculated according to the formula:
-<blockquote>''CR (i,t) = (qt (q-1)) / (qt-1) = ((1+i)t i) / ((1+i)t - 1)'' </blockquote> <blockquote>
+<blockquote>''CR (i,t) = (qt (q-1)) / (qt-1) = ((1+i)t i) / ((1+i)t - 1)'' </blockquote><blockquote>
 where
-</blockquote> <blockquote>
+</blockquote><blockquote>
-''q = 1+i<br> i = assumed interest rate in percent<br> t = time in years''
+''q = 1+i<br>i = assumed interest rate in percent<br>t = time in years''
 </blockquote>
 ----
 ==== Assumed interest rate (i)  ====
 The assumed interest rate must be determined with due regard to specific individual conditions. In this context, the assumed interest rate is defined as a real interest rate, i.e. after adjustment for inflation. In the case of cash outlay, the real interest rate would equal the rate of interest that the capital would have borne on the money market. Accordingly, the assumed interest rate is equal to the current mean debt interest rate demanded by the bank for the loan capital, when the entire project is financed with borrowed money. Moreover, money costs in the form of bank service charges, the owner's own administrative overhead, etc. must also be included. Since, however, most projects involve a certain degree of mixed financing, the assumed interest rate will take on a value located somewhere between the debt interest rate and the credit-interest rate, depending on the case situation. (Note: All rates adjusted for inflation!).
-[[Category:Financing, promotion schemes and subsidies]]
+[[Category:Financing,_promotion_schemes_and_subsidies]]

← Older revision		Revision as of 12:47, 28 April 2009
Line 83:		Line 83:

	The assumed interest rate must be determined with due regard to specific individual conditions. In this context, the assumed interest rate is defined as a real interest rate, i.e. after adjustment for inflation. In the case of cash outlay, the real interest rate would equal the rate of interest that the capital would have borne on the money market. Accordingly, the assumed interest rate is equal to the current mean debt interest rate demanded by the bank for the loan capital, when the entire project is financed with borrowed money. Moreover, money costs in the form of bank service charges, the owner's own administrative overhead, etc. must also be included. Since, however, most projects involve a certain degree of mixed financing, the assumed interest rate will take on a value located somewhere between the debt interest rate and the credit-interest rate, depending on the case situation. (Note: All rates adjusted for inflation!).		The assumed interest rate must be determined with due regard to specific individual conditions. In this context, the assumed interest rate is defined as a real interest rate, i.e. after adjustment for inflation. In the case of cash outlay, the real interest rate would equal the rate of interest that the capital would have borne on the money market. Accordingly, the assumed interest rate is equal to the current mean debt interest rate demanded by the bank for the loan capital, when the entire project is financed with borrowed money. Moreover, money costs in the form of bank service charges, the owner's own administrative overhead, etc. must also be included. Since, however, most projects involve a certain degree of mixed financing, the assumed interest rate will take on a value located somewhere between the debt interest rate and the credit-interest rate, depending on the case situation. (Note: All rates adjusted for inflation!).
		+
		+
		+	[[Category: Z - Not really categorized]]