Economics of Solar Heating Systems - ACS Symposium Series (ACS

2 Economics of Solar Heating Systems

Downloaded by UNIV OF ROCHESTER on January 19, 2018 | http://pubs.acs.org Publication Date: June 15, 1983 | doi: 10.1021/bk-1983-0220.ch002

JOHN W. ANDREWS Brookhaven National Laboratory, Solar and Renewables Division, Upton, NY 11973

The development of solar space heating systems has required assessment of the allowable cost of such systems. Such assessments have most often utilized life-cycle costing with a 20-year period of analysis. The use of this method, especially in conjunction with high energy cost escalation rates, makes i t possible to justify theoretically almost any system cost. Thus, a Gresham's Law has come in play: in the competition for research doll a r s , costly, material-intensive, technically safe systems have crowded out more innovative but technically more risky approaches keyed to more realistic cost goals. Methods of Economic Analysis Three methods of analysis commonly used in evaluating r e s i dential solar systems are 1) simple payback; 2) positive cash flow; 3) l i f e cycle costing. Simple Payback is an answer to the question, "If I spend more now for a solar system than for a conventional alternative, how long w i l l i t take for my cumulative fuel savings to equal my extra i n i t i a l outlay?" The HVAC industry generally considers a three- to five-year payback to be necessary in order to justify new, more efficient products. The solar industry is accustomed to much longer periods, often 20 years or longer. It has been suggested that seven or eight years is a reasonable compromise which allows for an increased energy consciousness on the part of the public, but does not d i verge totally from current practice. If no allowance were made for the increasing cost of energy, this would mean that the i n cremental solar system cost, or difference between the f i r s t cost of the solar system and that of the conventional alternative, should be no more than eight times the f i r s t year's fuel 0097-6156/83/0220-0019$06.00/0 © 1983 American Chemical Society Gebelein et al.; Polymers in Solar Energy Utilization ACS Symposium Series; American Chemical Society: Washington, DC, 1983.


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savings. When both f u e l c o s t e s c a l a t i o n and time value of money are taken i n t o account, t h i s l i m i t i n g r a t i o might be r a i s e d t o about 10. The required payback time i s a matter of judgement, and upon t h i s judgement can depend the e n t i r e d i r e c t i o n of a development program. Let us t h e r e f o r e look at some a d d i t i o n a l ways of addressing t h i s problem. P o s i t i v e Cash Flow i s based upon the i d e a t h a t people w i l l buy a s o l a r system i f t h e i r t o t a l payments f o r mortgage, maintenance, and energy are l e s s f o r the s o l a r system than f o r the conv e n t i o n a l one. Depending on the r a t e of i n t e r e s t , t h i s c r i t e r i o n could be compatible w i t h r e l a t i v e l y long payback p e r i o d s . In order to assess t h i s c r i t e r i o n , the c a p i t a l recovery f a c t o r s (CRF) f o r nine mortgages of terms 10, 20, and 30 years and i n t e r est r a t e s 6, 10, and 14% have been c a l c u l a t e d . The CRF i s the r a t i o of the annual mortgage payment ( i n t e r e s t plus p r i n c i p a l ) t o the face amount of the l o a n . The loan amount i s taken as the incremental s o l a r system c o s t , that i s , the d i f f e r e n c e between the f i r s t cost of the s o l a r system and that of the c o n v e n t i o n a l one. This i s then modified by s u b t r a c t i n g the tax savings due to the d e d u c t i b i l i t y of the i n t e r e s t and by adding the incremental maintenance and miscellaneous c o s t s , where these are assumed to equal 2% of the incremental system c o s t . The net c a p i t a l r e covery f a c t o r represents the amount of f u e l savings r e q u i r e d , per d o l l a r of Incremental system c o s t , to achieve zero i n i t i a l cash flow r e l a t i v e to the competing conventional system. The i n v e r s e of the CRF i s the r a t i o of incremental s o l a r system cost to f i r s t year's f u e l s savings needed to achieve zero r e l a t i v e cash flow i n the f i r s t year. Values of t h i s Cost/Savings R a t i o are d i s p l a y e d i n Table I . A Cost/Savings R a t i o of 10 i s c o n s i s t e n t w i t h a 20year 10% loan and a marginal tax r a t e of 37%, or e l s e a 20-year 14% l o a n w i t h a 50% marginal tax r a t e . Table I Ratios of Incremental S o l a r System Cost to F i r s t Year F u e l Savings Consistent w i t h Zero R e l a t i v e Cash Flow f o r the F i r s t Year. Values Given f o r Marginal Tax Brackets of 30% and 50%. Term of Loan (years) 10

20

30

Interest Rate (%) 14 10 6 14 10 6 14 10 6

Cost/Savings R a t i o 30% 50% Marginal Tax Rate Marginal Tax Rate 5.9 6.5 7.2 7.8 9.3 11.2 8.3 10.4 13.3

7.0 7.5 7.9 9.9 11.5 13.0 10.8 13.2 15.9

Gebelein et al.; Polymers in Solar Energy Utilization ACS Symposium Series; American Chemical Society: Washington, DC, 1983.


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Economics of Solar Heating Systems

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L i f e - C y c l e C o s t i n g i s a method of t a k i n g i n t o account a l l of the v a r i o u s c o s t s and b e n e f i t s which occur i n the course of a c h i e v i n g an o b j e c t i v e over time. A cost which i s i n c u r r e d i n the f u t u r e i s not as great a l i a b i l i t y as the same cost i n c u r r e d now. This i s true even i n the absence o f i n f l a t i o n . Q u a l i t a t i v e l y i t i s human nature to defer pain as long as p o s s i b l e . Q u a n t i t a t i v e l y , by d e f e r r i n g a cost one can i n the meantime earn i n t e r e s t on the money set aside to pay the c o s t , and the longer one defers the payment, the more i n t e r e s t w i l l be earned. I t may a l s o happen, however, that the f u r t h e r i n the f u t u r e a cost may be d e f e r r e d , the greater i t w i l l be. I n an era of r i s i n g energy p r i c e s , the cost of a given amount of f u e l w i l l increase over time. A way i s needed to put on an equal f o o t i n g costs i n curred at d i f f e r e n t times. This i s accomplished by means of the present value f u n c t i o n (PVF) which i s defined (1) as the amount of money which must be set aside now, a t an annual r a t e of r e t u r n d, to cover over the next N years an annually o c c u r r i n g expense which now costs one d o l l a r but i s expected to e s c a l a t e a t an annual r a t e e:

PVF

( d , e, N)

d-e N 1+d

1-

1+e 1+d

i f d^e (1) i f d=e

In e v a l u a t i n g the r e l a t i v e m e r i t s o f a s o l a r and a convent i o n a l HVAC system the present values o f the various costs (or b e n e f i t s ) are added (or subtracted) to o b t a i n a t o t a l present value (TPV) o f the l i f e - c y c l e costs of the s o l a r system and of the conventional system. The system having the lower TPV i s the more cost e f f e c t i v e under the given assumptions. For r e s i d e n t i a l systems the f o l l o w i n g costs and b e n e f i t s must be considered: 1) system f i r s t c o s t ; 2) maintenance and miscellaneous c o s t s ; 3) energy c o s t s ; and 4) tax b e n e f i t s due to d e d u c t i b i l i t y of i n t e r est payments. The s o l a r tax c r e d i t , because i t i s expected to e x p i r e soon, i s not considered. ( I t could be included i n the a n a l y s i s by s u b t r a c t i n g i t s value from the system f i r s t cost.) To i l l u s t r a t e what can be done w i t h l i f e - c y c l e c o s t i n g the PVF was c a l c u l a t e d f o r periods of a n a l y s i s of 5 to 25 years and f u e l cost e s c a l a t i o n r a t e s from 5% t o 30% w i t h a 10% discount r a t e . The values so c a l c u l a t e d are shown i n Table I I . The PVF i s approximately equal to the allowed c o s t - t o - s a v ings r a t i o under the s i m p l i f y i n g assumptions of equal d i s c o u n t , i n t e r e s t , and i n f l a t i o n r a t e s and o f c a n c e l i n g e f f e c t s of maintenance costs and of the b e n e f i t due to tax d e d u c t i b i l i t y of


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Table I I Values of the Present Value Function f o r Various Fuel E s c a l a t i o n Rates and Periods of A n a l y s i s 5


Fuel E s c a l a t i o n Minus Discount Rate -0.05 0 0.05 0.10 0.20

Present Value Function ( C a l c u l a t e d f o r d = 0.1)

Fuel Cost Escalation 0.05 0.10 0.15 0.20 0.30

Periods of A n a l y s i s (Years) 20 25 10 15

4.2 4.5 5.0 5.5 6.5

7.4 9.1 11.2 13.9 21.6

10.0 13.6 19.0 26.9 56.3

12.1 18.2 28.7 47.0 136.2

13.8 22.7 40.1 78.0 320.6

mortgage i n t e r e s t . * The point that i s i l l u s t r a t e d by Table I I i s that i t i s p o s s i b l e t h e o r e t i c a l l y to j u s t i f y very high c o s t - t o savings r a t i o s and hence very high s o l a r system costs by u s i n g high f u e l cost e s c a l a t i o n r a t e s and long periods of a n a l y s i s . The use of long system l i f e t i m e s such as 25 years and l a r g e f u e l e s c a l a t i o n r a t e s such as 30% r e s u l t s i n very high PVF's and appears to suggest that one should r a t i o n a l l y pay 320 times the f i r s t year's energy savings f o r a s o l a r system. I n a d d i t i o n to noting that these assumptions imply a 700-fold increase i n the p r i c e of f o s s i l f u e l s , one may observe as w e l l that t h i s apparent p r i c e freedom i s l i m i t e d by c e r t a i n a d d i t i o n a l c o n s t r a i n t s : 1. The period of a n a l y s i s should not exceed the system life. Indeed, i t should probably be enough s h o r t e r than the expected system l i f e that purchases w i l l be induced w i t h the exp e c t a t i o n of a p r o f i t . Since experience with s o l a r systems i s l i m i t e d , the use of system l i f e t i m e s as long as 20 years i s probably not warranted. Even 15 years may be too long. 2. The e x p e c t a t i o n of high f u e l cost e s c a l a t i o n r a t e s w i l l probably not be borne out as much f o r e l e c t r i c i t y as f o r f o s s i l f u e l s . Fuel costs are only a p o r t i o n of the t o t a l cost of e l e c t r i c power generation, and cheaper s o l i d f u e l s are i n any case expected to d i s p l a c e o i l i n e l e c t r i c power generation. 3. Insofar as f u e l costs do e s c a l a t e a t a r a p i d r a t e , t h i s w i l l l i k e l y lead to r e l a t i v e l y r a p i d i n n o v a t i o n i n s o l a r heating and other forms of energy c o n s e r v a t i o n . Thus a l o n g - l i f e h i g h *The l a t t e r two e f f e c t s are of the same order of magnitude and cancel e x a c t l y , f o r example, i f f i r s t - y e a r maintenance costs are 1.7% of system f i r s t c o s t , the consumer i s i n the 50% tax bracke t , and a 15-year period of a n a l y s i s i s used.



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cost s o l a r system may be rendered obsolete w e l l before the end of i t s service l i f e . Recently there has been evidence of a change of heart i n £he s o l a r community concerning cost c r i t e r i a . At a meeting of t h e U.S. Department of Energy (DOE) s o l a r c o n t r a c t o r s h e l d i n September, 1981, the consensus moved away from 20-year l i f e c y c l e c o s t ing. For r e s i d e n t i a l systems, payback was seen as the most app r o p r i a t e c r i t e r i o n with a median recommended payback time of 6 years. For commercial systems, where the purchaser i s more s o p h i s t i c a t e d , l i f e - c y c l e c o s t i n g was seen as a p p r o p r i a t e , but w i t h a 10-year time horizon.(2^) A d d i t i o n a l l y , a recent DOE mark e t i n g study (3) I n d i c a t e d that a d e f i n i t e r e l a t i o n s h i p e x i s t s between payback and market p e n e t r a t i o n , w i t h p e n e t r a t i o n dropping below 20% f o r payback periods greater than 8 years. In l i n e w i t h the above d i s c u s s i o n , a Cost/Savings R a t i o of 10 was s e l e c t e d as an upper l i m i t , c o n s i s t e n t with a f u e l cost e s c a l a t i o n r a t e of 5% above i n f l a t i o n and a breakeven time of under 10 years. Consequences f o r S o l a r System Engineering The amount of energy obtained annually from a s o l a r c o l l e c tor i n a well-designed system depends on the c o l l e c t o r performance c h a r a c t e r i s t i c s , the type of load to which the c o l l e c t o r i s matched, the s i z e of the c o l l e c t o r array r e l a t i v e to the l o a d , and the s o l a r a v a i l a b i l i t y and ambient temperatures experienced by the system. For a r e s i d e n t i a l space-and-water heating system using f l a t - p l a t e c o l l e c t o r s , however, 100,000 B t u / f t - y r (1.14 GJ/m -yr) represents a reasonable average over much of the U n i t ed States.(4) Current gas and o i l p r i c e s are t y p i c a l l y ^$0.50/ therm and ^$1.20/gallon r e s p e c t i v e l y . I f an average conversion e f f i c i e n c y o f 70% i s assumed, then the energy savings per u n i t area w i l l equal $ 0 . 7 1 / f t ($7.69/m ) against gas or $ 1 . 2 2 / f t ($13.18/m ) against o i l . A l l o w i n g f o r the l i k e l i h o o d that the p r i c e of gas w i l l r i s e t o near p a r i t y w i t h o i l , we chose $1.20/ f t ($13/m ) as the benchmark value of the energy savings, based on u n i t c o l l e c t o r area. The f a c t o r - o f - t e n r u l e then r e q u i r e s a system cost o f $12/ f t ($130/m ) of c o l l e c t o r . I s there any hope of meeting such a cost goal using current technology based on extruded metal and g l a s s c o l l e c t o r s ? The answer i s no. The m a t e r i a l s costs alone for such c o l l e c t o r s are $ 5 - $ 6 / f t ($55-$65/m ) .(5) By the time manufacturing, d i s t r i b u t i o n , and i n s t a l l a t i o n costs are i n c u r r e d , the p r i c e r i s e s t o $20-$25/ft ($220-$270/m ). The balance o f system ( s t o r a g e , p i p i n g , pumps, heat exchangers, v a l v e s , and cont r o l s ) c o n t r i b u t e s another $ 2 0 / f t ($220/m*). Thus the o v e r a l l system cost i s over budget by n e a r l y a f a c t o r of f o u r . I t i s c l e a r that both the c o l l e c t o r and the balance of s y s tem must experience d r a s t i c cost reductions before a c t i v e s o l a r space heating can be s a i d t o be c o s t - e f f e c t i v e . The approach 2

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taken a t Brookhaven N a t i o n a l Laboratory (BNL) was to a l l o c a t e a budget o f $ 5 / f t ($55/m ) f o r the i n s t a l l e d cost of the c o l l e c t o r and the remainder of $ 7 / f t ($75/m ) f o r the balance of system. The design o b j e c t i v e s were then set t o : 1) reduce the m a t e r i a l s c o s t s of the c o l l e c t o r to ^ $ l / f t ( $ l l / m ) , and 2) design the c o l l e c t o r to be compatible w i t h balance-of-system cost savings. M a t e r i a l s cost r e d u c t i o n has been achieved through the use of t h i n - f i l m polymeric m a t e r i a l s i n both the absorber and g l a z i n g p o r t i o n s of the c o l l e c t o r . The f i l m s , attached to a l i g h t w e i g h t bent-metal frame, form a set of s t r e s s e d membranes that c o n t r i b ute to the o v e r a l l s t r e n g t h of the panel. In t h i s design water i s used as the h e a t - t r a n s f e r medium. T h i s water flows through the absorber at atmospheric pressure from the top to the bottom of the panel. The use of o r d i n a r y water without a n t i f r e e z e makes p o s s i b l e the e l i m i n a t i o n of a t l e a s t one heat exchanger and two pumps and can lead to an improvement i n system e f f i c i e n c y . The nonpressurized operating mode r e l a x e s design requirements i n the p i p i n g and storage as w e l l as i n the c o l l e c t o r . A companion paper (6) d e s c r i b e s the Brookhaven t h i n - f i l m c o l l e c t o r i n greater d e t a i l . 2

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Acknowledgment Work performed under the auspices o f the U.S. Department o f Energy under Contract No. DE-ACO2-76CH00016.

Literature Cited 1. 2.

3.

4.

Perino, A. M., A Methodology for Determining the Economic Feasibility of Residential or Commercial Energy Systems, SAND 78-0931, 1979, p.11. Active Solar Heating and Cooling Contractors' Review Meeting, U.S. Dept. of Energy, Roundtable Discussion on Solar Systems Evaluation, Washington, D.C., September, 1981, Proceedings in preparation. Lilian, G. L. and Johnston, P.E., A Market Assessment for Active Solar Heating and Cooling Products, Category B: A Survey of Decision Makers in the HVAC Market Place, OR/MS Dialogue, Inc., Final Report DO/CS/30209-T2, September 1980. For example, using the Balcolm-Hedstrom load-collector ratio method (Solar Engineering, January 1977, p.18) the median collectable solar energy was 99,000 Btu/ft -yr over a sample of 84 cities, for systems providing 50% of the building heating load from solar energy. All but 6 cities fell in the range 70,000 to 160,000 Btu/ft -yr. See also the editorial by Bruce Anderson in Solar Age, January 1978: " . . . there is no evidence, and little possibility, that any solar space-heating system will ever deliver more, annually, than 2

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100,000 Btus per square foot of aperture area in a climate where sunshine is possible 50 percent of the time." 5. "Cost Reduction Opportunities: Residential Solar Systems," Booz, Allen & Hamilton, Bethesda, MD, 1981 (Draft subject to revision). 6. Wilhelm, W. G., "The Use of Polymer Films and Laminate Technology for Low Cost Solar Energy Collectors," submitted to the Am. Chem. Soc. Polymers in Solar Energy Symposium, Las Vegas, NV, March 28- April 2, 1982. November 22,1982


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Economics of Solar Heating Systems - ACS Symposium Series (ACS

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