p. 1



# OAR Box 

# 1828 Prepped byOllie Stewart



### Document

Number: 

# 143 ) ll-K
- (B ) -14 2
Docket Number: 

# A-83-2 7

Printed 11/12/2008 11:12:53 AM Sheet 143 of 325P. 2



### V UNITE D STATE S ENVIRONMENTA LPROTECTIO N AGENC Y Offic e o fAi rQualit yPlannin g an d Standard s Researc h Triangl e Park , Nort h Carolin a 2771 1 

### Jun e15 , 198

4

MEMORANDU

M SUBJECT : Estimatin g Interest-During-Constructio n Cost s (CO-06 ) FROM :


### TO : Bil l Vatavu k

CEIS , EAB , SAS D(MD-12 ) Dal e Pah l SDB , ESE D(MD-13 ) Thi s memo present s a genera l procedur e fo r estimatin g interest-during constructio ncost s fo r a project . I discusse dthi s wit hJi m Laughli n (Radian ) o

nJun e 13 . Althoug hth e procedur e i s vali dfo r an y constructio n period , i t i s especiall y applicabl e t o period s exceedin g on e year . T o begi nwith- , th e procedur e i s base do nfou r assumptions : 1 . Th e "opportunit y

cost " (or interes t rate ) o f th e constructio n fund s equal s tha t o f al l othe r projec t expenditure s (e.g. , operatin g an

dmaintenanc e costs) . 2 . Th e constructio nfund s ar e pai dt o th e contractor , vendor , etc. , i nsevera l discret e payment s betwee nth e beginnin g an dend o f th e constructio nperio d(inclusive) . However , th e simple , undiscounte dsu

m o f thes e payment s exactl y equal s th e tota l projec t investmen t ("P") . 3 . No income taxeffect s ar e considere d(e.g. , investmen t taxcredits ) 4 . Al l pre - an

dpost-constructio nexpenditure s ar e i nrea l (i.e. , non-inflated ) dollars . Eve nthoug hth e lengt ho f th e constructio nperio dma y b e fixed , th e schedul e o f constructio npayment s ma y vary considerably . Payment s ma y b e mad e monthly , quarterly , annually--o r upo ncompletio no f certai nphase s o f th e project . Regardless , th e maximu m interest-during-constructio n charg e (o r "los t opportunit y cost, " i f yo uwill ) woul dbe : IDC (max ) = P [(l+i) k-1 ] where : P = tota l projec t investmen t

i 

### (1 )

annua l interes t rat e o r opportunit y cos t (10 % inou r cos t analyses ) k= constructio nperio d(years )P. 3

Fo r instance , fo r i=10 % an dk=2 , ID

C (max ) = 21 % o f th e tota l investment . Th e followin gdevelopmen t wil l mak e equatio n(1 ) easie r t o understand . Conside r th e cas hflo w diagram below . Eac hexpenditur e i representedb

y a vertica l arrow ) occur s ono r befor e th e start-u pdat e (yea r "0") . Thi s particula r schedul e show s a partia l paymen t (P* ) bein g mad e a t th e beginnin go f constructio n(yea r "-2") , followe db y 2 4 equa l monthl y payment s (p) , suc htha t th e simpl e su m o f al l payment s i s "P" . Now , t o obtai nth e presen t wort ho f thes e payment s i nyea r 0 , (year ) - 2 - 1 0 

# HtltHHIHHHHHHH '

w e multipl y

P * an dth e variou s p' s b

y compoun dinteres t factors , eac ho f whic hi s a functio no f precisel y whe neac hpaymen t occurs . Fo r P* , th e facto r i s simpl y

"(1+i) 2 " , bu t fo r th e p's , th e proces s i s somewha t mor e complex . T o simplif y matters , thinko f th e monthl y payment s a s analogou s t o 2 4 annua l payment s mad e a t aninteres t rat e o f 0.833 % (10%/yea r * 1 2 months/year) . Andeac ho f thes e payment s i s assume dt o occu r a t the en d o f th e month . Then , th e presen t wort ho f thos e payment s i nyea r - 2 i s th e produc t o f pan

dth e uniform

serie s presen t wort hfacto r (USPWT) . Thi s factor , whic hi s th e reciproca l o f th e capita l recover y factor , i s calculate d.a

s follows :
USPWF 

### * ft + 

### i*) j 

### - 1 (2 )

i*(l+i*) J where : i * = periodi c interes t rat e (0.833% )

j = numbe r o f period s (24 ) Onc e th e presen t wort ho f th e monthl y payment s inyea r - 2 i s calculated , the nth e presen t wort hi nyea r 0 i s obtaine db y multiplyin g i t b y (1+ij 2 , th e sam

e facto r use dwit hP* . Puttin gthi s al l together : (l+i*)J- l 

### PW(year0)=P * (1+i) 2 

### + p(l+i) 2 

### ~7~7T i < 3 

### > i*(l+i*) J Substitutin gfo r i , i* , andj yields : P W (yea r 0 ) = 1.2 1 P * + 26. 2 p(4 )P. 4

Durin g ou rmeeting , Ji m Laughli n sai d he' d lik e t o kno wth e interes t durin g constructio n fo rthi s cas e i f20 % o fth e investmen t cos t wer e pai d initially , an d th e balanc e i n 2 4 equa l monthl ypayments

. Then , P * = 0.20 P an d p=0.80P/24=0.0333P

. Substitutin g thes e value s int o eq
. (4 ) yield s a presen t wort h o f1.107P

. B you rdefinition , IDC i s th e differenc e betwee n th e presen t wort h (a t yea r0 ) o fperiodi cconstructio n payment s an d th e presen t wort h (als o a t yea r0 ) o fon e lum p su m payment

. Th e latte rpresen t wort h is , o f course , jus t P_

. Therefore , i n thi s case : ID C = 1.107 P - P = 0.107 P (5 ) I n othe rwords , th e interes t durin g constructio n woul d b e 10.7 % o fP

. A s yo u migh t imagine , thi s percentag e woul d depen d o n ho wth e payment s wer e distribute d throughou t th e (i n thi s case ) two-yea rconstructio n period

. Th e percentag e woul d rang e fro m zer o (i.e. , on e lum p su m paymen t a t yea r0 ) t o 21 % ( a singl e paymen t a t yea r-2)

. (Recal l tha t th e maximu m ID C was obtaine d fro m equatio n (1). ) Clearly , th e longe rthes e payment s ar e mad e befor e start-u p (yea r 0 ) , th e longe rwil l b e th e IDC

. Thi s i s especiall ys o whe n th e constructio n perio d i s fairl ylong--fiv e year s o rmore
. I n fact , lon g constructio n period s ca n hav e significan t advers e impact s o n a project' s retur n o n investment

. Thi s i s simpl ybecaus e a firm' s fund s ar e tie d u p whil e n o revenue s ar e bein g generate d t o offse t them

. Finally , recogniz e tha t thi s i s a somewhat simplisti canalysi s whic h ignore s ta xeffects , differentia l inflatio n rates , an d othe r"rea l world " complications

. Nonetheless , I thin k tha t thi s methodolog yi s genera l enoug h t o accommodat e thes e complication s an d ye t stil l yiel d meaningfu l estimate s o fIDC

. I hop e thi s help s yo u t o estimat e IDC

. I fyo u hav e an yquestion s o r woul d lik e more help , pleas e phon e o rsto p by

. cc : J

. Laughlin , Radia n y R

. Shor t A

. Wehe