p.1 

OAR Box 1828 

Prepped by Ollie Stewart 

Document Number: 

143) ll-K- (B) -142 

Docket Number: 

A-83-27 

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

V 

UNITED STATES ENVIRONMENTAL PROTECTION AGENCY 

Office of Air Quality Planning and Standards 

Research Triangle Park, North Carolina 27711 

June 15, 1984 

MEMORANDUM 

SUBJECT: Estimating Interest-During-Construction Costs (CO-06) 

FROM: 

TO: 

Bill Vatavuk 

CEIS, EAB, SASD (MD-12) 

Dale Pahl 

SDB, ESED (MD-13) 

This memo presents a general procedure for estimating interest-duringconstruction costs for a project. I discussed this with Jim Laughlin 

(Radian) on June 13. Although the procedure is valid for any construction 

period, it is especially applicable to periods exceeding one year. 

To begin with-, the procedure is based on four assumptions: 

1. The "opportunity cost" (or interest rate) of the construction 

funds equals that of all other project expenditures (e.g., 

operating and maintenance costs). 

2. The construction funds are paid to the contractor, vendor, 

etc., in several discrete payments between the beginning and end 

of the construction period (inclusive). However, the simple, 

undiscounted sum of these payments exactly equals the total 

project investment ("P"). 

3. No income tax effects are considered (e.g., investment tax credits) 

4. All pre- and post-construction expenditures are in real (i.e., 

non-inflated) dollars. 

Even though the length of the construction period may be fixed, the 

schedule of construction payments may vary considerably. Payments may be 

made monthly, quarterly, annually--or upon completion of certain phases 

of the project. Regardless, the maximum interest-during-construction 

charge (or "lost opportunity cost," if you will) would be: 

IDC (max) = P [(l+i)k -1] 

where: P = total project investment 

i 

(1) 

annual interest rate or opportunity cost (10% 

in our cost analyses) 

k = construction period (years) 
P.3 

For instance, for i=10% and k=2, IDC (max) = 21% of the total investment. 

The following development will make equation (1) easier to understand. 

Consider the cash flow diagram below. Each expenditure irepresented by a 

vertical arrow) occurs on or before the start-up date (year "0"). This 

particular schedule shows a partial payment (P*) being made at the 

beginning of construction (year "-2"), followed by 24 equal monthly 

payments (p), such that the simple sum of all payments is "P". Now, to 

obtain the present worth of these payments in year 0, 

(year) -2 -1 0 

HtltHHIHHHHHHH' 

we multiply P* and the various p's by compound interest factors, each of 

which is a function of precisely when each payment occurs. For P*, the 

factor is simply "(1+i)2", but for the p's, the process is somewhat more 

complex. To simplify matters, think of the monthly payments as analogous 

to 24 annual payments made at an interest rate of 0.833% (10%/year * 12 

months/year). And each of these payments is assumed to occur at the end 

of the month. Then, the present worth of those payments in year -2 is 

the product of p and the uniform series present worth factor (USPWT). 

This factor, which is the reciprocal of the capital recovery factor, is 

calculated .as follows: 

USPWF * ft+i*)j

 -1 (2) 

i*(l+i*)J 

where: i* = periodic interest rate (0.833%) 

j = number of periods (24) 

Once the present worth of the monthly payments in year -2 is 

calculated, then the present worth in year 0 is obtained by multiplying 

it by (1+ij2, the same factor used with P*. 

Putting this all together: 

(l+i*)J-l 

PW(year 0)=P* (1+i)2 + p(l+i)2 ~7~7T i <3> 

i*(l+i*)J 

Substituting for i, i*, and j yields: 

PW (year 0) = 1.21 P* + 26.2 p (4) 
P.4 

During our meeting, Jim Laughlin said he'd lik e to know the interes t 

during construction for thi s case i f 20% of the investment cost were paid 

initially , and the balance in 24 equal monthly payments. Then, P* = 

0.20P and p=0.80P/24=0.0333P. Substituting these values into eq. (4) 

yields a present worth of 1.107P. 

By our definition , IDC i s the difference between the present worth 

(at year 0) of periodic construction payments and the present worth (also 

at year 0) of one lump sum payment. The latte r present worth is , of 

course, jus t P_. Therefore, in thi s case: 

IDC = 1.107P - P = 0.107P (5) 

In other words, the interes t during construction would be 10.7% of P. 

As you might imagine, thi s percentage would depend on how the payments 

were distributed throughout the (in thi s case) two-year construction 

period. The percentage would range from zero (i.e. , one lump sum payment 

at year 0) to 21% (a single payment at year -2). (Recall that the maximum 

IDC was obtained from equation (1).) 

Clearly, the longer these payments are made before start-up (year 

0 ), the longer wil l be the IDC. This i s especially so when the construction 

period is fairl y long--five years or more. In fact , long construction 

periods can have significant adverse impacts on a project' s return on 

investment. This i s simply because a firm' s funds are tied up while no 

revenues are being generated to offset them. 

Finally , recognize that thi s i s a somewhat simplisti c analysis which 

ignores tax effects , differentia l inflatio n rates, and other "real world" 

complications. Nonetheless, I think that thi s methodology i s general 

enough to accommodate these complications and yet stil l yiel d meaningful 

estimates of IDC. 

I hope thi s helps you to estimate IDC. I f you have any questions or 

would lik e more help, please phone or stop by. 

cc: J . Laughlin, Radian 

y R . Short 

A. Wehe