Energy Project Financing : Resources and Strategies for Success

246 Energy Project Financing: Resources and Strategies for Success

of the exact values and interpolation. The best and theoretically correct

approach is to calculate the exact values of needed factors, based on the

formulas in Table A-6.

Example 22

Determine the exact value for (F|P,13%,7).

From Table A-6,

(F|P,i,n) = (1+i)n = (1+.13)^7 = 2.3526

Interpolation is often used instead of calculation of exact values

because, with practice, interpolated values can be calculated quickly.

Interpolated values are not “exact,” but for most practical problems they

are “close enough,” particularly if the range of interpolation is kept as

narrow as possible. Interpolation of some factors, for instance (P|A,i,n),

also tends to be less error prone than the exact calculation due of simpler

mathematical operations.

Interpolation involves determining an unknown time value of money

factor using two known values that bracket the value of interest. An as-

sumption is made that the values of the time value of money factor vary

linearly between the known values. Ratios are then used to estimate the

unknown value. The example below illustrates the process.

Example 23

Determine an interpolated value for (F|P,13%,7).

The narrowest range of interest rates that bracket 13%, and for which

time value of money factor tables are provided in Appendix 4A, is 12%

to 15%.

The values necessary for this interpolation are

i values (F«F,i%,7)

12% 2.2107

13% (F|P,13%,7)

15% 2.6600