244 Energy Project Financing: Resources and Strategies for Success
Example 19
Determine the longest life planning horizon for projects A, B, C with
lives 3, 5, and 6 years, respectively.
The longest life planning horizon is 6 years based on Project C. Project
A must be repeated twice, with the second repetition ending at year 6,
so no termination of cash flows is required. Project B’s second repetition
extends to year 10; therefore, a salvage value at t = 6 must be established
for B’s repeated cash flows in years 7, 8, 9, and 10.An approach that eliminates the truncation salvage value issue from
the planning horizon question is the least common multiple approach.
The least common multiple planning horizon is set by determining the
smallest number of years at which repetitions of all projects would ter-
minate simultaneously. The least common multiple for a set of numbers
(lives) can be determined mathematically using algebra. Discussion of
this approach is beyond the scope of this appendix. For a small number
of projects, the value can be determined with trial and error by examining
multiples of the longest life project.Example 20
Determine the least common multiple planning horizon for projects
A, B, C with lives 3, 5, and 6 years, respectively.The least common multiple of 3, 5, and 6 is 30. This can be obtained by trial
and error, starting with the longest project life (6) as follows:1st trial: 6*1 = 6; 6 is a multiple of 3 but not 5; reject 6 and proceed
2nd trial: 6*2 = 12; 12 is a multiple of 3 but not 5; reject 12 and proceed
3rd trial: 6*3 = 18; 18 is a multiple of 3 but not 5; reject 18 and proceed
4th trial: 6*4 = 24; 24 is a multiple of 3 but not 5; reject 24 and proceed
5th trial: 6*5 = 30; 30 is a multiple of 3 and 5; accept 30 and stopUnder a 30-year planning horizon, A’s cash flows are repeated 10 times,
B’s 6 times, and C’s 5 times. No truncation is required.The standard planning horizon approach uses a planning horizon
that is independent of the projects being evaluated. Typically, this type of