Question

A life-cycle cost analysis (LCCA) is being performed for a project. Two competing surface types are being evaluated. For surfacing type 1, the initial construction will cost $1 million and have an associated user cost of $220,000. Three additional rehabilitation strategies, at a cost of $250,000 each, will be incurred in years 10, 20 and 30. Associated user cost in years 10, 20 and 30 will be $220,000, $330,000 and $440,000, respectively. For surfacing type 2, the initial construction will cost $1.2 million and have an associated user cost of $240,000. Two additional rehabilitation strategies, at a cost of $300,000 each, will be incurred in years 15 and 30. Associated user cost in years 15 and 30 will be $220,000 and $330,000, respectively. Assume a salvage value equal to the 10% of the initial construction cost. If LCCA results are the only factors that influence the ultimate selection of this pavement surfacing type, which type would you like to select for a 3% discount rate and over a 35-year analysis period?

Answer 1

Well, let us first tablulize the entire data we have as below (all figures, except years, in $):

Surfacing Type 1
Year	Initial cost	Associated user cost	Additional rehabilitation	Salvage Value
0	1000000	220000
10		220000	250000
20		330000	250000
30		440000	250000
35				100000

And

Surfacing Type 2
Year	Initial cost	Associated user cost	Additional rehabilitation	Salvage Value
0	1200000	240000
15		220000	300000
30		330000	300000
35				120000

Now, let us calculate the Net Cash Outflow (mentioned at E column below) and also compute the present value of the future net cash outflow. For this we have used the following formula:

Present value = Net cash outflow * (1/(1.03)^t)
(here t stands for number of years)

When we carry out the above, we get the following tables:

Surfacing Type 1
Year	Initial cost A	Associated user cost B	Additional rehabilitation C	Salvage Value D	Net Cash outflow E=A+B+C-D	Present Value @ 3% p.a.
0	1000000	220000			1220000	1220000
10		220000	250000		470000	349724
20		330000	250000		580000	321132
30		440000	250000		690000	284271
35				100000	(100000)	(35538)
Net Present value of the cost to be incurred at the initial stage and later across 35 years	2139589

Surfacing Type 2
Year	Initial cost A	Associated user cost B	Additional rehabilitation C	Salvage Value D	Net Cash outflow E=A+B+C-D	Present Value @ 3% p.a.
0	1200000	240000			1440000	1440000
15		220000	300000		520000	333768
30		330000	300000		630000	259552
35				120000	(120000)	(42646)
Net Present value of the cost to be incurred at the initial stage and later across 35 years	1990674

Conclusion: The discounted cost of Surfacing Type 2 is less than that of Surfacing Type 1. Type 2 is cost efficient by a whopping worth of $148915, hence we must go for Type 2.