Present Cost-Future Cost vs Present Value-Future Worth « Construction Analytics

A reader asked an interesting question, one that does not often come up in construction analytics. The following is an example to explain the difference.

The question: Our firm engages in construction projects that must be fully funded from cradle to grave to secure approval. A portion of these projects is remediation that will occur 10 years from now. What would be the Present Value to fund a project needed to be performed 10 years from now based on a similar project that cost $1,000,000 three years ago?

There are really two parts to this question. 1) What is the construction cost of remediation 10 years from now? 2) What is the Present Value of money today needed to fund that construction cost ten years from now?

  1. is determine the construction cost in 10 years based on inflation rates and a known project cost.
  2. is What is the value of money. How much do I need today to fund the project 10 years from now.

For the sake of this example we must assume some rates. Assume construction cost inflation the last three years was a total 25% and long term average inflation is 4%.

Present Cost to Future Cost is solved by applying construction inflation. To estimate cost of a project 10 years from now, we can only rely on long term average inflation for the type of work being performed. Long term average inflation is not the same as the inflation we have experienced over the last three years. So first let’s inflate the project from three years ago at 25% to today’s construction cost.

$1,000,000 (three years ago) x (1+25%) = $1,250,000 = similar project cost today.

Now let’s use long term average inflation (4%) to determine the construction cost 10 years from now. Inflation (like interest) must be compounded. So total interest over 10 years is interest for one year raised to the 10th power.

$1,250,000 (today’s cost) x (1+4%)^10 = $1,250,000 x 1.48 = $1,850,000

We would never assume the long term inflation to be repetitive of what we’ve seen over the last three years, so we use what we know occurred over the last three years to get to today, then project forward at the long term average historical rate.

The remedial work 10 years from now is estimated to cost $1,850,000. That is the Future Worth (FW) of the construction work needed. What is the Present Value (PV) of money needed to fund that Future Worth (FW)? How much must be invested in an account today so that it will grow to provide the funds needed to perform the FW work?

The growth rate of money is not the same as the inflation rate of construction. For the sake of this example, we need to make some assumption here for the growth rate of money. Let’s assume 3%. If we were to invest money today it can grow at 3%/year for 10 years. The answer to how much is needed to invest today (PV) to provide the full sum needed to fund the future (FW) is entirely dependant on the interest rate that can be secured for the term of the investment. We need $1,850,000 ten years from now. Divide the FW by the compounded rate of interest or money growth to find PV.

$1,850,000 (FW) / (1+3%)^10 = $1,850,000 / 1.34 = $1,376,000 (PV)

A Present Value (PV) of $1,376,000 must be invested today at a rate of 3% growth to ensure enough funds are available 10 years from now to perform the remediation work, a (FW) of $1,850,000.

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