More on the economics of commutation: Three models

  • Posted on: 10 December 2014
  • By: Michael Brydon

I got some questions last week from members of the Area F Parks Commission about the commutation option for the West Bench water system.  I appreciate that not everyone spends a lot of time doing discounted cash flow calculations so I have provided a simplified spreadsheet model (see the link below).  We identified three options:

  1. Pay the capital charge outright from savings: This was not really an option for the younger folks at the table (no savings) but was included as a possibility for others.  The appeal here is that you do not pay loan interest if you pay your share of the capital cost immediately.  The downside--and people seem to forget this--is that you do not earn interest on that money if you take it out of savings.  In other words, prepayment has an opportunity cost that must considered against the costs of the other alternatives.
  2. Take a bank loan in order to reduce the prepayment time.  Some people, if they are going to pay interest, would rather pay interest over a shorter period (say five years).  The RDOS anticipates funding the capital costs of the West Bench water system over 20 years.  At least one member of the Parks Commission secured a loan through his bank.  He was going to pay the RDOS his lump sum and then pay his bank back over 60 months.  The only catch with this approach is that unsecured demand loans from banks typically come at a high interest rate.  Let's assume it is 6%, but it could be higher.
  3. Let the RDOS borrow on your behalf.  This is the default option. The primary advantage of having the RDOS borrow the money on your behalf through the Municipal Finance Authority (MFA)  is that MFA has a triple-A bond rating.  Thus, when investors buy MFA bonds, they are willing to accept lower yields (interest rates) in return for the security of the bond.  As noted above, the duration of MFA financing is 20 years.  Personally, I would have liked to go longer.  The idea under true user-pay is to match the term of the financing to the expected life of the asset. In this case, we expect the water infrastructure to last 30-50 years.  However, no one will buy 50 year bonds.  In fact, MFA only sells 10 year bonds.  Accordingly, to finance the West Bench water system, we have to do two rounds of ten-year bonds.  All this is invisible to you (and me) of course.  All you see is a $540 charge on your annual water bill for the next 20 years.


The obvious question is the following: Which of these three alternatives is best?  As noted above, the answer is not obvious given the very different timing of cash flows and the need to account for interest.  Moreover, there is significant uncertainty about future interest rates and so on.

What I have done below is create a simple three-alternative model.  The critical metric in these kinds of models is Present Value (PV).  PV is the cost at the end of Year 0 (i.e., "today", or at the time of the project).  A good way to think about PV is in terms of a bank.  As noted above, a bank will enthusiastically exchange money now in return for a series of payments in the future.  That is, a bank will lend you money. However, the bank will charge you interest to offset its own opportunity costs.  Conversely, the bank will accept your money and pay you interest to offset your opportunity costs.  The market price at which these exchanges of money occur is, of course, the interest rate.

Commutation model (Excel spreadsheet)

PDF version of the model

Results of the model:

  1. Pay the capital charge outright from savings: The present value of this option is easy: It is $6562.  The money would be worth more in the future (if you left it in your savings account or investments) but it is worth $6562 today.

  2. Take a bank loan in order to reduce the prepayment time: The second model assumes the following transaction: You borrow money from your bank and then walk across the street to the RDOS and pay off the capital charge.  You thus owe the RDOS nothing but owe your bank $6265.  As noted above, you negotiate  an interest rate and a term for payback with your bank.  Let's assume 6% interest for a 60-month term.  You could likely get a lower rate if you offered up your home as collateral (as a second mortgage or home-equity line of credit). The critical piece of this model is that your annual payments to your bank need to be discounted to PV,  To illustrate, say you contract with your bank to pay them $1,487,29 every year for five years in order to pay back your debt.  You could start planning now for that payment at the end of Year 5.  Specifically, you could put $1,111.39 in an investment yielding 6% and, at the end of five years, you would have the $1,487.29 needed to make your last payment.  The present value of that last payment is thus $1,111.39.  If we calculate the PV for all the bank payments, we see the sum of PVs is $6265.  It is identical to the original principal.  This is because I have used the same interest rate for borrowing and investing (6%).  You may find you can invest at a higher rate (for more risk) or a lower rate (e.g., a savings account).  This personal return is unknown and depends on many factors.  You can change the "discount rate" value in the spreadsheet model to see the sensitivity PV to this value.

  3. Let the RDOS borrow on your behalf.  The accounting here is a bit trickier since MFA funding is through bonds rather than loans.  In addition, as noted above, there are two 10-year bonds rather than one 20 year loan.  We thus have to estimate four parameters: the interest rate (or yield) for the first bond (I have guessed 3.15% based on current MFA rates), the yield for the second bond in Year 11 (I have estimated 8% assuming interest rates climb between now and then), an investment rate for the sinking fund (bonds are repaid by investing a small amount each year for the term of the bond until enough is in the sinking fund to give bondholders back their original investment--I have estimated this investment rate at 4%), and a discount rate (6% as before).  The PV of all these payments to the RDOS over 20 years is roughly $6,200.  Part of the advantage of the RDOS option right now is that MFA can lock in a low interest rate (say 3.15% but possibly lower) for the first 10 years.  This counterbalances some more conservative assumptions in the model, such as the spike in yields in Year 11 and the meager investment return of 4%.


The bottom line is that all three of these options (as modeled here) result in very similar present values.  This should come as no surprise.  Or course, the models (and thus the optimal alternative) diverge significantly if more radical assumptions are made about (a) bond yields in 10 years or (b) investment returns now and in the future.  If you think bond yields (interest rates) are going up you might want to limit your debt now and prepay, If, in contrast, investment rates continue to be strong, you have a strong incentive to borrow from the RDOS.

This last point is especially true for some of the younger residents of the West Bench.  Registered education savings plans (RESPs) provide an immediate 20% kicker on any contribution you make to a plan.  Registered retirement savings plans (RRSPs) reduce taxable income.  Although I am not a financial planner, I can image financial planners advising younger couples to--in effect--borrow from the RDOS at 3% to invest in these investment vehicles.

As noted above, the real issue for me is not the interest rate risk but the risk of moving (ie. leaving the West Bench) that comes with prepayment.  My preference is user pay/pay as you go.  That is, whoever is in the house should pay the full cost in a given year, including the cost of debt servicing.

Let me know if you have any questions about these models, discounted cash flow methodology, 



If you sell your house within the next 20 years, would the new owner have to take over the payments, or does the seller have to pay off the remaining balance at the time of the sale?

The capital charge for the water system will show up on the property's annual property taxes.  Accordingly, whoever is the owner of the house in a given year pays the tax for that year.  The capital charge is "attached" to the property, not the property owner. If you sell, property taxes become the next guy's problem.

Now if you sell mid-year there is typically a process of pro-rating the taxes (all property taxes, not just this one).  But that is done by the lawyers during conveyance as part of the buy-and-sell contract.